The flow of Casson–Williamson fluid on a stretching surface is considered for the study. The movement of fluid is examined under the effect of external magnetic field, thermal radiation and chemical consequences. The model is formed by considering all the physical aspects responsible for the physical mechanism. The formed mathematical model (partial differential equation) is numerically solved after transforming it into an ordinary one (ordinary differential equation) via similarity invariants. The physical mechanism for velocity, temperature, and concentration is examined through the associated parameters like radiation index, Williamson and Casson parameter, suction/injection parameter, porosity index, and chemical reaction parameter.

The present work reveals the aspects of MHD Prandtl nanofluid flow under consideration of convective boundary condition over stretched sheet. The current flow model of PDE’s is transmuted to non-linear ODE’s using similarity variables after which numerically treated by Runge-Kutta scheme clubbed with a shooting method. The physical virtues of flow restrictions $B=M=1,Pr=Sc=2$ and $\delta =\text{R}=\lambda =Nb=Nt=0.5,G=\nu =-0.5,ϵ=0.1$on velocity, energy and concentration are discussed vividly. The flow geometry shows the improvement in the velocity distribution for rising value of the fluid parameter, while decrement in energy and concentration distribution. Also, escalation of radiative parameter and Biot number creates ample amount of energy into the system which increases fluid temperature. However, the concentration distribution diminishes as the chemical reaction parameter increases.

The present research paper highlights the effect of multiple slips and inclined magnetic fields on chemically reacting Casson-Williamson with Buongiorno modeled nanofluid flow past a permeable stretching surface. Considered physical factors associated with heat transfer are viscous dissipation, Joule's heating, radiation, and double diffusion effects. The ordinary differential equations (ODEs) are formulated from governing system of highly nonlinear Partial differential equations (PDEs) by a suitable implementation of similarity invariants. The numerical results are obtained by programming the resulting equations in MATLAB software via Runge-Kutta (R-K) fourth-order technique along with the shooting scheme. The graphical illustration provides the behavior of velocity, temperature, and concentration on different non-dimensional parameters. It is worth to notice the slip parameters are greatly analogs with various physical properties of the flow field. The effect of a magnetic parameter ([ ]), Casson parameter ([ ]), Williamson parameter ([ ]), velocity slip effect ([ ]), and the inclination ([ ]) on axial velocity are shown graphically. The outstanding agreement is observed after a comparison of numerical outcomes with previously published work. The applied magnetic field and thermal radiation insert more energy into the system which improves the thermal boundary layer.

Heat and mass transmission of non-Newtonian fluids get considerable attention due to their complexity and high nonlinearity in rheology. Among the various fluid models, Williamson fluid model very well describes the low as well as high-viscosity situations. With this perspective, the present work deals with heat and mass transfer of MHD Williamson nanofluid flow past a porous stretching surface with thermal radiation and chemical reaction. Highly nonlinear governing equations are transformed into ordinary ones by employing similarity invariants. The reduced systems of ODEs are numerically treated with R-K’s fourth-order method along with the shooting technique. Using MATLAB the associated nondimensional parameters are graphically interpreted and found to be in good agreement with the literature. For the higher values of magnetic and Williamson parameters, fluid motion becomes a decreasing function whereas the temperature profile is enhanced for the magnetic, Williamson, and radiation parameters. The investigation will serve in the process involving fluids such as food processing, glass manufacturing, oil extraction, etc.