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.
Highlights
Combined natural and forced convection in channels occurs in many applications [1]
Thermal radiative emission from a hot surface to a cold surface plays an important role in many uses, including energy conversion [6], with radiation effects and viscous heating in a channel partially filled by a porous material [7], viscous heating in a porous channel [8], microchannels [9], heat exchangers with vertical hexagonal rod bundle geometries [10], buoyancy-driven vortical flow [11], biofidelity corridors [12], fluid flow control [13,14], in various boundary conditions [15], and pressure dependent viscosity flows [16]
Mixed convection viscoelastic slip flow through a porous medium in a vertical porous channel with thermal radiation flow [17] is found in industrial processes and has acquired substantial importance due to its Entropy 2016, 18, 147; doi:10.3390/e18040147
Summary
Combined natural (free) and forced convection in channels occurs in many applications [1]and geometries such flow between parallel vertical walls [2], including flow reversal [3], inclined parallel plates [4], and vertical channels [5], etc. Thermal radiative emission from a hot surface to a cold surface plays an important role in many uses, including energy conversion [6], with radiation effects and viscous heating in a channel partially filled by a porous material [7], viscous heating in a porous channel [8], microchannels [9], heat exchangers with vertical hexagonal rod bundle geometries [10], buoyancy-driven vortical flow [11], biofidelity corridors [12], fluid flow control [13,14], in various boundary conditions [15], and pressure dependent viscosity flows [16]. Bocquet and Barrat [30] explained the probability of temperature slip simultaneously with velocity discontinuity at boundary conditions. The slip relations should be applied at the fluid solid boundaries in microchannels in other textbooks [31]
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