Impacts of activation energy and binary chemical reaction on MHD flow of Williamson nanofluid in Darcy–Forchheimer porous medium: a case of expanding sheet of variable thickness

Abstract

An expanding sheet problem is more relevant when the thickness of the sheet is variable and it bears frequent applications in polymer press, paper production, metallic plate cooling, etc. On the other hand, activation energy is an important phenomenon of chemical reaction in flow dynamics of Newtonian and non-Newtonian fluids. The activation energy and chemical reaction have vital applications in food preparing, the mechanism of water and oil emulsions, chemical engineering, and more. So in this project, the impacts of activation energy and binary chemical reaction on MHD two-dimensional boundary layer flow of Williamson nanofluid on an expanding surface of variable thickness embedded in Darcy–Forchheimer porous medium are investigated. Using suitable transformations, the governing equations are transformed into a set of non-linear ordinary differential equations (ODEs). Later, numerical solutions have been achieved by well-known MATLAB inbuilt function ‘bvp4c’. Several vital results are explored for variations of involved physical parameters and those are presented in graphical and tabular modes. The achieved results suggest that when wall thickness parameter increases, there is a contrast in behaviors of velocity, temperature and nanoparticle concentration if there is a condition that the shape parameter is greater than or less than unity. For the former case, the above flow properties reduce with wall thickness parameter, whereas, for the latter case, those are showing significant growth. The Brownian motion of nanoparticles causes an increase in temperature and a reduction in nanoparticle concentration, whereas due to thermophoretic force, both temperature and nanoparticle concentration rise. Due to the presence of activation energy in chemical reaction, the nanoparticle concentration enhances, while, temperature decreases(increases) near(away from) the sheet. With increasing reaction rate parameters, nanoparticle concentration diminishes, but temperature increases near the sheet. The surface drag force decreases with Williamson fluid parameter, while it increases with the magnetic parameter, inverse Darcy number, and Forchheimer parameter. On the other hand, the surface heat flux and surface mass flux are decreasing functions of Williamson fluid parameter, magnetic parameter, inverse Darcy number, and Forchheimer parameter. It also reveals that surface heat flux reduces with increasing reaction rate parameters, whereas surface mass flux increases. Finally, for the growth of activation energy parameter, initially surface heat flux rises and surface mass flux declines, but for its larger values, the quantities turn out to be constants. Also, the surface heat and mass fluxes are decreasing functions of thermophoresis parameter.