Viscous dissipation analysis of Williamson fluid over a horizontal saturated porous plate at constant wall temperature

Abstract

Williamson fluid flux and heat transfer characteristics over horizontal plate via a saturated porous medium at constant surface temperature are examined in this study to determine the impact of forced viscous dissipation. The flow is modeled using a Darcy-Forchheimer-Brinkman model based on conservation laws and associated governing equations. Using appropriate dimensionless variables, the modeled governed equations are transformed into dimensionless differential forms. The higher constrained coupled non-linear differential equations have been reduced to the first order differential equations to find a reliable numerical solution. The Runge-Kutta method and the built-in Matlab function bvp4c are applied in the shooting method to produce a numerical solution. The impact of λx, ϵ, ζx, βx on the velocity profile, temperature, shear stress, and skin friction are illustrated graphically. It is found that the increasing of the Darcy number leads to enhance both velocity and shear stress while the temperature and the Nusselt number are diminished inside the boundary layer. Additionally, it is found that the raising Williamson's parameter causes the temperature to rise while decreasing velocity, shear stress, heat transfer coefficient, and Nusselt number inside the boundary layer. The method applied in the current work is supported by earlier research.

Keywords

• Constant surface temperature
• Darcy–Forchheimer
• Saturated porous media
• Shooting technique
• Viscous dissipation
• Williamson fluid