An analytic solution of micropolar flow in a porous channel with mass injection using homotopy analysis method

Purpose – The paper aims to find an accurate analytic solution (series solution) for the micropolar flow in a porous channel with mass injection for different values of Reynolds number. Design/methodology/approach – In this paper, the homotopy analysis method (HAM) with different numbers of unknown convergence-control parameters has been used to derive accurate analytic solution for micropolar flow in a porous channel with mass injection. The possible optimal value of convergence-control parameter determined by minimizing the averaged residual error. Findings – The results obtained from HAM solution with two parameters are compared with numerical results and that obtained from HAM solution with only one parameter. The results show that this method gives an analytical solution with high order of accuracy with a few iterations. As shown in this paper, by minimizing the averaged residual error, the authors can get the possible optimal value of the convergence-control parameters which may give the fastest convergent series. Practical implications – The HAM with different numbers of unknown convergence-control parameters can be used to obtain analytic solutions for many problems in sciences and engineering. Originality/value – This paper fulfils an identified need to evaluate the accurate analytic solution (series solution) of practical problem.

Porous channel, Homotopy analysis method, Micropolar flow, Optimal convergence-control parameter