A Chebyshev Spectral Collocation Method-Based Series Approach for Boundary Layer Flow and Heat Transfer in a Micropolar Fluid past a Permeable Flat Plate

Abstract

This paper demonstrates the applicability of the large parameter spectral perturbation method (LSPM) to a coupled system of partial differential equations that cannot be solved exactly. The LSPM is a numerical method that employs the Chebyshev spectral collocation method in the solution of a sequence of ordinary differential equations (ODEs) that are derived from decomposing coupled systems of nonlinear partial differential equations (PDEs) using series expansion about a large parameter. The validity of the LSPM is applied to the problem of boundary layer flow and heat transfer in a micropolar fluid past a permeable flat plate in the presence of heat generation and thermal radiation. The coupled nature of the PDEs that define the problem under investigation precludes the option of using series-based methods that seek to generate analytical solutions even in the presence of small or large parameters. The present study demonstrates that the LSPM can easily overcome this limitation while giving very accurate results in a computationally efficient manner. For qualitative validation of the results and the numerical method used, calculations were carried out to graphically obtain the velocity, microrotation, and temperature profiles for selected physical parameter values. The results obtained were found to correlate with the results from a published literature. For quantitative confirmation of our findings, the LSPM numerical solutions were again validated against known results from the literature and against results obtained using the multidomain bivariate spectral quasilinearisation method (MD-BSQLM), and the results were observed to be in perfect agreement. Further accuracy validation is displayed by using residual error and solution error analysis on the governing PDEs and their underlying solutions. This study’s findings indicate that the heat generation and thermal radiation parameters have related effects on the temperature profile, enhancing both the fluid temperature and the thermal boundary layer thickness.