Abstract
In this paper, Adomian decomposition sumudu transform method is introduced and used to solve the temperature distribution in a solid and porous fin with the temperature dependent internal heat generation for a fractional order energy balance equation. In this study, we assume heat generation as a variable of fin temperature for solid and porous fin and the heat transfer through porous media is simulated by using Darcy’s model. The results are presented for the temperature distribution for the range of values of parameters appeared in the mathematical formulation and also compared with numerical solutions in order to verify the accuracy of the proposed method. It is found that the proposed method is in good agreement with direct numerical solution.
Highlights
Fins are commonly used to facilitate the dissipation of heat from a heated wall to the surrounding environment
Solid fin with temperature dependent internal heat generation and constant thermal conductivity Temperature distribution for this case is shown in Figs. 2 and 3 where M = 1 that is common in fin design
The comparison of obtained results with numerical results reveals that Adomian decomposition sumudu transform method (ADSTM) has good efficiency and accuracy
Summary
Fins are commonly used to facilitate the dissipation of heat from a heated wall to the surrounding environment. Examples of fin are the radiator in vehicles and heat exchangers in power plants. In electrical devices like motors and transformers, the generated heat can be efficiently transferred. In the study of heat transfer, fin is a surface, made by metallic material which is used to increase the rate of heat transfer to the environment. The rate of heat transfer depends on the surface area of the fin. Fins are extensively used to improve the rate of heat dissipation from a hot surface, especially in thermal engineering applications (Bergman et al.; Nield and Bejan)
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