Abstract
We investigate the applicability of the compact finite difference relaxation method (CFDRM) in solving unsteady boundary layer flow problems modelled by nonlinear partial differential equations. The CFDRM utilizes the Gauss-Seidel approach of decoupling algebraic equations to linearize the governing equations and solve the resulting system of ordinary differential equations using compact finite difference schemes. The CFDRM has only been used to solve ordinary differential equations modelling boundary layer problems. This work extends its applications to nonlinear partial differential equations modelling unsteady boundary layer flows. The CFDRM is validated on two examples and the results are compared to results of the Keller-box method.
Highlights
The many, important applications associated with boundary layer flow and heat transfer induced by a stretching surface have made them one of the most studied problems in the field of fluid dynamics
We investigate the applicability of the compact finite difference relaxation method (CFDRM) in solving unsteady boundary layer flow problems modelled by nonlinear partial differential equations
Liao proposed the use of the homotopy analysis method (HAM) instead and since the HAM has been dominantly used in solving the unsteady boundary layer flow problems
Summary
The many, important applications associated with boundary layer flow and heat transfer induced by a stretching surface have made them one of the most studied problems in the field of fluid dynamics. The Keller-box method of Cebeci and Bradshaw [3] has been very popular in solving this kind of problems amongst researchers These include Seshadri et al [4] who combined the Keller-box and perturbation series approach for the solution of unsteady mixed convection flow along a heated vertical plate. Nazar et al [5, 6] solved the unsteady boundary layer flow problem due to an impulsively stretching surface in a rotating fluid by means of the Kellerbox numerical method, and they obtained a first-order perturbation approximation of the solution. The advantage of the HAM over the perturbation techniques is that it is able to produce solutions valid for all time
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