Analytical Evaluation of Heat Transfer Conductivity with Variable Properties

Most scientists believe that the combination of numerical and semi-exact analytical methods can also end with useful results. Recently, several approximate methods have been developed to analyze the nonlinear problems [112]. Homotopy analysis method (HAM) which was recently developed by [13] is one of the most successful and efficient methods in solving non-linear equations. In comparison with previous analytical techniques, the HAM has the following advantages. Firstly, unlike all previous analytical techniques, the HAM provides us with great freedom to express solutions of a given non-linear problem by means of different base functions. Secondly, the HAM always provides us with a family of solution expressions in the auxiliary parameter , even if a non-linear problem has a unique solution. Thirdly, unlike perturbation techniques, the HAM is independent of any small or large quantities and eventually, through previous works [14-18], it is also shown that the HAM method logically contains some previous techniques such as Adomian's decomposition method, Lyapunov's artificial small parameter method, and the d-expansion method. Many authors [19-24] have successfully applied the HAM in solving different types of non-linear problems i.e. coupled, decoupled homogeneous and non-homogeneous equations arising in different physical problems such as heat transfer, fluid flow, oscillatory systems, etc. Ghasemi et al. [22] analyzed the steady twodimensional laminar forced MHD Hiemenz flow against a flat plate with variable wall temperature in a porous medium. They utilized homotopy analysis method for solving the transformed nonlinear boundary layer equations. The velocity and temperature profiles for various values of Prandtl number , the Hartmann number , exponent of wall temperature , the permeability parameter and suction and injection parameter were presented h