Approximate solution of couple stress fluid with expanding or contracting porous channel

Purpose - The purpose of this paper is to investigate the approximate solution of the couple stress fluid equations in a semi-infinite rectangular channel with porous and uniformly expanding or contracting walls. Design/methodology/approach - Perturbation method is a traditional method depending on a small parameter which is difficult to be found for real-life nonlinear problems. The governing partial differential equations are transformed using a transformation into an ordinary differential equation that is solved by homotopy analysis method (HAM) and shooting technique. Findings - To assess the accuracy of the solutions, the comparison of the obtained results reveals that both methods are tremendously effective. Analytical and numerical solutions comparison indicates an excellent agreement and this comparison is also presented. Graphs are portrayed for the effects of some values of parameters. Practical implications - Expansion or contraction problems occur naturally in the transport of biological fluids, the air circulation in the respiratory system, expanding or contracting jets and the synchronous pulsating of porous diaphragms. This work provides a very useful source of information for researchers on this subject. Originality/value - In the present study, the flow of couple stress fluids in expanding and contracting scenarios is investigated.