Analytical accuracy of the one dimensional heat transfer in geometry with logarithmic various surfaces

In this study, heat transfer and temperature distribution equations for logarithmic surface are investigated analytically and numerically. Employing the similarity variables, the governing differential equations have been reduced to ordinary ones and solved via Homotopy perturbation method (HPM), Variational iteration method (VIM), Adomian decomposition method (ADM). The influence of the some physical parameters such as rate of effectiveness of temperature on non-dimensional temperature profiles is considered. Also the fourth-order Runge-Kutta numerical method (NUM) is used for the validity of these analytical methods and excellent agreement are observed between the solutions obtained from HPM, VIM, ADM and numerical results.