Vol.:(0123456789) Journal of Thermal Analysis and Calorimetry (2024) 149:11239–11267 https://doi.org/10.1007/s10973-024-13184-7 A critical review on various factors affecting the thermohydraulic performance in transition‑flow regime Devendra Kumar Vishwakarma1  · Suvanjan Bhattacharyya1  · Mohsen Sharifpur2 · Varun Goel3 · Josua P. Meyer4 Received: 31 August 2023 / Accepted: 4 April 2024 / Published online: 18 June 2024 © Akadémiai Kiadó, Budapest, Hungary 2024 Abstract Heat transfer and pressure drop in laminar and turbulent flow have been studied for a long time. However, the thermohydraulic of fluid flow in transition flow is still in the embryonic stage and needs further exploration. Primarily, this article complied all the fragmented research works linked to thermal and flow performance in transition-flow regimes. Several detailed research works pertaining to developing and fully developed transition flow were reported in the past three decades which significantly contribute to the field. It was also found that the transition-flow regime shifted with the change in the operating conditions such as free, forced and mixed convection, developing and fully developed flow, inlet geometries, type of work- ing fluid, channel geometries, roughness, the orientation of test section, etc. Hence, by altering the shape of the entrance, the amount of heat passing through, or the surface of the tube, one could manipulate the range of Reynolds numbers where the transition took place. The temperature of fluids affects their densities, so when heat is applied to the tube wall, it creates temperature differences within the thermal boundary layer. These differences in temperature then cause changes in density and buoyancy due to the force of gravity. Several novel correlations have been developed based on these findings to determine the heat transfer and pressure drop in different flow regimes. In order to develop accurate correlations for heat transfer and pressure drop in the transitional-flow regime, it is necessary to comprehend the factors that impact the beginning and end of this regime. This understanding is crucial for selecting or creating suitable correlations. Keywords Transition flow · Heat transfer · Forced convection · Mixed convection · Developing and fully developed flow Introduction In the year 1883, Reynolds published a research work which was focused on fluid-flow regime and its dependence on the dimensionless parameter later known as the Reynolds number. The conditions which demonstrate the transition of laminar flow to turbulent flow were determined. Slowly, the investigations in the field of flow regimes behavior started getting momentum. The disruption of the flow field while the flow is transitioned from a laminar to a turbulent-flow regime enhances the thermal transport capacity. By disrupt- ing the boundary layer, mixing of fluid can be intensified which leads to the enhancement in heat transfer. The studies related to heat transfer and pressure drop in the laminar flow have already matured, while hydrothermal behavior in turbulent flow is still being investigated. The thermohydraulics of flow in the transition flow is still in an embryonic stage. The reasons for less research in the field of transition flow are the unpredictable nature of flow as well as very little to no previous works to support the research. Still, * Suvanjan Bhattacharyya suvanjan.bhattacharyya@pilani.bits-pilani.ac.in Devendra Kumar Vishwakarma p20190451@pilani.bits-pilani.ac.in 1 Department of Mechanical Engineering, Birla Institute of Technology and Science, Pilani, Pilani Campus, Vidya Vihar, Pilani 333 031, Rajasthan, India 2 School of Mechanical, Industrial & Aeronautical Engineering, University of the Witwatersrand, Johannesburg 2017, South Africa 3 Department of Mechanical Engineering, National Institute of Technology Hamirpur, Hamirpur 177005, Himachal Pradesh, India 4 Department of Mechanical & Mechatronic Engineering, Stellenbosch University, Stellenbosch 7599, South Africa http://orcid.org/0000-0002-5593-7031 http://orcid.org/0000-0002-3619-0518 http://crossmark.crossref.org/dialog/?doi=10.1007/s10973-024-13184-7&domain=pdf 11240 D. K. Vishwakarma et al. few research works are available in the area of flow dynam- ics in transition-flow regimes. As per the authors' knowl- edge, very few manuscripts are available focusing on the hydrothermal characteristics in the transition-flow regime. The results obtained from the various research work allow the design and fabrication engineers to incorporate the changes in the existing designs of heat exchangers to get better and improved results. Understanding the thermal and flow behavior in transition-flow regime is very essen- tial for solar, oil and piping industries. Because of high vis- cosity fluid usage in these industries, the Reynolds number remains restricted to the early turbulent-flow regime so that the pumping losses associated with higher flow rate remain lower. But with the aging of the equipment, the range of flow regimes shifted due to deposition inside the channels. This forced the equipment to work in the transition-flow regime. Hence, most of the time, these devices are working in the transition-flow regime unknowingly. This review work helps these industries by summarizing the results of various researchers working in the field of solar, piping, oil, heat exchanger, power plants, etc. The main intention behind the present review paper is to create a concise document which covers the important findings in the field of transition-flow regime. In the following subsection, the thermohydraulic charac- teristics of laminar and turbulent flow will be discussed to create basic knowledge about the physical significance of flow behavior in different flow regimes. Heat transfer and pressure drop in laminar‑flow regime and turbulent‑flow regime In laminar-flow regime, fluid flows in the form of lamina (layers of fluid) parallel to each other without disturbing the adjacent fluid layers. The fluid flows in a parallel layer without any eddies and disruption in the boundary layer (Fig. 1). This flow regime is governed by momentum dif- fusion, i.e., viscous forces dominate over inertia forces. Since the disturbance in this flow regime is minimal and the heat transfer and friction factor remains low. However, transport characteristics in this flow regime can be studied to improve the hydrothermal characteristics by introducing the various types of vortex generators [1], roughness, fins, nanofluids [2–4], electric field, magnetic field, ultrasound [5], etc., in the channel which increase the agitation in the flow field and allows the breaking of boundary layer result- ing secondary fluid flow and hence the heat transfer rate can be enhanced [6–9]. Several experimental and numeri- cal works are available in the open literature to support the flow dynamics of the laminar flow. It was found through various reports that the fluid remains in the laminar-flow regime up to a Reynolds number value of 2300 [10–12]. Authors are exploring various combinational methods to enhance thermal transport in the laminar flow. The com- bined impact of nanofluid and longitudinal vortex gen- erator on the heat transfer attribute in laminar flow has been studied by Asaadi and Abdi [11]. An increase in heat transfer coefficient and pressure drop (friction factor) is reported with an increase in the volumetric concentration of the nanoparticles. This increase in heat transfer coef- ficient is due to the incorporation of nanoparticles in the base fluid which led to the increase in the effective thermal conductivity as well as the Prandtl number [13]. It was also reported that an increase in the size of nanoparticles has an adverse effect on the heat transfer coefficient [12, 14]. Feng et al. [15] ran experiments to study the influence of the length and twist ratio of twisted tapes on the heat transfer aspects in square mini channels. It was reported that the larger the length of twisted tapes, higher will be the augmentation in heat transfer coefficient. Bain et al. [16] reported on the flow and transport characteristics of nanodiamond-based dielectric oil for cooling applications and found that nanodiamond-based dielectric oil is a prom- ising coolant for transformer applications. Hwang et al. [17] effectuated experiments to evaluate the heat trans- fer proliferation with Al2O3–water nanofluid in a lami- nar-flow regime. The usage of nanoparticles in the base fluid enhances the heat transfer coefficient by 8%. Shah and London [18–22] studied the laminar flow for paral- lel plates, circular tubes, elliptical tubes, triangular tubes and rectangular tubes for different boundary conditions, heat flux, viscous dissipation and momentum diffusion to understand the flow dynamics for different geometries. Bhattacharyya and Saha [23] performed an experimental evaluation to demonstrate the hydrothermal aspect inside a corrugated tube fitted with center-cleared twisted tapes for laminar-flow regime. It was found that combination of corrugated tube along with twisted tapes performed far better than individual techniques acting alone. Laminar flow Turbulent flow Fig. 1 Schematic representation of flow in laminar and turbulent regime 11241A critical review on various factors affecting the thermohydraulic performance in… From the preceding discussion, it is clear that enhance- ment of heat transfer in the boundary layer is possible with insertion or modification, usage of high thermal conductiv- ity fluids, nanofluids, etc. Appreciable enhancement in the thermal performance was noted when combined techniques of heat transfer enhancement were used. The disturbance in the boundary layer due to insertions of vortex generators, roughness on the surface of duct, etc., allows turbulence in the flow field which leads to better mixing of fluid elements and enhances thermal transport. The physical relevance of heat transfer in turbulent-flow regime is completely vice versa in comparison with laminar- flow regime. In turbulent-flow regime, the heat transfer and pressure drop both are very high. This is due to the turbu- lent nature of fluid