Comparison of Analytical and Numerical Solutions for ODE-BVP Arising in Heat Transfer Exchanger with a Fin

Abstract

This research provides the analytical and numerical solution for ODE-BVP (Ordinary differential equation-Boundary value problems) arising in heat transfer exchanger with a fin, and a comparison between these solutions to arrive to a good model of heat transfer process that can use in many kinds of designs of heat exchangers with high efficiency. The comparison of calculations confirmed that the matrix and SOR methods are more accuracy to solve the equation, but they need more work, whereas; the shooting method is easier to solve, faster to converge, but it does not offer a good accuracy because it depends on assuming the initial value of theta. The results showed an agreement between the analytical and the numerical solution, which indicates that the constructed design of the fin, is appropriate to understand the principles of heat transfer by engineers.