Abstract
The purpose of the present investigation deals with the unsteady free convective flow of a viscous incompressible gray, absorbing-emitting but non-scattering, optically-thick fluid occupying a semi-infinite porous regime adjacent to an infinite moving hot vertical plate with constant velocity. We employ a Darcian viscous flow model for the porous medium. The momentum and thermal boundary layer equations are non-dimensionalized using appropriate transformations and then solved subject to physically realistic boundary conditions using the Laplace transform technique. Thermal radiation effects are simulated via a radiation-conduction parameter, Kr, based on the Rosseland diffusion approximation. The influence of Grashof (free convection) number, radiation-conduction parameter (Kr), inverse permeability parameter (Kp) and dimensionless time (t) are studied graphically. We observe that increasing thermal radiation parameter causes a noticeable increase in the flow velocity, u. Temperature, θ, is significantly increased within the boundary layer with a rise in Kr since the latter represents the relative contribution of thermal radiation heat transfer to thermal conduction heat transfer. Increased radiation therefore augments heat transfer, heats the fluid and increases the thickness of the momentum and thermal boundary layers. Velocity is found to decrease with an increase in Kp (inverse permeability parameter) as are shear stress function ( ∂u/∂y | y=0) magnitudes owing to greater resistance of the porous medium for lower permeabilities, which decelerate the flow. An increase in Kr however boosts the shear stress function magnitudes i.e. serves to accelerate the flow. Temperature gradient, ∂θ/∂y | y=0 is also positively affected by an increase in thermal radiation (Kr) and with time. The present study has applications in geological convection, forest fire propagation, glass heat treatment processes at high temperature, metallurgical processing etc.
Highlights
Radiative-convective heat transfer flows find numerous applications in glass manufacturing, furnace technology, high temperature aerodynamics, fire dynamics and spacecraft re-entry [1]
Further studies in the context of boundary layer aerodynamics were communicated by Tabaczynski and Kennedy [9], Taitel and Hartnett [10], Cogley et al [11] who considered non-grey gases, England and Emery [12] who analyzed absorption effects of the gas, Adunson and Gebhart [13], Bankston et al [14] who considered both absorption and emission properties of the fluid and Dombrowski [15] who reported on optically-thick flat plate boundary layers
To gain a perspective of the physics of the flow regime, we have numerically evaluated the effects of Grashof number (Gr), radiation-conduction parameter (Kr), dimensionless time (t) and inverse permeability parameter (Kp), on the velocity, u, temperature, θ, shear stress function
Summary
Radiative-convective heat transfer flows find numerous applications in glass manufacturing, furnace technology, high temperature aerodynamics, fire dynamics and spacecraft re-entry [1]. More recently Chamkha et al [27] studied Rosseland radiation-conduction number effects on boundary layer wedge convection of a viscoelastic fluid in non-Darcian porous material. Very recently Zueco et al [31] have presented two-dimensional numerical solutions for non-Darcian radiation-convection heat and mass transfer from an impulsively-started vertical surface in porous media. In the present study we consider analytically the transient convectiveradiative heat transfer in an isotropic, homogenous porous regime adjacent to a hot vertical plate using the Laplace transform method. Such a study has not appeared in the literature and constitutes an important addition to the area of porous media convection studies
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