flow which allows mixing of the fluid (Fig. 1). The heat transfer appreciation in turbulent-flow regime can be further enhanced with the help of twisted tapes, ribs, fins, roughness, etc. The inserts or roughness enhance the effectiveness of heat transfer, but at the same time increase the drag also which results in a higher pres- sure drop (friction factor). Heat transfer in this flow region has been studied for the past five or six decades aiming for a higher heat transfer rate. One of the key parameters to evaluate the combined influence of the effective heat trans- fer aspect along with pressure drop is thermal performance factor (TEF or η). Thermal performance factor (TEF), also sometimes referred to as thermal enhancement factor or per- formance enhancement coefficient, is the ratio of increase in the Nusselt number (Nu/Nuo) to the increase in the friction factor (f/fo). This parameter gives a vivid idea of amplifica- tion in heat transfer rate. If the value of thermal performance is above unity, it means for the given conditions heat transfer is more in comparison to the friction factor. The physics of heat transfer enhancement in turbulent-flow regime has been investigated by many authors in the past few decades. For example, Chang et al. [24] conducted experiments to evalu- ate the thermal and flow performance in a tube fitted with serrated twisted tapes of different twist ratios. Air is taken as the working fluid with Re varied from 5000 to 25,000. It was reported that Nusselt number increases with a decrease in twist ratio. The overall performance of the serrated twisted tape is appreciable when compared with plain twisted tapes. The experimental finding of Eiamsa-ard et al. [25] demon- strates the influence of twisted tapes with center wings and alternate axis on the thermal and flow performance in a turbulent-flow regime. The unique tape geometry splits the two streams of fluid into four streams around the alternate axis. Past alternate axis the fluid streams recombine into two streams. This allows the better mixing of fluid streams and enhances the thermal transport rate. The wings on the sur- face of tapes also allow furious mixing of fluid by disturbing the thermal boundary layer, leading to higher heat transfer. Sometimes, heat exchangers are operated in a transi- tion-flow regime unknowingly. This unknown shift in the regime is due to the presence of roughness in the flow chan- nel. Besides this entrance of the channel, usage of twisted tape inserts, corrugation on the surface of channel, amount of heat flux, etc., also significantly control the flow regime shift. Hence, in this work, an effort is made by the author to concise all the available research work related to heat trans- fer and flow characteristics in the transition-flow regime. This document will provide an easy and thorough summari- zation of previous research works for single-phase-flow heat transfer and pressure drop in transition-flow regime. Transition‑Flow regime The transition-flow regime falls between the laminar-flow regime and turbulent-flow regime when fluid passes from the laminar and enters the turbulent-flow regime. This regime is characterized by its unpredictable and chaotic nature of the fluid flow. Generally, plain channel transition occurred between 2000 and 4000 Reynolds numbers in case of inter- nal flow (refer Fig. 2). But it can start as early as 700 Reyn- olds number and delays up to 10,500 Reynolds number [26, 27] depending upon the disturbances and geometry of the flow channel. The length of the transition regime depends upon various factors such as the inlet geometry of the con- duit, surface geometry of conduit, heat flux, type of fluid, etc. (Figs. 3 and 4). The engineers of heat exchangers generally recommend working in a turbulent-flow regime due to commenda- tory heat transfer rate. However, with the aging of the heat exchangers mineral deposition takes place on the wall of heat exchanger tubes. Due to this, the flow regime shifted and unknowingly the heat exchangers start operating in the transition-flow regime. Similarly, the usage of the insert also shifts the initiation and termination of the transition- flow regime. These inserts enhance the heat transfer, but at the same time, it may also increase the friction factor. This may increase power consumption. Because of such reasons, Laminar flow t u Transition flow Turbulent flow Fig. 2 Velocity trend for laminar (viscous)-, transition- and turbulent- flow regime 11242 D. K. Vishwakarma et al. researchers need to understand the physics of heat transfer and pressure drop in transition-flow regime. Besides this, the new data obtained from the experimental and numerical investigations help in understanding the flow dynamics. For oil industries, such as refineries, the fluid does not allow to flow at very high speed. This is done to optimize the cost associated with pumping the viscous fluids in the channel. The fluid flow in such industries in generally early turbulent regime. Moreover, this can be further shifted to transition with time due to deposition in the channel. The research in transition-flow regime is still in the early stage with less than a hundred manuscripts published so far. The unpredictable and unstable nature of flow makes this regime very challeng- ing to capture. Figure 3 compares the number of publications in different flow regimes in the field of heat transfer and pressure drop. 1985 1990 1995 2000 2005 2010 2015 2020 2025 0 2500 5000 7500 10000 12500 15000 N o. o f p ub lic at io n Year Laminar flow regime Transition flow regime Turbulent flow regime Fig. 3 Year-wise publications in laminar-, transition- and turbulent- flow regime. [https:// www. scien cedir ect. com/, https:// schol ar. google. com/] Fig. 4 Inlet Geometries a Bell mouth inlet b Square edge inlet c Re-entrant d Boundary layer chopping e Fully developed inlet f Multi-tube with small protrusion [28–31] (a) Bell mouth Bell–mouth Inlet section Test Section 23.5 cm Flow 1.93 cm Re-entrant Flow Flow Squared–edged inlet (b)Square edge inlet (c) Re-entrant (d)Boundary layer chopping (e) Fully developed inlet (f) Multi-tube inlet with small protrusion Dhose = 7.16 mm Di = 5.16 mm D0 = 6.16 mm t = 0.5 mm Start of cooling Fully developed A B C A B C A B C t (e) A B C https://www.sciencedirect.com/ https://scholar.google.com/ https://scholar.google.com/ 11243A critical review on various factors affecting the thermohydraulic performance in… Factor influencing the boundaries of transition‑flow regime Several factors influence the heat transfer and friction char- acteristics in the transition-flow regime. A few of them are discussed below. Inlet geometry Inlet geometries greatly influenced the boundaries of tran- sition flow [32]. Most of the researchers investigated the majorly three inlet configurations, namely bell mouth, re- entrant and square edge [28, 33]. Figure 4 shows the sche- matics of various inlet configurations explored previously for transition regime. Smoother inlets result in a late laminar to turbulent transition, while rough or blunt inlets result in an early transition [28, 29, 33, 34]. Ghajar and Madon [33] and Ghajar and Tam [34] car- ried out an experimental investigation with three different inlet configurations, namely re-entrant, square edge and bell mouth, for skin friction and heat transfer analysis in the transition-flow regime. The measuring section used for the investigation was 6.10 m in length and 15.8 mm in diam- eter. To measure the pressure drop, three differential pres- sure gauges of different capacity were installed over the test section, while to measure the temperature across the test section, thermocouples were installed at 31 stations over the test section. A mixture of water and ethylene glycol was used as the working fluid. A shift in transition boundaries has been reported by the authors for different inlets geometries. It is also vital to note that smoother inlets delayed the tran- sition most, while the blunt inlets result in early transition. Ghajar and Tam [35] carried out experiments to develop a flow regime map for horizontal circular channel for uniform heat flux and three inlets applicable in both developing and fully developed flow. The developed map helps in determin- ing the coordinates for considering the mixed convection. Meyer et al. [36] and Olivier and Meyer [28] performed experiments inside a smooth tube with different inlet pro- files for adiabatic and diabatic operating conditions and gathered data for pressure drop and heat transfer. Four inlet configurations, namely hydrodynamically fully developed, bell mouth, re-entrant and square edge, were investigated. Tam and Ghajar [37] reported on the influence of bell mouth configuration on the local heat transfer coefficient in transi- tion-flow regime and turbulent-flow regime. They reported an unusual behavior of local heat transfer coefficient in the transition-flow regime which causes changes in the average heat transfer coefficient. Tam and Ghajar [27] in another investigation reported on the influence of inlet geometry as well as heating on the thermal and flow performance. As expected, re-entrant and square edge inlet show earlier transition, while the bell mouth inlet shows a delayed transi- tion. Influence of heat flux was also investigated. Increase in heat flux increases the friction factor for a fixed value of Reynolds number. Also, increased heat flux delayed the transition for all the inlet geometries and Reynolds num- ber. Osman et al. [30] investigated a novel inlet geometry “boundary layer chopping inlet” for thermohydraulic char- acteristic in transition-flow regime and reported early occur- rence of transition when inlet geometry is employed. How- ever, termination limit of transition does not vary for the given inlet configuration. Surface roughness Numerous technical methods have been developed over time to increase the rate of convective heat transfer from wall surfaces. To boost the heat transfer coefficient from the flow surface by increasing turbulent motion, roughness ele- ments are frequently used in this application. It is preferable that the heat