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.