Numerical Simulation of Williamson Combined Natural and Forced Convective Fluid Flow between Parallel Vertical Walls with Slip Effects and Radiative Heat Transfer in a Porous Medium

Abstract

Numerical study of the slip effects and radiative heat transfer on a steady state fully developed Williamson flow of an incompressible Newtonian fluid; between parallel vertical walls of a microchannel with isothermal walls in a porous medium is performed. The slip effects are considered at both boundary conditions. Radiative highly absorbing medium is modeled by the Rosseland approximation. The non-dimensional governing Navier-Stokes and energy coupled partial differential equations formed a boundary problem are solved numerically using the fourth order Runge-Kutta algorithm by means of a shooting method. Numerical outcomes for the skin friction coefficient, the rate of heat transfer represented by the local Nusselt number were presented even as the velocity and temperature profiles illustrated graphically and analyzed. The effects of the temperature number, Grashof number, thermal radiation parameter, Reynolds number, velocity slip length, Darcy number, and temperature jump, on the flow field and temperature field and their effects on the boundaries are presented and discussed.

Numerical Study of the Magnetic Field Effects on the Heat Transfer and Entropy Generation Aspects of a Power Law Fluid over an Axisymmetric Stretching Plate Structure

“…The non-dimensional first order differential governing Equation (48) is solved numerically by using the Runge-Kutta-Fehlberg method with shooting technique [51] for various finite boundary layer lengths. The grid size of 0.01 is chosen were the maximum change in final value is less than 10 −4 .…”

Fluid flow and heat transfer characteristics of Williamson fluids flowing in saturated porous media

“…Besides, the mathematical study was performed to figure out the slip effects and radiation in a fully developed incompressible Newtonian fluid Williamson flow. 8 Moreover, the Duwairi et al 9 found that the increase in squeezing and extrusion of a viscous fluid in an unstable approach between two parallel plates at fixed temperature caused a decrease in the fluid velocity and enhanced the rates of heat transfer. Additionally, Kausar et al 10 studied the Darcy_Brinkman flow across a stretched sheet in the existence of frictional heating and porous dispersion.…”

Optimal Design of Isothermal Sloshing Vessels by Entropy Generation Minimization Method

“…The ship maneuver-induced motion in the partially-filled tanks by liquid, sloshing poses a thoughtful danger to the controllability and stability of this phenomenon. The entropy generation minimization method is used for the design of fluid flow motion system [1] as well as thermal systems [2][3][4] in recent years. Although the method is applied to the thermodynamic optimization of many finite-size systems and finite-time processes [5], the application in isothermal fluid flow is rare [6].…”