Analytical Solution and Numerical Simulation for One-Dimensional Steady Nonlinear Heat Conduction in a Longitudinal Radial Fin with Various Profiles

摘要

In this article we consider a model describing the temperature profile in a longitudinal fin with rectangular, concave, triangular, and convex parabolic profiles. Both thermal conductivity and the heat transfer coefficient are assumed to be temperature-dependent, and given by a linear function and by power laws, respectively. In addition, the effects of the thermal conductivity gradient have been investigated. Optimal homotopy analysis method (OHAM) is employed to analyze the problem. The effects of the physical applicable parameters such as thermo-geometric fin, thermal conductivity, and heat transfer mode are analyzed. The OHAM solutions are obtained and validity of obtained solutions is verified by the Runge-Kutta fourth-order method and numerical simulation. A very good agreement is found between analytical and numerical results. Also for investigation of lateral effects on the accuracy of results, numerical simulation (by Ansis software) is compared with the homotopy analysis method (HAM) and numerical solution (by Runge-Kutta) of the energy balance equation.