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

Authors : Majeed ALJAWARY, Alzahraa ABDUL NABI

Pages : 967-989

Doi:10.35378/gujs.429896

View : 21 | Download : 8

Publication Date : 2019-09-01

Article Type : Research Paper

Abstract :In our article, three iterative methods are performed to solve the nonlinear differential equations that represent the straight and radial fins affected by thermal conductivity. The iterative methods are the Daftardar-Jafari method namely insert ignore into journalissuearticles values(DJM);, Temimi-Ansari method namely insert ignore into journalissuearticles values(TAM); and Banach contraction method namely insert ignore into journalissuearticles values(BCM); to get the approximate solutions. For comparison purposes, the numerical solutions were further achieved by using the fourth Runge-Kutta insert ignore into journalissuearticles values(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 maximum error remainder values are also evaluated which indicates that the proposed methods are efficient and reliable. Our computational works have been done by using the computer algebra system MATHEMATICA®10 to evaluate the terms in the iterative processes.
Keywords : Thermal conductivity