transfer be meliorated with the least amount of drag. It has been observed that surface roughness changes the width of transition-flow regime significantly. The rough- ness causes disruption in the flow field which in turn results in the shift of the transition-flow regime. Surface roughness includes ribs [38–40], protrusions [41–43], dimples [44–46], surface unevenness [47–49], etc. Meyer and Olivier [50] experimented with an enhanced tube for developing and developed flow to investigate the influence of surface rough- ness on pressure drop. Four enhanced tubes and three inlet geometries [34] were employed for the experiments. It was found that for a smooth tube, the transition depends upon the type of inlet geometry. Transition starts and ends early for blunt inlet, while it starts and ends later for a smooth inlet. For enhanced tubes, transition begins earlier than the tran- sition of smooth tube. A secondary transition-flow regime was also reported by the investigators between Reynolds number 3000 and 10,000. Meyer and Olivier [51] in the second part of investigation reported on the heat transfer characteristics. It was reported that for adiabatic flow, no changes in the transition-flow regime were reported due to changes in the inlet geometry. Additionally, it seems that the transition area is seldom affected, if at all, by roughness during the heat transfer process. Another reason for lower enhancement was reported obstruction of secondary flow by the roughness of the tube at lower velocity. Everts et al. [52] also reported on the influence of microroughness over the surface of tube on the transition-flow regime. Tubes used for the investigations were having relative roughness close to 0.0003 and 0.0006. The Reynolds number of water varied from 500 to 9800. Three heat fluxes 1, 2 and 3 kW  m−2 were used for heating the test section. The results obtained from the investigation show enhancement in the heat transfer in the laminar-flow regime, while no enhancement is reported 11244 D. K. Vishwakarma et al. for transition-flow regime and turbulent-flow regime. For isothermal and diabatic conditions, roughness delayed the transition, reduced the width of transition-flow regime and increased the transition gradient. Vicente et al. [53] executed experiments with corrugated tube for mixed convection heat transfer and pressure drop characteristics in laminar-flow regime and transition-flow regime and reported that rough- ness on the tube surface accelerate the transition below 1300 Reynolds number. In another investigation by Vicente et al. [54], dimpled tube was explored for thermal and flow characteristics and changes associated with surface rough- ness. Srinivasan and Christensen [55] carried out experi- ments with spiral tubes and reported early occurrence of transition at Reynolds number approx. 300 and termination at approx. Reynolds number 1000. Besides, a significant improvement in heat transfer and friction factor was also reported when spiral tubes were used. Similar results were also reported by Obot et al. [56]. Olsson and Sundén [57] carried out experimental investigation for solar air heater with various configurations of rib roughness for wide range of Reynolds number. It was found that swirl tube performed better than the other configuration for Reynolds number range between 1000 and 2000. Afterward, the difference is not appreciable. Vicente et al. [58] reported on mixed con- vection in dimpled tubes (T01–T10) for laminar-flow regime and transition-flow regime. Water and ethylene glycol were used for working fluid. Transition for dimpled tube started at Reynolds number 1400. Both heat transfer and pressure drop were found augmented with dimpled tubes. Zhang [59] presented a numerical study to evaluate the thermal and flow performance inside a cross corrugated heat exchanger in transition-flow regime. K-omega turbulence model was used to model the transition flow. The results were presented in terms of temperature, velocity and turbulence intensity. García et al. [60] carried out experiments with corrugated tube, dimpled tube and wire coils for heat transfer augmen- tation. They concluded that smooth tube performed best for Reynolds number lower than or equal to 200, while using wire coils for heat transfer enhancement is recommended for Reynolds number range of 200–2000. Beyond Reynolds number 2000, dimpled or corrugated tube performed better. Transition begins earliest for tube with wire coil, followed by the corrugated tube, dimpled tube and smooth tube (in given order). Popov et al. [61] estimated the thermofluidic nature in transition-flow regime. It was reported that roughened tubes performed better over the other in terms of efficiency. Insertions or turbulators Turbulators or tape inserts are commonly used tools for the enhancement of heat transfer in heat exchangers also influ- ence the transition-flow regime boundaries. It is very com- mon practice to use tape inserts or turbulators for increased performance of the thermal system. It is established by the studies of Abolarin et al. [62–64] that tape insertion in a heat exchanger tubes shifts the transition boundaries sig- nificantly. They investigated the conventional twisted tapes, clockwise and anticlockwise connected twisted tapes and twisted tapes with conical rings and peripheral U-cuts (refer Fig. 5). Water is used as the working fluid for all the inves- tigations. Meyer and Abolarin [62] experimentally inves- tigated the influence of conventional simple twisted tapes (three twist ratio) and heat flux (three heat fluxes) on the transition-flow regime. A circular test section with an inter- nal diameter 19 mm and length 5.27 m was employed for the experiments. For uniform heat flux, the Colburn j-factor was reported to be highest for the lowest twist ratio, while an increase in twist ratio resulted in decreased j-factor value. Also, transition begins earlier for lower twist ratio. For uni- form twist ratio, the transition begins earlier for higher heat fluxes. In another experimental investigation, Abolarin et al. [63] also examine u-cut twisted tapes inside a heat exchanger duct with and without ring inserts. A constant twist ratio tape was used, while the depth of u-cut and ring space was varied. The results obtained from the investigation show the impact of both u-cut and ring space on the transition boundaries. It was revealed that an increase in depth ratio as well as an increase in ring spacing results in early transition. Similar to the above two investigations, Abolarin et al. [64] employed alternating clockwise and anticlockwise twisted tapes joined at 0°, 30° and 60° angle. The experiments were carried out at different heat flux conditions with water as the working fluid. It was revealed from the investigation that both joining angle and heat flux influence the limits of the transition-flow regime. Transition begins and ends earliest for 60° connection angle for all heat fluxes while delayed most for 0° connection angle. Transition begins and ends early for lower heat flux. They also developed several cor- relations based on their investigation for Nusselt number and friction factor prediction. Chougule and Sahu [61] carried out experiments in a circular tube fitted with helical screw inserts and compared the obtained results for performance in transition-flow regime for two nanofluids. García et al. [65] experimentally evaluated the augmentation of heat transfer and pressure drop in circular tube fitted with wire coil in laminar-flow regime and transition-flow regime. Insertion of wire coil changes the critical Reynolds number for heat transfer and pressure drop. Fiebig [66] carried out experi- ments to study heat transfer enhancement using various winglets configurations. They identified three methods of heat transfer enhancement, namely boundary layer develop- ment on vortex generator, swirl and flow destabilization. It was found that the flow destabilization results in momentous decrement in the critical Reynolds number (300) for the start of transition-flow regime. 11245A critical review on various factors affecting the thermohydraulic performance in… Figure 6 shows the boundaries of transition-flow regime for different tape inserts discussed above. It is clearly depicted from Fig. 5 that transition boundaries vary sig- nificantly with the geometry of inserts as well as heat flux. For lower heat flux, transition begins and ends earlier, while for higher heat fluxes, the start and end of transition is delayed. Similarly, for complex geometries, the transi- tion begins earlier, while for lesser complex geometries it is delayed. One of the very important conclusions made from the above investigations is that transition started and ended way earlier than Reynolds number value of 2300 Fig. 5 Tape inserts explored by Abolarin et al. [62–64] a Simple Twisted tapes b U-cut twisted tape with ring inserts c Clock- wise and counterclockwise tapes joined at different angles (a) Simple twisted tapes Ti T1 T2 (b) U Counter clockwise Clockwise Clockwise Clockwise Counter clockwise Counter clockwise -Cut twisted tape with ring inserts (c) Clockwise and counterclockwise tapes joined at different angles. Flow direction Pressure tap 1 Working fluid Insulation Thermocouple Heating wire Copper tube Twisted tape insert Pressure tap 2 T21 Te Dw D r W Pr Pr Dt dcut d cu t Lcut = 0°θ = 30°θ = 60°θ 11246 D. K. Vishwakarma et al. Zagarola et al. [67] also reported on the thermal perfor- mance improvement in laminar-flow regime and transition- flow regime when eddy promoters were employed perpen- dicular to flow direction. Few other works which moderately discussed the thermal and flow parameters in transition-flow regime included research of Elison and Webb [68], Mikic et al. [69]. García et al. [70] employed hydrogen bubble and PIV techniques to determine the flow mechanism inside a tube fitted with wire coil inserts of three pitches. It was found that the transition for W01 starts at Reynolds number 700, followed by W02 and W03. From the above discussion, it can be concluded that tur- bulators enhance the heat transfer efficiency by introducing disruption in