Numerical simulation on the MHD time-dependent Williamson nanofluid flow with cross diffusion and heat generation/absorption over a stretching plate

This novel study unfolds the heat and mass transfer investigation of Williamson nanofluid (WNF) through a porous medium past a stretching plate, along with considering heat generation/absorption. Nanoparticles hold significant significance in thermal engineering, industrial operations, and biomedical advancements, contributing to enhanced heat transfer, cooling mechanisms, thermal extrusion processes, and applications in cancer treatment, particularly in addressing brain tumors. The coupled ordinary differential equations (ODEs) are gained from governing partial differential equations (PDEs) by applying sufficient transformations. Then the ODEs of a nonlinear nature, along with boundary conditions, are solved through bvp4c, a built-in MATLAB program. A good agreement has been found in comparing the present study with already published papers. Numerical values for skin friction, mass transfer, and heat transfer are shown through a table against involved physical parameters, especially for both injection (S<0) and suction (S>0) cases, by varying the values of unsteadiness parameter A and Weissenberg number We. The effects of the physical parameters on velocity, temperature, and mass profile are graphically depicted and illustrated minutely. It is noted that both the magnetic and Williamson parameters cause the thickness of the boundary layer to be reduced. It can be deduced from these findings that the rate of heat transfer over the surface of the plate decreases as the unsteadiness parameter increases. Furthermore, it is observed that an increase in the parameters of thermophoresis and Brownian motion leads to a higher temperature of the nanofluid.