3. Electronic Theses and Dissertations (ETDs) - All submissions
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Item Thermal analysis of continuously moving solid and porous fins using approximate analytical methods(2019) Ndlovu, Partner LuyandaIn various industrial and engineering applications, fins (extended surfaces) are frequently adopted to enhance the rate of heat dissipation between a system and its surroundings. The heat transfer mechanism of a fin is to conduct heat from a heat source to the fin surface via conduction, and then dissipate heat to the surrounding fluid via convection, radiation, or simultaneous convection-radiation. In order to improve the rate of heat transfer through finned surfaces, it is necessary to understand a fin’s dynamic response to change in temperature. The study of heat transfer though fins continues to be of scientific interest and recently, the study of moving fins has attracted a lot of research interests. The study of heat transfer through fins is modeled by differential equations. In search for solutions to differential equations arising in physics and engineering, analytical methods are very useful as it is difficult if not impossible to find the exact solutions. In recent years, the availability of faster processing equipment further means that we are able to compute analytical solutions to highly nonlinear equations that are more accurate in representing the physical phenomena. The modeling of heat transfer through fins reduces the experimental costs and gives insight into various parameters influencing the heat transfer process. In this thesis, the Variational Iteration Method (VIM) and the Differential Transform Method (DTM) are used to solve the nonlinear boundary value problems describing heat transfer in solid and porous fins undergoing convective-radiative heat dissipation. Validation of analytical solutions is also obtained by comparison with numerical solutions. The aim is to derive mathematical models describing heat transfer though fins, analyze the impact of the embedding thermo-physical parameters, compare the accuracy and computational efficiency of these two modern day analytical methods. The study of porous fins is performed using Darcy’s model to formulate the governing heat transfer equations. As far as we know, the transient study of heat transfer through moving fins has not been performed anywhere in literature. Related work on finned heat transfer is modeled using steady state models with the assumption that the transient response dies out quickly. Since a broad range of governing parameters are investigated, the results could be useful in a number of industrial and engineering applications.Item Analytical solutions and conservation laws of models describing heat transfer through extended surfaces(2013-07-29) Ndlovu, Partner LuyandaThe search for solutions to the important differential equations arising in extended surface heat transfer continues unabated. Extended surfaces, in the form of longitudinal fins are considered. First we consider the steady state problem and then the transient heat transfer models. Here, thermal conductivity and heat transfer coefficient are assumed to be functions of temperature. Thermal conductivity is considered to be given by the power law in one case and by the linear function of temperature in the other; whereas heat transfer coefficient is only given by the power law. Explicit analytical expressions for the temperature profile, fin efficiency and heat flux for steady state problems are derived using the one-dimensional Differential Transform Method (1D DTM). The obtained results from 1D DTM are compared with the exact solutions to verify the accuracy of the proposed method. The results reveal that the 1D DTM can achieve suitable results in predicting the solutions of these problems. The effects of some physical parameters such as the thermo-geometric fin parameter and thermal conductivity gradient, on temperature distribution are illustrated and explained. Also, we apply the two-dimensional Differential Transform Method (2D DTM) to models describing transient heat transfer in longitudinal fins. Furthermore, conservation laws for transient heat conduction equations are derived using the direct method and the multiplier method, and finally we find Lie point symmetries associated with the conserved vectors.