the flow field. Along with that, turbulators also cause the shift in the boundaries of transition-flow regime. The higher the complexities in the design of turbulators, earlier the transition begins. This is due to the higher rate of disturbance due to turbulators in the flow field. Heat flux The amount of heat energy that flows across a surface is known as heat flux or thermal flux. External heat flux or intensity can greatly influence the flow regimes. The impact of heating on the performance of heat exchangers has been evaluated thoroughly by many researchers in the past. However, due to the uncertain nature of the transition-flow regime, very few studies related to transition-flow regime are available in open literature. This also causes a paucity of data. An extensive investigation of transition-flow regime is the need of the time. If investigated, the research will help in optimizing the heat transfer and pressure drop in the heat exchangers. This will help in saving the cost associated with pumping. Saeedinia et al. [71] experimented with heat exchanger tube subjected to 6.2 kW  m−2 to 9.9 kW  m−2 of heat flux and reported that increasing the heat flux result in enhanced heat transfer for both base fluid and nanofluid. However, the augmentation in heat transfer is more with nanofluid in comparison to the base fluid. Andrade et al. [72] also varied the heat flux from 5.5 to 21.1 kW  m−2 for internal corrugated tube and revealed relevant heat trans- fer augmentation in turbulent-flow regime. Ghajar and Tam [34] experimented with a circular heat transfer tube having length approximately 5.5 m which is subjected to heat flux of 4–6.70 kW  m−2. A combined influence of heat flux and inlet geometry was evaluated and reported a delayed transi- tion when results were compared with no heating condition. Tam and Ghajar [27] reported on the influence of heating on the laminar to turbulent transition-flow regime. The findings showed that, for a constant Reynolds number, the value of the fully developed friction factor rose as the heating rate increased. Heating also causes a delay in the transition for all the inlet geometries. It was found that for 16 kW  m−2 of heat flux and re-entrant inlet, the transition initiated at Re = 4100 and ends at Re = 5900, for the square edge the transition begins at Re = 4500 and ends at Re = 6400, while for bell mouth inlet, the transition initiated at Re = 7300 and ends at Re = 9600. Martínez et al. [73] used heat flux ranges between 4.5 and 66.4 kW  m−2 for investigating the heat transfer and pressure drop for heat exchanger tube fit- ted with a wire coil and reported that the critical Reynolds number goes below 500 for transition. Meyer and Abolarin [62] and Abolarin et al. [64] investigated various heat fluxes, i.e., 1.35, 2, 3 and 4 kW  m−2 for circular channel fitted with a twisted tape of various configurations and reported that greater heat fluxes delayed the transition. Abolarin et al. [63] in another geometry carried out experiments with a uniform heat flux of 1.35 kW  m−2 in a circular channel fitted with u-cut twisted tapes with and without ring inserts and reported amplification of heat transfer and pressure drop. Meyer and Everts [74] carried out experiments to under- stand the effect of natural convection on local heat transfer. The experiments were carried out for uniform heat flux. The investigated heat fluxes varied from 0 to 9.5 kW  m−2. Higher heat flux results in higher Nusselt value. Duct diameter also plays a significant role in heat transfer enhancement. Based on the aforementioned investigations, it is evident that heat flux plays a significant role in influencing the tran- sition-flow regime. An increase in applied heat flux led to a delayed transition compared to lower heat flux under similar operating conditions. This effect was accompanied by higher Nusselt numbers and friction factors. Geometry of test section Chen et  al. [75] employed a grooved channel to aug- ment the thermal performance of the tube in a tube heat 400 M ey er a nd A bo lar in Y = 3 M ey er a nd A bo lar in Y = 4 M ey er a nd A bo lar in Y = 5 Abo lar in et a l. 600 800 1000 1200 Reynolds Number 1400 1600 1800 4 kW 3 kW 2 kW 2000 Abo lar in et a l. θ = 0 Abo lar in et a l. θ = 3 0 Abo lar in et a l. θ = 6 0 Fig. 6 Transition-flow regime variation for different tapes and heat flux conditions explored by Meyer and Abolarin and Abolarin et al. [62–64] 11247A critical review on various factors affecting the thermohydraulic performance in… exchanger. It was reported that the grooved channel signifi- cantly improves the heat transfer coefficient while decreas- ing the critical Reynolds number for the transition-flow regime. Osman et al. [76] accomplished experiments in a rectangular tube with Al2O3–water nanofluid (Vol. % 0.3, 0.5 and 1) for heat transfer and pressure drop perfor- mance in visco-laminar and transition-flow regime. It was found that transition occurs earlier for a rectangular chan- nel. Besides 54% increment in the convective heat transfer coefficient is reported in the transition-flow regime fol- lowed by 11% improvement in the turbulent-flow regime for 1% vol. concentration. Water was employed in a single channel with a rectangular cross section by Dirker et al. [77] employed water as the working fluid in a single chan- nel with a rectangular cross section. They wanted to find out how intake layout affected heat transfer coefficients when frictional elements such as adiabatic and diabatic friction were present. For the bell mouth intake type, a smoother and longer transition was observed, with the adiabatic transition starting at a Reynolds number 1050 and the diabatic transition starting at a Reynolds num- ber 1200. However, the change for the smooth contrac- tion inlet type was more sudden, starting at a Reynolds number 1800 for the adiabatic transition and a Reynolds number 2000 for the diabatic transition. Minhas and Lock [78] numerically studied the fluid flow characteristics for the refluent heat exchanger. It was found that the transi- tion initiated at Reynolds number 875, whereas it is ter- minated at Reynolds number 1480 for both air and water. Minhas and Lock [79] in another work reported on the forced convection heat transfer and fluid flow in the reflu- ent heat exchanger. An increase in the Nusselt number with an increase in the Reynolds number was reported. Joye et al. [80] experimented with vertical channel for opposing water flow and compared the heat transfer for wide range of Reynolds number. They reported that mixed convection occurs between Reynolds number 4000 and 10,000. Peng and Peterson [81] performed experiments in microchannel (total eight) for forced convection single phase flow of water and methanol mixture. For test section 1, 2 and 3, the transition occurs between Reynolds num- ber 300–700 and a decrease in critical number was found with decrease in the hydraulic diameter of microchannel. For other microchannels the critical Reynolds number for start of turbulent region was found near to Reynolds num- ber 200, while the transition occurs at Reynolds number 70. Besides, the concentration of methanol in water also majorly influences the laminar to turbulent transition. Hence, it can be concluded that the shape of the test sec- tion also has a significant impact on the initiation and con- clusion of the transition-flow regime. Diverse shapes can lead to differences in the formation of the boundary layer, which in turn affects the shift from smooth to chaotic flow. Specific shapes may naturally disrupt the smooth flow, encouraging the transition to turbulence. Engineers and researchers meticulously analyze these geometric aspects to enhance efficiency and forecast the characteristics of fluid flow in different scenarios. Angular position of test section Meyer et al. [82] experimented with inclined channel to inspect and evaluate the influence of buoyancy on heat trans- fer and pressure drop. At heat fluxes of 4–8 kW  m−2, the tests were carried out at various inclination angles between 1000 and 6000 Reynolds numbers. It was discovered that decreasing the buoyancy force effects from horizontal flow (0°) to vertical flow (90° flow) lowered the laminar heat transfer coefficients and friction factor for both uphill and downhill flows. It was discovered that when the inclination angles grew from horizontal to vertical, the critical Reynolds numbers at which transition began increased. However, the termination of transition remains unaffected due to varia- tion in the inclination angle. Everts et al. [10] carried out heat transfer and fluid flow experiments in vertical channel to understand the influence of assisting and opposing flow at very Reynolds number. At three distinct heat fluxes of 1, 1.5 and 2 kW  m−2, experiments and simulations were carried out for vertically upward and downflow between Reynolds numbers of 180 and 2300. Free-convection effects were reported to no longer be repressed by the fluid's veloc- ity at Reynolds numbers below 250 and 600 for upward and downflow, respectively, and aiding and opposing flow became important. Using both single-phase and multi-phase models, Saha and Paul [83] conducted a computational study to examine the transition-flow behavior of nanofluids flow in an inclined pipe. Alzwayi and Paul [84] reported on the influence of angular inclination and channel width on the heat transfer and pressure drop in transition-flow regime. The results demonstrated how the channel's width and angle affect the average heat transfer coefficient. The findings also demonstrate that the channel's width and inclination have a significant role throughout the transition. Al-Arabi and Sakr [85] examined the local and average natural convection heat transfer from isothermal vertical and inclined plates facing upward to air in both visco-laminar and turbulent zones and suggested empirical correlations to estimate the local and average heat transfer coefficient in the transition- flow regime. Kumar and Premachandran [86] numerically investigated the influence of inclination of fluid domain on the transition-flow regime and reported that the