Heat transfer study on solid and porous convective fins with temperature-dependent heat generation using efficient analytical method

S. E. Ghasemi¹, P. Valipour², M. Hatami³, D. D. Ganji⁴

(1. Young Reseachers and Elite Club, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran;
2. Department of Textile and Apparel, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran;
3. Department of Mechanical Engineering, Esfarayen University of Technology, North Khorasan, Iran;
4. Department of Mechanical Engineering, Babol University of Technology, Babol, Iran)

Abstract:A simple and highly accurate semi-analytical method, called the differential transformation method (DTM), was used for solving the nonlinear temperature distribution equation in solid and porous longitudinal fin with temperature dependent internal heat generation. The problem was solved for two main cases. In the first case, heat generation was assumed variable by fin temperature for a solid fin and in second heat generation varied with temperature for a porous fin. Results are presented for the temperature distribution for a range of values of parameters appearing in the mathematical formulation (e.g. N, e_G, and G). Results reveal that DTM is very effective and convenient. Also, it is found that this method can achieve more suitable results in comparison to numerical methods.

Key words:heat transfer; convective fin; solid and porous fin; heat generation; analytical method; thermal analysis