Investigation of Nonlinear Problems of Heat Conduction in Tapered Cooling Fins Via Symbolic Programming

In this paper, symbolic programming is employed to handle a mathematical model representing conduction in heat dissipating fins with triangular profiles. As the first part of the analysis, the Modified Adomian Decomposition Method (MADM) is converted into a piece of computer code in MATLAB to seek solution for the mentioned problem with constant thermal conductivity (a linear problem). The results show that the proposed solution converges to the analytical solution rapidly. Afterwards, the code is extended to calculate Adomian polynomials and implemented to the similar, but more generalized, problem involving a power law dependence of thermal conductivity on temperature. The latter generalization imposes three different nonlinearities and extremely intensifies the complexity of the problem. The code successfully manages to provide parametric solution for this case. Finally, for the sake of exemplification, a relevant practical and real-world case study, about a silicon fin, for the complex nonlinear problem is given. It is shown that the numerical results are very close to those calculated by the classical Finite Difference Method (FDM)

Meshless Approach for Computing the Heat liberation from Annular Fins of Tapered Cross Section

This technical note addresses an extremely simple computational procedure for solving the complex quasi-one dimensional heat equation with variable coefficients that governs the temperature change in annular fins of hyperbolic profile cooled by a fluid. The salient feature of the computational procedure is the convenient linkage of the finite-difference method with a meshless approach. Using a very coarse mesh, accurate estimates for the temperature distribution and heat liberation from annular fins of hyperbolic profile have been obtained by hand solving small systems of three algebraic equation