transition is delayed and the transition area moves downstream as the degree of inclination rises. Angular orientation of heat exchanger tubes also plays a crucial role in determination of transition-flow regime [82]. However, this aspect is not very well studied and 11248 D. K. Vishwakarma et al. Table 1 Critical Reynolds number and important findings of selective previous works Authors and year Type of inlet Developing flow Developed flow Critical Reyn- olds number (Start) Critical Reyn- olds number (End) Width of transition-flow regime Inlet geometry Ghajar and Madon [33] Re-entrant ✗ ✓ 1980 2600 620 Square edge ✗ ✓ 2070 2840 770 Bell mouth ✗ ✓ 2125 3200 1075 Ghajar and Tam [34] Re-entrant ✗ ✓ 2000 8500 6500 Square edge ✗ ✓ 2400 8800 6400 Bell mouth ✗ ✓ 3800 10,500 6700 Olivier and Meyer [28] Adiabatic friction factor 15.88 mm Hydrodynamically fully developed ✗ ✓ 2212 2600 388 Square edge ✓ ✗ 2717 2850 133 Re-entrant ✓ ✗ 2192 2542 350 Bell mouth ✓ ✗ 7000 7700 700 Adiabatic friction factor 19.02 mm Hydrodynamically fully developed ✗ ✓ 2350 2560 210 Square edge ✓ ✗ 2600 2770 170 Re-entrant ✓ ✗ 2194 2480 286 Bell mouth ✓ ✗ 12,000 17,500 5500 Meyer et al. [36] Adiabatic friction factor Hydrodynamically fully developed ✗ ✓ 2000 2900 900 Square edge ✓ ✗ 2600 3110 510 Re-entrant ✓ ✗ 2000 2760 760 Bell mouth ✓ ✗ 7000 7800 800 Diabatic friction factor Hydrodynamically fully developed Transition independent of inlet geometry Square edge Re-entrant Bell mouth Tam and Ghajar [27] Re-entrant ✗ ✓ 2900 3500 600 Square edge ✗ ✓ 3100 3700 800 Bell mouth ✗ ✓ 5100 6100 1000 Osman et al. [30] Adiabatic friction factor Boundary layer chopping inlet ✓ ✗ 2100 3200 1100 Diabatic friction factor Boundary layer chopping inlet ✓ ✗ 2067 3225 1158 Authors and year Type of Surface roughness Developing flow Developed flow Important findings Surface roughness Meyer and Olivier [50] Internal helical grooves ✓ ✓ The kind of inlet employed in the case of smooth tubes had an impact on transition, with the smoothest inlet delaying transi- tion the most Meyer and Olivier [51] Internal helical grooves ✓ ✓ The critical Reynolds numbers were unaffected by intake distur- bances, contrary to the findings for adiabatic flow in Part I Everts et al. [52] Surface microroughness ✗ ✓ The transition began later for low relative surface roughness levels, but it started sooner when the relative surface roughness climbed to moderate and high values Vicente et al. [53] Corrugation – – Corrugation on the surface of test section causes the transition to start as early as Reynolds number 1300 Vicente et al. [54] Helical dimples – – Enhancement in heat transfer and pressure drop was reported 11249A critical review on various factors affecting the thermohydraulic performance in… Table 1 (continued) Authors and year Type of turbulator or insert heat flux Critical Reyn- olds number (Start) Critical Reyn- olds number (End) Width of transition-flow regime Insertions or turbulators Meyer and Abolarin [62] Conventional twisted tapes y = 3 2 kW  m−2 593 1125 532 3 kW  m−2 819 1274 455 4 kW  m−2 1093 1404 311 y = 4 2 kW  m−2 669 1027 358 3 kW  m−2 951 1418 467 4 kW  m−2 1172 1524 352 y = 5 2 kW  m−2 1023 1604 581 3 kW  m−2 1108 1683 575 4 kW  m−2 1278 1775 497 Abolarin et al. [63] Peripheral u-cut twisted tape with and without ring inserts 1.35 and 2 kW  m−2 554 1037 483 Abolarin et al. [64] Clockwise and anticlockwise twisted tapes 1.35, 2, 3 and 4 kW  m−2 498 818 320 Authors and year Heat flux range Flow type Important findings Heat flux Saeedinia et al. [71] 6200–9900 W  m−2 Laminar-flow Increasing the heat flux results in higher enhancement in the heat transfer coefficient Andrade et al. [72] 5.5–21.1 kW  m−2 Adiabatic and diabatic flow conditions Compared to smooth tubes, corrugated tubes' friction fac- tor demonstrated a smoother transition-flow regime Ghajar and Tam [34] 4–670 kW  m−2 Fully developed flow The boundaries of transition were inlet dependent Tam and Ghajar [27] 3, 8 and 16 kW  m−2 Fully developed flow Transition is heating flux dependent. Increase in heat flux causes delay in the start and end of the transition Meyer and Everts [74] 0–8 kW  m−2 Developing and developed flow Increase in the Nusselt number and free convection effect was reported with increase in the heat flux and tube diameter Authors and year Cross section of test section Developing flow Developed flow Critical Reynolds number (Start) Critical Reynolds number (End) Width of transition-flow regime Geometry of test section Chen et al. [75] Transversely grooved duct – – 1300 6000 4700 Osman et al. [76] Rectangular ✓ ✗ 1731 1876 145 Dirker et al. [77] Adiabatic friction factor Microchannel ✓ ✗ 1100 1800 700 Diabatic friction factor Microchannel ✓ ✗ 1250 2000 750 Authors and year Angular position Flow type Important findings Angular position of test section Meyer et al. [82] − 90o to + 90o Fully developed flow Critical Reynolds number for start of transition increase with an increase in inclination without affecting the termi- nation critical Reynolds number Everts et al. [10] 90o Fully developed upward and downward laminar flow Deviation in Nusselt number from Nu = 4.36 was observed. The reason cited was the dominance of free convec- tion effect 11250 D. K. Vishwakarma et al. required further investigation. It was highlighted that heat transfer enhancement is highest for horizontal channel and decreases with an increase in the angular orientation. This is because of the decreased buoyancy forces at inclined position and then the horizontal position. Others Yuan et al. [87] performed experiments inside a rectangular channel to assess the influence of rolling motion on heat transfer and flow characteristics to simulate offshore nuclear reactors. The study reveals increment in the heat transfer and friction factor when operated in the transition-flow regime. The fluctuation in the flow rate was quoted as the main cause of enhanced heat transfer. Demirkır and Ertürk [88] investigated the hydrothermal performance of heat exchanger tube carrying graphene–water nanofluid (0.025, 0.1 and 0.2 Vol%) as the working medium. It was found that nanofluid accelerates the transition by Re = 2315, while for water the transition begins at Re = 2475. Amplification in both heat transfer and pressure drop was reported. Ali et al. [89] performed experiments in a parallel plate solar collector with staggered plated for thermal and flow performance in transition-flow regime. Air is used as the working fluid. In addition to demonstrating that the local Nusselt number is not a unique function of the axial distance, the experimen- tal findings revealed a linear connection between Re and the apparent friction factor. Bhuiyan et al. [90] numerically examined the heat transfer and fluid flow characteristics of a fin-and-tube heat exchanger. This research investigates the impact of geometrical features such fin pitch, longitudinal pitch and transverse pitch of tube spacing. With increasing longitudinal and transverse tube pitch spacing, heat transfer and friction factor are reduced for both laminar- and tran- sition-flow regimes, while the efficiency index increases. Table 1 shows the critical Reynolds number for various cases discussed in this article, while Table 2 summarizes the dis- cussion of this section for easy understanding of parameters and variables used for the investigation purpose. In order to calculate the heat transfer coefficients in circular pipes for the three potential flow regimes of laminar, transition and turbulent flow, Abraham et al. [91] proposed a theory. For the range Re > 4800, it was noted that the experimental results strongly confirmed the predictions given by Gniel- inski [92]. However, the experimental results corroborated Churchill's [93] predictions in the range of 2300–3100. Meyer et al. [94] investigated the effect of multi walled car- bon nanotubes on hydrothermal performance in transition- flow regime. The experiments were carried out with volume concentrations (vol. conc.) of 0.33%, 0.75% and 1.0% at a constant heat flux of 13 kW  m−2. Higher vol. concentration causes the transition to start and ends early when compared with low vol. concentration nanofluid. The pressure drop data showed that when volume concentration increased, the pressure drop also increased, which is a consequence of the viscosity rising. Peixinho [95] investigated in transition-flow regime with Carbopol aqueous solution for thermal and flow performance. It was reported that with shear thinning and yield stress, the critical Reynolds number for transitional flow rises. Stamatopoulos et al. [96] experimentally evalu- ated the performance of thermal sensor for gas flow in lami- nar-, transition- and turbulent-flow regime. Abraham et al. [97] numerically demonstrated the breakdown of laminar flow into transition and turbulent. Celata et al. [98] per- formed experiments in seven surface roughened microcir- cular pipes (30–500 �m ) for gas flow and reported on the fluid flow behavior in terms of friction factor. For smooth tube, the transition begins at Reynolds number 2000, while for roughened tube it may delays up to 4500. The transition for microtubes having diameter less than 100 μm occurs at almost similar Reynolds numbers with marginal changes. However, for tubes with larger diameter, a delay in the start of transition was observed. Besides it was also found that for micropipes with lesser roughness, the transition was smooth, while for roughened pipes, transition was sharp. Yang et al. [99] also carried out similar nature of investigation with microtubes and reported that if the compressibility of gase- ous fluid was taken well into consideration, then microtube Table 1 (continued) Authors and year Angular position Flow type Important findings Saha and Paul [83] 0°, 15°, 30°, 45°, 60° and 75o Forced convection of nanofluid With inclination angle, distortion in flow field and turbulent kinetic energy was observed Alzwayi and Paul [84] 0°, 10°, 30°, 50°, 70°, 80o and 85o Natural convection of air Heat transfer coefficient depends upon inclination as well as the width of channel Al-Arabi and Sakr [85] 0°, 15°, 30°, 40°, 60° and 80o