Abstract
In this article, the effect of electromagnetic force with the effect of thermal radiation on the Williamson nanofluid on a stretching surface through a porous medium was studied considering the effect of both heat generation/absorption and Joule heating. On the other hand, the effect of Brownian motion and thermophoresis coefficients was considered. The system of nonlinear partial differential equations governing the study of fluid flow has transformed into a system of ordinary differential equations using similarity transformations and nondimensional variables which were subsequently solved numerically by using the Rung-Kutta fourth-order method with shooting technique. Moreover, the effect of the resulting physical parameters on the distributions of velocity, temperature, and concentration of nanoparticles has been studied by using graphical forms with an interest in providing physical meanings to each parameter. Finally, special diagrams were made to explain the study of the effect of some physical parameters on the skin friction coefficient and the local Nusselt number; these results led to reinforcement in the values of the skin friction coefficient for the increased values of the magnetic field and the Darcy number while the effect on the local Nusselt number by thermal radiation as well as the heat generation/absorption coefficients became negative.
Highlights
In recent years, the study of non-Newtonian fluids has received the attention of researchers in the field of hydrodynamics around the world due to the enormous scientific developments in their applications
The main objective of the present work is to study the flow of a non-Newtonian Williamson fluid that contains nanoparticles on a stretching sheet through a porous medium under the influences of the magnetic field, nonlinear thermal radiation, and Joule heating in the presence of heat generation/absorption and chemical reaction on the distributions of velocity, temperature, and concentration of nanoparticles taking into account studying effects of the Brownian motion coefficient and thermophoresis coefficient
After converting the system of partial differential equations ruling to study the flow of fluid into a system of ordinary differential equations, it has a set of important parameters that we list in the following order M, Da, and λ which are the magnetic field, the Darcy number, and non-Newtonian Williamson parameters, respectively, while R, θw, and S represent the nonlinear thermal radiation, the ratio temperature, and the heat generation/absorption parameters, respectively; Pr is the Prandtl number and Nt is the thermophoresis parameter, while Ec, γ, Le, and Nb are the Eckert number, the chemical reaction, the Lewis number, and Brownian motion parameters, respectively
Summary
The study of non-Newtonian fluids has received the attention of researchers in the field of hydrodynamics around the world due to the enormous scientific developments in their applications. The Williamson fluid is one of the most important non-Newtonian fluids characterized by less viscosity with an increase in the rate of shear stress and very similar in its properties of polymeric solutions, for example. In another meaning, in the Williamson fluid model, the effective viscosity should lessen indefinitely with the rising shear rate, which is nothing but infinite viscosity at stationary and nil viscosity as the shear rate tends to infinity. Hamid et al [5] discussed an investigation of thermal and solutal stratification effects on mixed convection flow and heat transfer of Williamson nanofluid
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