Nonsimilar analysis of magneto Carreau–Yasuda nanofluid flow in a porous medium over convectively heated surface with new concept of modified Darcy's law

Abstract The current study presents a non‐similar analysis regarding the magnetohydrodynamic (MHD) flow of Carreau–Yasuda (CY) nanofluid across a non‐linearly stretching surface through a porous medium with the concerns of zero mass flux, thermal radiations, and convective boundary conditions. Modified Darcy's model is presumed here to specify the porous medium. The Buongiorno model, which includes thermophoresis and Brownian motion mechanisms, is used here for nanofluid transport analysis. The governing convection boundary layer (BL) equations are transformed into nondimensional coupled nonlinear partial differential equations (PDEs) by utilizing suitable nonsimilar transformations. The solution of the transformed dimensionless system is computed by adopting a well‐known local nonsimilarity (LNS) approach up to the second level of truncation with the bvp4c (MATLAB built‐in solver). The influence of the key emerging nondimensional parameters on velocity, thermal, and concentration profiles is depicted pictorially. A comprehensive description is given to show how the graphical features justify the physical prospect. Graphical illustrations portray that the velocity distribution increases for larger dimensionless Weissenberg numbers and it declines for greater estimations of the porosity parameter. It is observed that increasing radiation and Eckert numbers have an ascending impact on the thermal profile of the considered fluid. Moreover, the result reveals that the nanoparticle concentration upsurges along with thermophoresis and Brownian motion parameters. For larger estimations of the porosity parameter and Hartmann number, the coefficient magnitude of skin friction rises. The numerical computations are verified in a restricted case by comparing them to previously published results and confirming a close agreement.