Natural convection of air Correlations for local heat transfer were used to estimate the transition regime Kumar and Premachandran [86] 15°, 30° and 60o Natural convection of air Delay in transition with increase in the inclination angle was reported 11251A critical review on various factors affecting the thermohydraulic performance in… Ta bl e 2 C om pa ris on o f p ar am et er s, ge om et rie s o f v ar io us e xp er im en ts a nd th ei r fi nd in gs A ut ho rs Te st se ct io n ge om et ry In le t g eo m et ry W or ki ng fl ui d D ev el op ed o r de ve lo pi ng fl ow Pr an dt l N um - be r Re yn ol ds n um - be r r an ge H ea t fl ux C rit ic al R ey no ld s nu m be r Im po rta nt fi nd in gs G ha ja r a nd M ad on [3 3] H or iz on ta l se am le ss 3 16 st ai nl es s s te el Re -e nt ra nt , s qu ar e- ed ge d, b el l m ou th C om bi na tio n of D ist ill ed w at er an d et hy le ne gl yc ol Fu lly d ev el op ed – 50 0– 15 × 10 3 – Re -e nt ra nt = 19 80 – 26 00 , S qu ar e- ed ge d = 20 70 – 28 40 , B el l m ou th = 21 25 – 32 00 Th e gr ow th o f t he fr ic tio n fa ct or th ro ug ho ut th e pi pe a nd th e st ar t a nd fi ni sh of th e tra ns iti on - flo w re gi m e ar e su bs ta nt ia lly in flu - en ce d by th e ki nd of in le t g eo m et ry G ha ja r a nd T am [3 4] H or iz on ta l se am le ss 3 16 st ai nl es s s te el Re -e nt ra nt , s qu ar e- ed ge d, b el l m ou th C om bi na tio n of D ist ill ed w at er an d et hy le ne gl yc ol Fu lly d ev el op ed 4– 15 8 28 0– 49 × 10 3 4 to 67 0  kW   m − 2 Re -e nt ra nt = 20 00 – 85 00 , S qu ar e- ed ge d = 24 00 – 88 00 , B el l m ou th = 38 00 – 10 ,5 00 Th e in le t c on fig ur a- tio n si gn ifi ca nt ly in flu en ce s t he h ea t tra ns fe r c oe f- fic ie nt , a s w el l as th e on se t a nd te rm in at io n of th e tra ns iti on -fl ow re gi m e. T he in le t ge om et ry a ls o re sp on si bl e fo r se co nd ar y flo w in th e flo w fi el d Ta m a nd G ha ja r [2 7] H or iz on ta l se am le ss 3 16 st ai nl es s s te el Re -e nt ra nt , s qu ar e- ed ge d an d be ll m ou th Et hy le ne g ly co l– w at er m ix tu re s Is ot he rm al fu lly de ve lo pe d 6– 30 1 × 10 3 to 17 × 10 3 3, 8 a nd 16  k W   m − 2 Re -e nt ra nt = 29 00 – 35 00 , S qu ar e- ed ge d = 31 00 – 37 00 , B el l m ou th = 51 00 – 61 00 W ith a n in cr ea se in th e he at in g ra te a nd a g iv en Re yn ol ds n um be r, th e va lu e of th e fu lly d ev el op ed fr ic tio n fa ct or ro se . T he b ot to m an d up pe r l im it of th e is ot he rm al tra ns iti on b ou nd a- rie s i nc re as ed a s a re su lt of th is ri se in fr ic tio n fa ct or 11252 D. K. Vishwakarma et al. Ta bl e 2 (c on tin ue d) A ut ho rs Te st se ct io n ge om et ry In le t g eo m et ry W or ki ng fl ui d D ev el op ed o r de ve lo pi ng fl ow Pr an dt l N um - be r Re yn ol ds n um - be r r an ge H ea t fl ux C rit ic al R ey no ld s nu m be r Im po rta nt fi nd in gs K ar w a et  a l. [1 05 ] R ib -ro ug he ne d re ct an gu la r du ct Re ct an gu la r i nl et A ir Th er m al ly fu lly de ve lo pe d flo w – 3 × 10 3 to 2 × 10 4 1  kW – Th e pr es en ce o f r ib s at o ne w id e w al l of th e du ct re su lts in in cr ea se s i n th e St an to n nu m be r an d fr ic tio n fa c- to r o f u p to tw o an d th re e tim es , re sp ec tiv el y, a s co m pa re d to th e sm oo th d uc t Zh an g [5 9] C ro ss - C or ru ga te d Tr ia ng ul ar C ha nn el s Tr ia ng ul ar – Fu lly D ev el op ed Fl ow – 1 × 10 2 to 6 × 10 3 – – A c om pl ic at ed flo w p at te rn w ith flo w se pa ra tio n, re at ta ch m en t an d re ci rc ul at io n zo ne s r es ul ts fr om th e co rr ug at io ns . Th is re su lt in hi gh er N us se lt nu m be r a nd fr ic - tio n fa ct or D irk et e l a l. [7 7] Re ct an gu la r ch an ne l Su dd en c on tra c- tio n, b el l m ou th an d sw irl in le t W at er – – 30 0– 28 00 – su dd en c on tra c- tio n = 18 00 – 20 00 , be ll m ou th = 18 00 an d sw irl in le t = 15 00 In a ll flo w re gi m es , it w as d is co ve re d th at th e sw irl in le t ty pe c ha ng ed th e be ha vi or o f t he N us se lt nu m - be r a nd fr ic tio n fa ct or . D ue to a dr op in fl ui d vi sc os ity n ea r t he w al l, a de cr ea se in fr ic tio n fa ct or w as se en w ith a n in cr ea se in h ea t in pu t 11253A critical review on various factors affecting the thermohydraulic performance in… Ta bl e 2 (c on tin ue d) A ut ho rs Te st se ct io n ge om et ry In le t g eo m et ry W or ki ng fl ui d D ev el op ed o r de ve lo pi ng fl ow Pr an dt l N um - be r Re yn ol ds n um - be r r an ge H ea t fl ux C rit ic al R ey no ld s nu m be r Im po rta nt fi nd in gs A li et  a l. [8 9] Pa ra lle l p la te ch an ne ls w ith st ag ge re d pl at es – A ir – – 25 80 –4 65 0 40 0, 7 00 a nd 10 00 W   m − 2 – Th e m os t i m po rta nt co nfi gu ra tio n el em en t t ha t s ig - ni fic an tly a ffe ct s th e va lu es o f t he ap pa re nt fr ic tio n fa ct or a nd th e he at tra ns fe r c oe ffi ci en t (j) fo r s ho rte r pl at e le ng th s i s t he pl at e th ic kn es s B hu iy an e t a l. [9 0] C ro ss fl ow h ea t ex ch an ge r – A ir – – 4 × 10 2 –2 × 10 3 – – Th e th er m al an d hy dr au lic pr op er tie s o f fin -a nd -tu be he at e xc ha ng er s ar e si gn ifi ca nt ly in flu en ce d by th e tu be c on fig ur a- tio ns . S ta gg er ed tu be a rr an ge m en ts cr ea te b et te r fl ow m ix in g th an in - lin e ar ra ng em en ts do fo r l am in ar a nd tra ns iti on fl ow s, w hi ch re su lts in en ha nc ed h ea t tra ns fe r a nd pr es su re d ro p ch ar ac te ris tic s M ar tin ez e t a l. [7 3] 31 6L st ai nl es s ste el tu be w ith a w ire co il in se rt C irc ul ar Ps eu do pl as tic te st flu id s Fu lly d ev el op ed flo w 15 0– 19 00 10 –1 20 0 – – Re su lts in di ca te th at th e w ire c oi ls h av e lit tle im pa ct in th e la m in ar d om ai n, bu t s ea m le ss ly sh ift to tu rb ul en t flo w a t R e = 50 0 11254 D. K. Vishwakarma et al. Ta bl e 2 (c on tin ue d) A ut ho rs Te st se ct io n ge om et ry In le t g eo m et ry W or ki ng fl ui d D ev el op ed o r de ve lo pi ng fl ow Pr an dt l N um - be r Re yn ol ds n um - be r r an ge H ea t fl ux C rit ic al R ey no ld s nu m be r Im po rta nt fi nd in gs Zh an g et  a l. [1 06 ] Pl ai n pl at e– fin an d tu be – A ir – – 1 × 10 3 –5 × 10 3 – – W ith h ig he r f ro nt al ve lo ci tie s a nd fin p itc he s, th e ve lo ci ty o sc il- la tio ns b ec om e m or e pr on ou nc ed . H ea t t ra ns po rt is e nh an ce d an d pr es su re d ro p is in cr ea se d by th e po w er fu l m ix in g ac tio n of v or te xe s M ey er e t a l. [5 0, 5 1] En ha nc ed c ir- cu la r t ub e Sq ua re -e dg ed , re -e nt ra nt a nd be ll- m ou th W at er Fu lly d ev el op ed an d de ve lo pi ng flo w 4. 17 –5 .0 6 43 6– 21 ,0 84 1 59 8– 10 9 54 W St ar ts a t 2 00 0 an d en di ng a t 3 00 0 It w as d is co ve re d th at tr an si tio n oc cu rs a t l ow er Re yn ol ds n um be rs fo r c or ru ga te d tu be s t ha n fo r th ei r s m oo th tu be eq ui va le nt s. In ad di tio n, th e ty pe of in le t e m pl oy ed aff ec ts tr an si tio n, ju st as it d oe s w ith sm oo th tu be s 11255A critical review on various factors affecting the thermohydraulic performance in… Ta bl e 2 (c on tin ue d) A ut ho rs Te st se ct io n ge om et ry In le t g eo m et ry W or ki ng fl ui d D ev el op ed o r de ve lo pi ng fl ow Pr an dt l N um - be r Re yn ol ds n um - be r r an ge H ea t fl ux C rit ic al R ey no ld s nu m be r Im po rta nt fi nd in gs M ey er e t a l. [9 4] St ra ig ht c op pe r tu be – M W C N T– w at er na no flu id – – 1 × 10 3 –8 × 10 3 13  k W   m − 2 – Th e na no flu id s de m on str at ed a lo w er h ea t t ra ns fe r co effi ci en t t ha n w at er w he n re su lts fro m se ve ra l ex pe rim en ts w er e co m pa re d at th e sa m e flu id v el oc - ity . T he p re ss ur e dr op d at a sh ow ed th at w he n vo lu m e co nc en tra tio n in cr ea se d, th e pr es su re d ro p al so in cr ea se d, w hi ch is a c on se qu en ce of th e vi sc os ity ris in g Po po v et  a l. [6 1] Ro ug h Tu be s – W at er – – 3 × 10 3 –1 × 10 4 – – Re su lt in di ca te d en ha nc em en t i n th e he at tr an sf er an d pr es su re d ro p w he n tu be w ith sp he ric al p ro tru - si on is e m pl oy ed Ta m e t a l. [1 07 ] H or iz on ta l t ub e sq ua re -e dg ed a nd re -e nt ra nt in le ts M ix tu re s o f e th yl - en e gl yc ol a nd w at er En tra nc e an d fu lly de ve lo pe d flo w 4. 3– 46 .3 8 × 10 2 –2 2 × 10 3 4. 3– 8. 9  kW   m − 2 Sq ua re -e dg ed : 22 22 –3 58 8, Re -e nt ra nt : 20 32 –3 03 1 Th e st ar t a nd e nd of tr an si tio n w er e po stp on ed b y he at in g, w hi ch al so re du ce d th e la m in ar a nd tra ns iti on fr ic tio n fa ct or in th e en try an d fu lly d ev el - op ed fl ow re gi on G ar ci a et  a l. [6 5] 31 6 L st ai n- le ss st ee l t ub e w ith a w ire co il in se rt – W at er , p ro py l- en eg ly co l U SP gr ad e an d a m ix tu re o f pr op yl en e gl yc ol an d w at er Fu lly d ev el op ed flo w 20 0– 70 0 10 –2 50 0 – 10 00 –1 30 0 In se rti on o f w ire co il ch an ge s t he cr iti ca l R ey no ld s nu m be r f or h ea t tra ns fe r a nd p re s- su re d ro p 11256 D. K. Vishwakarma et al. Ta bl e 2 (c on tin ue d) A ut ho rs Te st se ct io n ge om et ry In le t g eo m et ry W or ki ng fl ui d D ev el op ed o r de ve lo pi ng fl ow Pr an dt l N um - be r Re yn ol ds n um - be r r an ge H ea t fl ux C rit ic al R ey no ld s nu m be r Im po rta nt fi nd in gs G ha ja r e t a l. [1 08 ] St ai nl es s s te el tu be s – di sti lle d w at er – – 70 0– 55 00 – 13 00 < R e < 17 00 , 15 00 < R e < 40 00 It ha s b ee n di sc ov er ed th at de cr ea si ng tu be di am et er s a nd in cr ea si ng re la tiv e ro ug hn es s h av e an im pa ct o n fr ic tio n fa ct or . T hi s a ls o le d to e ar ly o ns et of tr an si tio n in m ic ro tu be M ey er e t a l. [3 6] Sm oo th tu be sq ua re -e dg ed , r e- en tra nt a nd a b el l m ou th in le t w at er – 4– 6 1 × 10 3 to 2 × 10 4 – sq ua re - ed ge d = 26 00 , be ll m ou th in le t = 70 00 Th e tra ns iti on fro m la m in ar to tu rb ul en t fl ow w as su bs ta nt ia lly in flu en ce d by th e in ta ke p ro fil e, ac co rd in g to a di - ab at