New Analytical Solution Formula for Heat Transfer of Unsteady Two-Dimensional Squeezing Flow of a Casson Fluid between Parallel Circular Plates

Abstract

In this paper, the effect of physical parameters on the velocity and temperature distributions for heat transfer of unsteady two-dimensional squeezing flow of a Casson fluid between parallel circular plates is studied. Thrive similarity transforms is used to reduce the equations of problem into highly nonlinear ordinary differential equations. The resulting equations are solved by a new analytical technique and obtained new analytical approximate solution. This new analytical technique essentially depends on the coefficients of powers series that result from integration nth order of a differential equation. Fourth order Runge-Kutta method is also using to obtain numerical solution. The influence of involved physical parameters on the velocity and temperature distributions is discussed with the help of tables and graphics. Also, as novel idea in this work, some theorems to prove the convergence of a new analytical technique theoretically, and the verifications of these theorems computationally are introduced. The results of new analytical approximate technique are verified an excellent agreement by comparing it with Runge-Kutta method and homotopy perturbation method (HPM).