A numerical study of boundary layer flow of Williamson nanofluid in the presence of viscous dissipation, bioconvection, and activation energy

Abstract

Due to dynamical applications of nanoparticles in various engineering and biomedical applications, our work focuses on examining and exploring the numerical study of bioconvected unsteady Williamson fluid flow at a heated permeable stretched sheet in a porous medium, along with the existence of particular Cattaneo–Christov heat and mass flux, viscous dissipation, activation energy, Brownian and thermophoresis motion. A mathematical model has been developed by considering the effects of the aforementioned terminologies on the flow field which are expected to be similar to the physical behavior and already published work. By using suitable similarity transformations, the system of the flow field is transformed from partial differential equations to ordinary differential equations. The developed differential system is then solved numerically through bvp4c in the computational software MATLAB. The tabular and graphical analysis have been presented against velocity, temperature, concentration, and density profiles that imply the impact of physical parameters. The skin friction coefficient, rate of heat, and mass transfer are also examined. The results coincide very well to previous published work for limiting cases that authenticate the validity of the current work. It was observed that upon increasing magnetic field (M) and porosity (Kp) parameters, the velocity profile decelerates but the opposite behavior was seen for motile density, concentration, and temperature profiles. The temperature and concentration of Williamson nanofluid reduced by enhancing the significant thermal and mass stratification. The concentration profile declines for rising values of Schmidt number (Sc), the chemical reaction rate (σ), and temperature difference $(\delta )$ parameters but accelerates for higher values of Activation energy (Ea). Also, by increasing Peclet number (Pe), bioconvection Lewis number (Lb), and microorganism concentration difference parameter Ω motile density profile decreases.

Highlights

• Analyze the impacts of bioconvection and activation energy on Williamson nanofluid.

• We numerically imitate the outcomes of viscous dissipation, bioconvection, and activation energy at a heated permeable stretched sheet.

• We examine the effect of A, M, We, K_p, and S on $-\frac{1}{2}{C}_f{(Re)}^{\frac{1}{2}}.$

• We examine the effect of M, K_p, and We on $S{h}_x{(R{e}_x)}^{-\frac{1}{2}}.$

• We examine the effect of the local density number with M, K_p, We, A, and injection and suction parameters.

Keywords:

• MHD
• nanofluid
• porous medium
• skin friction
• viscous dissipation
• Williamson nanofluid