ic st ud ie s, an d it m ay ta ke u p to 7, 00 0 Re yn ol ds nu m be rs fo r t he sh ift to o cc ur M ey er a nd Pr ee z [1 09 ] C ou nt er flo w tu be -in -tu be – w at er – – 1 × 10 3 to 5 × 10 3 – – Re su lts fo r h ea t tra ns fe r a nd p re s- su re d ro p w er e pr es en te d 11257A critical review on various factors affecting the thermohydraulic performance in… Ta bl e 2 (c on tin ue d) A ut ho rs Te st se ct io n ge om et ry In le t g eo m et ry W or ki ng fl ui d D ev el op ed o r de ve lo pi ng fl ow Pr an dt l N um - be r Re yn ol ds n um - be r r an ge H ea t fl ux C rit ic al R ey no ld s nu m be r Im po rta nt fi nd in gs O liv er e t a l. [2 8] Sm oo th tu be s w ith H yd ro dy na m ic al ly fu lly d ev el op ed , sq ua re -e dg ed , r e- en tra nt a nd b el l m ou th D ist ill ed w at er 4– 6 1 × 10 3 –2 × 10 4 4– 61  k W   m − 2 21 00 –2 90 0 A di ab at ic fi nd in gs de m on str at ed th at th e in ta ke p ro fil e gr ea tly in flu en ce d th e tra ns iti on fr om la m in ar to tu rb u- le nt fl ow , d el ay in g it to R ey no ld s nu m be rs a s h ig h as 1 2, 00 0. R es ul ts fo r t he d ia ba tic he at tr an sf er a nd fr ic tio n fa ct or in di ca te d th at th e tra ns iti on w as in de pe nd en t o f th e in le t g eo m et ry an d to ok p la ce a t a Re yn ol ds n um be r of a ro un d 21 00 N ai k an d Su nd ar [1 10 ] C irc ul ar T ub e w ith H el ic al In se rts – w at er /p ro py le ne gl yc ol -b as ed C uO n an ofl ui d – – 25 × 10 2 to − 1 × 10 4 – – En ha nc em en t i n th e pr es su re d ro p an d he at tr an sf er is re po rte d B er ts ch e et  a l. [1 11 ] C irc ul ar p ip e – w at er –g ly co l m ix tu re – 7– 41 5 × 10 2 –2 3 × 10 3 – 23 00 –4 00 0 Im pr ov em en t i n th e he at tr an sf er a nd pr es su re d ro p w as re po rte d N de ng um a et  a l. [1 12 , 11 3] Tu be -in - tu be h ea t ex ch an ge r – w at er hy dr od yn am ic al ly fu lly d ev el op flo w – 10 0– 14 00 0 – 35 0 an d 50 0 fo r a co ol ed a nn ul us an d be tw ee n 43 0 an d 51 0 fo r a he at ed a nn ul us In c om pa ris on to th e tra ns iti on ba se d on fr ic tio n fa ct or , t he fl ow re gi m e tra ns iti on ba se d on th e N us - se lt nu m be r b eg an so on er 11258 D. K. Vishwakarma et al. Ta bl e 2 (c on tin ue d) A ut ho rs Te st se ct io n ge om et ry In le t g eo m et ry W or ki ng fl ui d D ev el op ed o r de ve lo pi ng fl ow Pr an dt l N um - be r Re yn ol ds n um - be r r an ge H ea t fl ux C rit ic al R ey no ld s nu m be r Im po rta nt fi nd in gs Ev er ts a nd M ey er [1 14 ] Sm oo th h or i- zo nt al tu be sq ua re -e dg ed in le t w at er D ev el op in g an d fu lly d ev el op ed flo w 7 × 10 2 –1 × 10 4 0– 3  kW   m − 2 25 40 A re la tio ns hi p be tw ee n he at tra ns fe r a nd pr es su re d ro p is c on fir m ed ex pe rim en ta lly , an d th e bo un da ry of tr an si tio n is sa m e fo r b ot h he at tra ns fe r a nd p re s- su re d ro p Ev er ts a nd M ey er [1 15 ] sm oo th c irc ul ar te st se ct io n sq ua re -e dg ed in le t w at er D ev el op in g an d fu lly d ev el op ed flo w 3– 7 50 0– 10 00 0 0– 3  kW   m − 2 2 36 1 C he n et  a l. [7 5] tra ns ve rs el y gr oo ve d tu be us in g ci rc ul ar m ol te n sa lt - 11 –2 7 3 × 10 2 – 6 × 10 4 - 13 00 O sm an e t a l. [7 6] re ct an gu la r ch an ne l re ct an gu la r al um in um o xi de – w at er n an ofl ui d – – 2 × 10 2 –7 × 10 3 cu rr en t o f 0 .7 5 A a nd v ol ta ge of 1 25  V , 20 0 W p ow er su pp ly 17 31 fo r t he 0 .3 vo l% n an ofl ui d, 1 72 3 fo r t he 0 .5 vo l% n an ofl ui d, an d 17 05 fo r th e 1. 0 vo l% na no flu id M ey er a nd A bo la rin [2 6, 62 –6 4] Sm oo th c irc ul ar tu be w ith an d w ith ou t tu rb ul at or s Sq ua re -e dg ed in le t, re -e nt ra nt in le t w at er Fu lly d ev el op ed flo w 2. 9– 6. 7, 3. 23 –6 .5 40 0– 11 40 0, 30 0– 11 40 0, 31 5– 11 ,4 04 , 65 3 to 1 0 55 3 1. 35 , 2 , 3 a nd 4  kW   m − 2 30 53 –3 33 1, 31 64 –3 45 2, 32 66 –3 56 5 B as hi r e t a l. [1 16 ] C irc ul ar tu be Sq ua re -e dg ed a nd re - e nt ra nt in le ts W at er H yd ro d yn am i- ca lly fu lly de ve lo pe d in le t – 1 × 10 3 to 6 × 10 3 4, 6 a nd 8  kW   m − 2 23 00 a nd 2 28 0 fo r th e em pt y an d or ig in al fl ow - ca lm in g se ct io n, re sp ec tiv el y B as hi r e t a l. [1 17 ] ci rc ul ar tu be C irc ul ar in le t W at er D ev el op in g an d fu lly d ev el op ed flo w 3. 5 an d 8. 1 4 × 10 2 –6 × 10 3 1– 8  kW   m − 2 – 11259A critical review on various factors affecting the thermohydraulic performance in… behaves similar to conventional tube for heat transfer and fluid flow characteristics. Meyer et al. [100] experimented to understand the flow and heat transfer characteristics of mul- tiwalled carbon nanotubes in transition-flow regime. It was found that transition initiated earlier for 1% volume concen- tration of nanotubes while it delays at lower concentrations. Varnaseri and Peyghambarzadeh [101] reported on the influ- ence of polyacrylamide on the friction factor and thermal performance. The inclusion of the drag-reducing polymer lowers heat transfer, but supplying a steady heat flux to the pipe minimizes the polymer's influence on the percentage of heat transfer reduction, according to the results. Briclot et al. [102] reported on the thermal and flow performance of Al2O3-water nanofluid in the transition-flow regime. It was reported that mass percentage does not impact the criti- cal Reynolds number and nanofluid acts as a single-phase fluid. Liu et al. [103] experimented with printed circuit heat exchanger for large range of Reynolds numbers. The working fluid used for the experimentation was supercriti- cal carbon dioxide. According to the results, the essential Reynolds values for the semi-circular channel are 2100 and 2700, respectively, to transition from laminar- to turbulent- flow regime. Jamali and Toghraie [104] studied the thermal performance characteristics of nanofluid computationally for different inlets. Their results indicate that transition for square edge inlets starts later than that of smooth tube. The studies reviewed offer valuable insights into heat transfer and flow characteristics across various fluid types, configurations and flow regimes. They highlight enhanced heat transfer and flow fluctuations in offshore nuclear reac- tors, accelerated transitions with nanofluids and the impact of geometrical features on heat-exchanger performance. Theoretical models for calculating heat transfer coefficients and experimental investigations into carbon nanotubes' effects on thermal performance provide further understand- ing. Additionally, exploration of shear thinning and yield stress effects on transitional flow, surface roughness influ- ence on fluid behavior and nanofluid behavior in thermal systems are discussed. These findings contribute to a broader understanding of thermal system optimization and design considerations across diverse applications. Correlation for heat transfer and pressure drop Correlations are developed using the data obtained from the experimental investigation for predicting the values. These correlations also show the dependence of different param- eters used in the investigation on the Nusselt number and friction factor. Several factors influence heat transfer and pressure drop which includes geometrical parameters, veloc- ity of flow, Reynolds number, Prandtl number, etc. Various Ta bl e 2 (c on tin ue d) A ut ho rs Te st se ct io n ge om et ry In le t g eo m et ry W or ki ng fl ui d D ev el op ed o r de ve lo pi ng fl ow Pr an dt l N um - be r Re yn ol ds n um - be r r an ge H ea t fl ux C rit ic al R ey no ld s nu m be r Im po rta nt fi nd in gs M ey er e t a l. [8 2] Sm oo th in cl in ed tu be s C irc ul ar in le t W at er D ev el op in g an d fu lly d ev el op ed flo w 3– 7 1 × 10 3 –6 × 10 3 4– 8  kW -m − 2 fo r h or iz on ta l flo w (θ = 0° ), 27 33 –3 07 0 It w as d is co v- er ed th at w he n th e in cl in at io n an gl es g re w fr om ho riz on ta l t o ve r- tic al , t he c rit ic al Re yn ol ds n um be rs at w hi ch tr an si tio n be ga n in cr ea se d 11260 D. K. Vishwakarma et al. Ta bl e 3 C or re la tio ns fo r N us se lt nu m be r a nd fr ic tio n fa ct or p ro po se d by v ar io us re se ar ch er s S. N A ut ho r a nd y ea r o f pu bl ic at io n N us se lt nu m be r Fr ic tio n fa ct or 1 G ha ja r a nd M ad on [3 3] – Fo r r e- en tra nt in le t C f, tr = − 9 .8 8 ∗ 1 0 − 3 + 1 .1 5 ∗ 1 0 − 5 R e − 1 .2 9 ∗ 1 0 − 9 R e2 Fo r s qu ar e ed ge in le t C f, tr = − 2 .5 6 ∗ 1 0 − 2 + 2 .4 9 ∗ 1 0 − 5 R e − 4 .2 5 ∗ 1 0 − 9 R e2 Fo r b el l m ou th in le t C f, tr = − 8 .0 3 ∗ 1 0 − 3 + 1 .0 5 ∗ 1 0 − 5 R e − 1 .4 7 ∗ 1 0 − 9 R e2 2 G ha ja r a nd T am [3 4] N u tr = { N u l + ex p [( a − R e) ∕ b ] + N u c t } c – Fo r r e- en tra nt in le t a = 17 66 , b = 27 6, a nd c = − 0. 95 5 Fo r s qu ar e ed ge in le t a = 26 17 , b = 20 7, a nd c = − 0. 90 5 Fo r b el l m ou th in le t a = 66 28 , b = 23 7, a nd c = − 0. 98 0 3 Ta m a nd G ha ja r [ 27 ] – C f = [ 1 + ( R e a ) b ] c ( � b � w ) m Fo r r e- en tra nt in le t a = 58 40 , b = − 0. 01 45 , a nd c = − 6. 23 Fo r s qu ar e ed ge in le t a = 42 30 , b = − 0. 16 , a nd c = − 6. 57 Fo r b el l m ou th in le t a = 53 40 , b = − 0. 09 90 , a nd c = − 6. 32 4 K ar w a et  a l. [1 05 ] fo r 7 ≤ e+ < 2 0 g = 1 0 3 .7 7 e− 0 .0 0 6 𝜙 (W ∕ H )0 .5 ( P e ) − 2 .5 6 * ex p [ 0 .7 3 4 3 { ln (p ∕ e ) } 2 ] ( e+ ) − 0 .3 1 fo r 2 0 ≤ e+ ≤ 6 0 g = 3 2 .2 6 e− 0 .0 0 6 � (W ∕ H )0 .5 ( P e ) − 2 .5 6 * ex p [ 0 .7 3 4 3 { ln (p ∕ e ) } 2 ] ( e+ ) 0 .0 8 fo r 5 ≤ e+ < 2 0 R = 1 .6 6 e− 0 .0 0 7 8 � (W ∕ H )− 0 .4 ( P e ) 2 .6 9 5 ∗ ex p [ − 0 .7 6 2 { ln (p ∕ e ) } 2 ] ( e+ ) − 0 .0 7 5 fo r 2 0 ≤ e+ ≤ 6 0 R = & 1 .3 2 5 e− 0 .0 0 7 8 � (W ∕ H )− 0 .4 ( P e ) 2 .6 9 5 * ex p [ − 0 .7 6 2 { ln (p ∕ e ) } 2 ] 5 G ra ci a et  a l. [1 18 ] N u a = 0 .3 0 3 (e ∕ d )0 .1 2 (p ∕ d )− 0 .3 7 7 R e0 .7 2 P r0 .3 7 N u a = 0 .1 3 2 (p ∕ d )− 0 .3 7 2 R e0 .7 2 P r0 .3 7 f a = 5 .7 6 (e ∕ d )0 .9 5 (p ∕ d )− 1 .2 1 R e− 0 .2 1 7 f a = 9 .3 5 (p ∕ e) − 1 .1 6 R e− 0 .2 1 7 6 G ra ci a et  a l. [6 5] N u = 0 .1 0 4 R e− 1 .0 1 ( R e = 2 ∗ 1 0 2 − 1 0 3 ,P r = 2 0 0 − 6 5 0 ) N u = 0 .1 0 0 R e− 0 .9 9 ( R e = 2 .5 ∗ 1 0 2 − 1 .1 ∗ 1 0 3 ,P r = 3 5 0 − 6 5 0 ) . N u = 0 .0 7 7 R e− 1 .0 3 ( R e = 5 ∗ 1 0 2 − 1 .1 ∗ 1 0 3 ,P r = 3 5 0 − 6 0 0 ) – 7 M ey er a nd O liv ie r [5 0] – f t e = 4 ( 1 6 R e c r ) 0 .9 4 ex p ( 0 .5 7 R e R e c r ) ( � 9 0 ) 0 .3 7 × ( e2 p fD e ) 0 .0 2 8 ( p f D e ) − 0 .0 0 9 ( e D e ) 0 .0 6 . 