Homotopy analysis on magnetized Williamson-micropolar nanofluid flow over a bi-directionally extending surface with multiple slip conditions

This current investigation examines the behavior of Williamson-micropolar nanofluid across a bi-directionally extending sheet with thermal radiation, heat source, and multiple slip conditions. It is noteworthy to measure heat transmission of the Williamson-micropolar flow filled with water-based alumina nanofluid subjected to the bi-directional stretching sheet. By utilizing the proper similarity transformation rules, the governing complex partial differential equations (PDEs) of the problem are altered to non-linear ordinary differential equations (ODEs). The Homotopy Analysis Method (HAM) is used to solve the transmuted system of non-linear ODEs. Graphical representations of findings are used to examine the effects of various physical factors on the velocity, angular velocity and temperature profiles. Convergence of the results has been presented. The HAM results, presented in tabular form, are compared to existing literature, demonstrating that our findings surpass previously published research. It has been revealed in this study that nanofluid volume fraction reduces the velocity profiles.