Reliable Iterative Methods for Solving Convective Straight and Radial Fins with Temperature-Dependent Thermal Conductivity Problems

Abstract

In our article, three iterative methods are performed to solve the nonlinear differential equationsthat represent the straight and radial fins affected by thermal conductivity. The iterative methodsare the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) andBanach contraction method namely (BCM) to get the approximate solutions. For comparisonpurposes, the numerical solutions were further achieved by using the fourth Runge-Kutta (RK4)method, Euler method and previous analytical methods that available in the literature. Moreover,the convergence of the proposed methods was discussed and proved. In addition, the maximumerror remainder values are also evaluated which indicates that the proposed methods are efficientand reliable. Our computational works have been done by using the computer algebra systemMATHEMATICA®10 to evaluate the terms in the iterative processes.