Significance of Darcy–Forchheimer law and magnetic field on the comparison of Williamson–Casson fluid subject to an exponential stretching sheet

Abstract

Non-Newtonian fluid mechanics is becoming more and more relevant as time marches on due to the increasing number of fluids encountered in everyday life that exhibit non-Newtonian behavior. It is our intention to cover the multitude of aspects of non-Newtonian fluid mechanics: The effects of magnetohydrodynamic (MHD) laminar boundary layer flow with heat and concentration transfers are considered in the case of Darcy–Forchheimer Williamson–Casson fluids installed over an exponentially extending sheet. There has been an examination and comparison of the effects of momentum fields, thermal radiation, Joule heating, suction/ injection, and compound responses. By using a suitable closeness change, the boundary conditions (BCs) and partial differential equations (PDEs) are reduced to dimensionless structures. The following set of ordinary differential equations (ODEs) and associated BCs are to be clarified using the bvp4c technique. The investigation’s findings indicate that boundary layer thicknesses for velocity, temperature, and concentration normally decline as we get farther from the sheet’s edge, and it is discovered that the Williamson–Casson parameter interferes with velocity profiles. Graphs are developed for Darcy–Forchheimer [Formula: see text], magnetic parameter M, Lewis number Le, radiation parameter [Formula: see text], porosity parameter [Formula: see text], and Eckert number [Formula: see text]. The numeric values of [Formula: see text] and [Formula: see text] are validated with available data and found to be in excellent agreement.