Analytical Solution to the Boundary Layer Slip Flow and Heat Transfer over a Flat Plate using the Switching Differential Transform Method

Abstract

In this paper, the two-dimensional steady boundary layer flow and heat transfer over a flat plate with slip velocity and temperature jump conditions at the walls were analyzed. Using similarity transforms, the governing equations were reduced to a system of ordinary differential equations. Semi-analytical solutions to the resulting boundary value problem were obtained using the differential transform method (DTM). In order to cover the asymptotic boundary conditions, a method of switching curves was proposed. In this switching approach, the traditional solution to the DTM, which is valid for finite horizons, was followed by another path that was also an analytical solution to the problem. The main preference of the resulting closed form solution with respect to numerical solution is the possibility of parametric studies. The method was verified using some available numerical data, and the results showed that our proposed method had reasonable efficiency and accuracy.