Abstract
We investigate the steady two-dimensional flow of a viscous incompressible fluid in a rectangular domain that is bounded by two permeable surfaces. The governing fourth-order nonlinear differential equation is solved by applying the spectral-homotopy analysis method and a novel successive linearisation method. Semianalytical results are obtained and the convergence rate of the solution series was compared with numerical approximations and with earlier results where the homotopy analysis and homotopy perturbation methods were used. We show that both the spectral-homotopy analysis method and successive linearisation method are computationally efficient and accurate in finding solutions of nonlinear boundary value problems.
Highlights
Laminar viscous flow in tubes that allow seepage across contracting or expanding permeable walls is encountered in the transport of biological fluids such as blood and filtration in kidneys and lungs
In the past four decades a considerable amount of research effort has been expended in the study of laminar flows in rectangular domains that are bounded by permeable walls 8–15
An analytical solution by means of the Liouville-Green transformation was developed for laminar flow in a porous channel with large wall suction and a weakly oscillatory pressure by Jankowski and Majdalani 13
Summary
Laminar viscous flow in tubes that allow seepage across contracting or expanding permeable walls is encountered in the transport of biological fluids such as blood and filtration in kidneys and lungs. Majdalani and Roh 4 and Majdalani 3 studied the oscillatory channel flow with wall injection, and the resulting governing equations were solved using asymptotic formulations WKB and multiple-scale techniques. Dinarvand et al 2 solved Berman’s model of two-dimensional viscous flow in porous channels with wall suction or injection using both the HAM and the homotopy perturbation method HPM. They concluded that the HPM solution is not valid for large Reynolds numbers, a weakness earlier observed in the case of other perturbation techniques. We use the spectral homotopy analysis method to solve the nonlinear differential equation that governs the flow of a viscous incompressible fluid in a rectangular domain bounded by two permeable walls. The results are compared with numerical approximations and the recent results reported in Xu et al 24 and Dinarvand and Rashidi 30
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