8 M ey er a nd O liv ie r [5 1] N u te = [ N u 7 L e + N u 7 T e 3 8 ] 1 ∕ 7 – 11261A critical review on various factors affecting the thermohydraulic performance in… Ta bl e 3 (c on tin ue d) S. N A ut ho r a nd y ea r o f pu bl ic at io n N us se lt nu m be r Fr ic tio n fa ct or 9 Ta m e t a l. [1 07 ] – C f, tr ,i so = ( 1 6 R e ) { [ 1 + ( 0 .0 0 4 9 R e0 .7 5 ) a ] 1 a + b } • Re -e nt ra nt : a = 0 .5 2 ,b = − 3 .4 7 fo r 2 0 2 6 < R e < 3 2 5 7 3 < x ∕ D < 2 0 0 • Sq ua re -e dg ed : a = 0 .5 0 ,b = − 4 .0 fo r 2 1 1 1 < R e < 4 1 4 1 3 < x ∕ D < 2 0 0 10 N ai k an d Su nd ar [1 10 ] N u R eg = 0 .3 2 R e0 .4 5 P r0 .4 8 (1 + � )0 .3 2 ( 1 + H D e ) − 0 .3 × ( D D e ) 1 .2 7 f R eg = 0 .1 8 R e− 0 .1 8 (1 + � )0 .2 3 ( 1 + H D e ) − 0 .0 9 ( D D e ) 0 .3 11 Ta le r [ 11 9] N u m ,q ,3 = 0. 92 4P r1 ∕3 ( Re d w L ) 1∕ 2 N u m ,T ,3 = ( 2 1+ 22 Pr ) 1∕ 6( Re Pr d w L ) 1∕ 2 – 12 N de ng um a et  a l. [1 12 ] N u = C 1 � n w he re C 1 = B 1 ( G r P r R e ) z 1 an d n = B 2 ( G r P r R e ) z 2 f d = f i so C 2 ( � b � iw ) � m w he re C 2 = E 1 (G ru P rv )z 2 m = E 2 (G ru P rv ) + E 3 13 N de ng um a et  a l. [1 13 ] N u = C  � − n W he re , λ = a L ∕ D h Fo r h ea te d an nu li: C = 1 3 4 ( G r P r R e ) 0 .4 0 1 n = 0 .3 2 ( G r P r R e ) 0 .1 4 7 Fo r c oo le d an nu li: C = 1 1 8 3 ( G r P r R e ) 0 .2 8 n = 0 .4 9 6 ( G r P r R e ) 0 .1 2 2 f i so = C is o (� )R e− m (i ) f d = f i so � z C d ( � b � iw ) Fo r h ea te d an nu li: C d = 4 6 .6 × 1 0 6 ( G r0 .0 1 P r2 .9 ) − 3 .1 2 z = 3 .8 × 1 0 − 3 ( G r0 .0 1 P r2 .9 ) − 0 .8 8 Fo r c oo le d an nu li: C d = 1 0 .9 5 ( G r0 .0 1 P r2 .9 ) 0 .1 9 z = − 0 .1 4 × 1 0 − 3 ( G r0 .0 1 P r2 .9 ) − 0 .4 5 14 Ev er ts a nd M ey er [1 15 ] N u = (0 .0 0 1 0 8 R e − 2 .4 9 )G r− 0 .0 4 P r2 f = ( 3 .7 4 R e− 8 .0 6 6 × 1 0 3 R e− 2 .3 2 0 × 1 0 3 ) N u R e P r0 .0 8 7 15 C he n et  a l. [7 5] [N u − 0 .3 ]3 .1 1 4 2 = [ 0 .6 2 R e1 ∕ 2 P r1 ∕ 3 [1 + (0 .4 ∕ P r) 2 ∕ 3 ]1 ∕ 4 ] 2 .7 6 + [ 0 .0 0 1 1 6 8 R eP r1 ∕ 3 [1 + (0 .4 ∕ P r) 2 ∕ 3 ]1 ∕ 4 ] 4 .9 8 4 7 – 16 M ey er a nd E ve rts [7 4] N u = 4 .3 6 + ( N u 6 1 + N u 6 2 ) 1 ∕ 6 N u 1 = ( 0 .3 3 G z0 .5 4 − 0 .8 4 ) P r− 0 .2 N u 2 = ( 0 .2 0 7 G r0 .3 0 5 − 1 .1 9 ) P r0 .5 G z− 0 .0 8 N u = 4 .3 6 + ( N u 6 1 + N u 6 2 ) 1 ∕ 6 N u 1 = ( 0 .3 3 G z0 .5 4 − 0 .8 4 ) P r− 0 .2 N u 2 = ( 0 .2 0 2 G r∗ 0 .2 5 4 − 1 .2 3 ) P r0 .4 5 G z− 0 .0 6 – 17 M or te an a nd M an te lli [1 20 ] N u tr an = [ ( N u la m ) 6 + ( N u tu rb ) 6 ] 1 ∕ 6 – 18 M ey er e t a l. [1 21 ] N u = (0 .0 1 7 R e − 3 0 .3 )P r0 .3 3 G r− 0 .0 8 – 19 B as hi r e t a l. [1 17 ] N u F C = 4 .3 6 + 5 .3 6 × 1 0 − 9 R e2 .3 9 f F C = N u F C (1 5 .8 8 − 0 .0 0 1 4 R e ) R e 11262 D. K. Vishwakarma et al. correlations developed in the past for predicting the heat transfer and pressure drop in the transition-flow regime are summarized in the tabulated format in Table 3 for the con- venience of the future reader of this article. Discussion Understanding the thermohydraulics of fluid flow in the transition-flow regime is becoming a necessity. This brings sudden momentum in the field of heat transfer and pressure drop in the transition-flow regime. Although the field is in the early stage of research, the effort made by researchers helps in the better understanding of the heat transfer and flow dynamics in the transition-flow regime. The research group of Ghajar initially begins to investigate the thermo- hydraulic of fluid flow in transition-flow regime with a motive to gather the data for the better realization of the physics. The group carried out a series of experiments and collected data for different operation conditions such as inlet geometry, uniform and variable heat flux, developed and developing flow, etc. Following the path of Ghajar and co- worker and understanding the gap in the research, Meyer and co-workers further investigate the transition-flow regime for different fluids, heat flux, channel geometries, channel inclination, turbulators, etc. The results obtained by Meyer and co-workers are remarkable in the field of heat transfer and fluid flow. The correlations developed by Meyer and co-workers are very much appreciated and challenge the previous correlations. The use of nanofluids and turbulators was also first investigated in this group which shed light on the flow dynamics. The clear shift in the transition-flow regime with changes in the geometry, flow condition, posi- tion, etc., was clearly notified and explained the detail. One of the main findings is the change in the value of Nusselt number for forced-convection heat transfer with an increase in Reynolds number which otherwise considered constant. This finding challenges the existing correlations and brings the need for changes in them. After carefully reviewing all the articles related to transi- tion flow heat transfer and pressure drop, it can be said that transition depends on lots of factors. Geometry of inlet, type of fluid, heat flux, turbulators, orientation of test channel, flow directions, etc., are the factors influencing the outset and cessation of the transition. The widely accepted range of transition is between 2100 and 2300 Reynolds numbers. However, after the research of almost three decades by sev- eral research groups, it can be said that start and end of transition changes with change in the operating conditions. It can start as early as Re = 600 and can be delayed up to Re = 10,000. Therefore, it can be said that understanding the ther- mohydraulics of fluid flow in the transition-flow regime is crucial for advancing heat transfer and pressure drop knowledge in the transition-flow regime. Research efforts by various groups, such as Ghajar and Meyer, contribute significantly to the understanding of heat transfer and flow dynamics in transition-flow regimes. Factors such as inlet geometry, fluid type, heat flux and channel orientation play significant roles in influencing the onset and cessation of transition. The research highlights that the transition range can vary depending on operating conditions, challenging the widely accepted transition range of 2100–2300 Reyn- olds numbers. In addition, it is also pointed out that while some research suggests that transition typically occurs within the range of 2100–2300 Reynolds numbers, other findings indicate that transition can start as early as Re = 600 and be delayed up to Re = 10,000, suggesting a broader variability in transition onset and end points. The research by Meyer and co-workers challenges existing correlations, indicat- ing a need for updating and revising them to accommodate the observed variations in transition behavior. There may be differing opinions on the specific factors contributing to transition onset and cessation, with some emphasizing the importance of inlet geometry, fluid type and heat flux, while others may prioritize other factors such as channel inclination or flow direction. Despite the agreement on the significance of understanding transition-flow regimes, there may be differing perspectives on the implications and applications of this knowledge, depending on the context and objectives of the research. Conclusions The prime intent of present review work is to summarize all the research works which studied the heat transfer and fluid flow characteristics in single-phase transition flow and compile them together to create a coherent body for ease for future readers and researchers. After reviewing various articles on developing and fully developed flow, it can be said that factors such as the geometry of inlet, type of fluid, heat flux, turbulators, orientation of test channel, flow directions, etc., remarkably influence the outset and cessation of the transition in the flow field. Due to the higher velocity of the fluid, the laminar–turbulent transi- tion happens quicker throughout the tube length as the Reynolds number rises. When opposed to forced convec- tion circumstances, free or natural convection effects first disrupt the fluctuations inside the test section, resulting in a delayed laminar–turbulent transition. The laminar–turbu- lent transition throughout the tube length occurs faster as a result of the improved mixing, and the magnitude of the Nusselt numbers escalates. The properties of developing 11263A critical review on various factors affecting the thermohydraulic performance in… and fully developed flow, particularly in the transition-flow regime, differ substantially in terms of heat transmission and pressure drop. Scope for future works Investigations in the transition-flow regime are still in the early stage and need to be explored extensively for improved under- standing of fluid flow and heat transfer in this intricate flow regime. This flow regime is known for its unsteady, chaotic and unrealistic flow behavior. The following recommendations for future work are outlined below: 1. The existing studies have predominantly focused on constant heat flux conditions. It is recommended to investigate the impact of constant wall temperature on the transition-flow regime for both heating and cooling scenarios. 2. Research on transition-flow regimes with turbulators remains limited, necessitating thorough investigations with various turbulator designs and inlet obstructions. 3. The influence of channel cross section has been omit- ted in previous literature and should be incorporated in future research. 4. The impact of orientation and flow direction on the transition-flow regime with inserted turbulators should be investigated in future studies. References 1. Sharaf MA, Marzouk SA, Aljabr A, Almehmadi FA, Kaood A, Alqaed S. Heat transfer enhancement in a double-pipe helical heat exchanger using spring wire insert and nano- fluid. J Therm Anal Calorim. 2024. https:// doi. org/ 10. 1007/ s10973- 024- 12992-1. 2. 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