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The purpose of the present study was to investigate of the effect of temperature variation on the logarithmic surface. By using the appropriate similarity transformation for the generation components and temperature, the basic equations governing flow and heat transfer are reduced to a set of ordinary differential equations. These equations have been solved approximately subject to the relevant boundary conditions with numerical and analytical techniques. The reliability and performance of the present method have been compared with the numerical method (Runge–Kutta fourth-rate) to solve this problem. Then, LSM is used to solve nonlinear equation in heat transfer. This method is useful and practical for solving the nonlinear equation in heat transfer. It is observed that the obtained results by present analytical method are very close to result of the numerical method. Furthermore, the results show that the temperature profiles decreased by increasing the α number, and, temperature profiles increased by increasing the β number

Analytical investigation of the one dimensional heat transfer in logarithmic various surfaces