Thermal analysis of continuously moving solid and porous fins using approximate analytical methods
Date
2019
Authors
Ndlovu, Partner Luyanda
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Abstract
In 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.
Description
A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy
in the Faculty of Sciemce to the School of Computer Science and Applied Mathematics,
University of the Witwatersrand, Johannesburg, 2019
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Citation
Ndlovu, Partner Luyanda (2019) Thermal analysis of continuously moving solid and porous fins using approximate analytical methods, University of the Witwatersrand, Johannesburg, https://hdl.handle.net/10539/29581