scholarly journals Theoretical Analysis of Radiative Effects on Transient Free Convection Heat Transfer past a Hot Vertical Surface in Porous Media

2008 ◽  
Vol 13 (4) ◽  
pp. 419-432 ◽  
Author(s):  
S. K. Ghosh ◽  
O. Anwar Beg
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Shear Stress ◽  
Free Convection ◽  
Thermal Radiation ◽  
Stress Function ◽  
Dimensionless Time ◽  
Permeability Parameter ◽  
Shear Stress Function

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.

The Effect of Longitudinal Oscillations on Free Convection From Vertical Surfaces

1965 ◽  
Vol 32 (1) ◽  
pp. 183-191 ◽  
Author(s):  
Siavash Eshghy ◽  
V. S. Arpaci ◽  
J. A. Clark
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Shear Stress ◽  
Steady State ◽  
Free Convection ◽  
Classical Problem ◽  
Vertical Cylinder ◽  
Convection Flow ◽  
Fluid Temperature ◽  
Average Coefficient

The free-convection flow along a vertical plate oscillating in its own plane is given analytical treatment. The basic equations of boundary-layer flow and heat transfer are linearized and the first three approximations are considered. The first approximation, being the case of steady-state free convection, is the classical problem of Schmidt and Beckman extended by Ostrach. The second approximation is the frequency response of the fluid temperature and velocity for which limiting solutions are obtained in two regions; namely, the regions of small and large ω* = ωδ2/ν where ω is the circular frequency, δ the steady-state velocity boundary-layer thickness, and ν the fluid kinematic viscosity. The approximate range of validity of the asymptotic solution is estimated in terms of parameter ω0* which is a function only of Prandtl number. Part of the third approximation is time independent and gives rise to a net change in the steady values of the wall heat flux and shear stress. It is found that within the domain of laminar flow this net change is a decrease for the rate of heat transfer and an increase for the shear stress both evaluated for large values of ω0*. Heat-transfer measurements are made for a vertical cylinder in air. It is found that in the laminar regime the average coefficient of heat transfer experiences a slight decrease relative to its measured steady state value. For higher values of oscillatory velocity amplitude the average coefficient of heat transfer undergoes an increase over its measured steady-state value. This reversal in the behavior of average coefficient of heat transfer appears to be due to flow transition which is confirmed by smoke studies along a vertical cylinder.

scholarly journals Thermal radiation effect on unsteady mixed convection boundary layer flow and heat transfer of nanofluid over permeable stretching surface through porous medium in the presence of heat generation

2021 ◽  
Vol 104 (3) ◽  
pp. 003685042110422
Author(s):  
Ahmed M. Sedki ◽  
S. M. Abo-Dahab ◽  
J. Bouslimi ◽  
K. H. Mahmoud
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Heat Generation ◽  
Convection Boundary Layer ◽  
Physical Parameters ◽  
Unsteady Mixed Convection ◽  
Special Cases

Here, we study the effect of mixed convection and thermal radiation on unsteady boundary layer of heat transfer and nanofluid flow over permeable moving surface through a porous medium. The effect of heat generation is also discussed. The equations governing the system are the continuity equation, momentum equation and the heat transfer equation. These governing equations transformed into a system of nondimensional equations contain many physical parameters that describe the study. The transformed equations are solved numerically using an implicit finite difference technique with Newton's linearization method. The thermo-physical parameters describe the study are the mixed convection parameter α, [Formula: see text], the Radiation parameter Rd, [Formula: see text] , porous medium parameter k, [Formula: see text], the nanoparticles volume [Formula: see text],[Formula: see text], the suction or injection parameter fw, [Formula: see text], the unsteadiness parameter At, [Formula: see text] and the heat source parameter λ  =  0.5 .The influence of the thermo-physical parameters is obtained analytically and displayed graphically. Comparisons of some special cases of the present study are performed with previously published studies and a good agreement is obtained.

Thermal Radiation Effects on the Laminar Free Convection Boundary Layer of an Absorbing Gas

1969 ◽  
Vol 91 (1) ◽  
pp. 37-44 ◽  
Author(s):  
W. G. England ◽  
A. F. Emery
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Free Convection ◽  
Thermal Radiation ◽  
Radiation Effects ◽  
Constant Heat Flux ◽  
Convection Boundary Layer ◽  
Flux Boundary Condition ◽  
Convection Boundary ◽  
Free Convection Boundary Layer

The effects of thermal radiation upon the laminar free convection boundary layer of a vertical flat plate were studied for absorbing and nonabsorbing gases. Experimental velocity and temperature profiles were obtained for a constant heat flux boundary condition in air and CO2 and these are compared to analytical calculations for optically thin gases and absorbing gray gases. A correlation is presented by which plate surface temperatures as a function of plate emissivity for optically thin gases may be predicted for use in determining the convective heat transfer through standard non-radiative film heat transfer correlations.

scholarly journals Effects of thermal radiation and heat transfer over an unsteady stretching surface embedded in a porous medium in the presence of heat source or sink

2011 ◽  
Vol 15 (2) ◽  
pp. 477-485 ◽  
Author(s):  
Elsayed Elbashbeshy ◽  
T.G. Emam
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Heat Source ◽  
Thermal Radiation ◽  
Skin Friction Coefficient ◽  
Integration Scheme ◽  
Stretching Surface ◽  
Boundary Layer Equations ◽  
Unsteady Stretching Surface ◽  
Permeability Parameter

The effects of thermal radiation and heat transfer over an unsteady stretching surface embedded in a porous medium in the presence of heat source or sink are studied. The governing time dependent boundary layer equations are transformed to ordinary differential equations containing radiation parameter, permeability parameter, heat source or sink parameter, Prandtl number, and unsteadiness parameter. These equations are solved numerically by applying Nachtsheim-Swinger shooting iteration technique together with Rung-Kutta fourth order integration scheme. The velocity profiles, temperature profiles, the skin friction coefficient, and the rate of heat transfer are computed and discussed in details for various values of the different parameters. Comparison of the obtained numerical results is made with previously published results.

scholarly journals Unsteady MHD Flow of Cassonnano Fluid with Chemical Reaction, Thermal Radiation and Heat Generation/Absorption

MATEMATIKA ◽  
2019 ◽  
Vol 35 (4) ◽  
pp. 33-52 ◽  
Author(s):  
Nur Azlina Mat Noor ◽  
Sharidan Shafie ◽  
Mohd Ariff Admon
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Heat Generation ◽  
Transfer Rate ◽  
Nanoparticles Concentration

The hydromagnetic mixed convection flow of Cassonnano fluid under the influence of chemical reaction,thermal radiation and heat generation or absorption is investigated. The flow is induced due to unsteady nonlinearly stretching sheet saturated in a porous medium. The governing nonlinear coupled partial differential equations are converted into the system of coupled ordinary differential equations using similarity transformations and then solved numerically via Keller box method. The effects of pertinent parameters on velocity, temperature and nanoparticles concentration as well as wall shear stress, heat and mass transfer rate are analyzed and displayed graphically. The results for skin friction coefficient and local Nusselt number are compared with previously published work and found to be in good agreement. Findings demonstrate that increase in Casson parameter enhanced the friction factor and heat transfer rate. It is noticed that the heat transfer rate is declined with increment in Brownian motion and thermophoresis parameters. The nanoparticles concentration is seen to be higherin generative chemical reaction and opposite effect is observed in destructive chemical reaction. Increase in unsteadiness parameter decreased the fluid velocity, temperature and nanoparticles concentration. The magnitude of wall shear stress is also reduced with increase in unsteadiness and porous medium parameters.

scholarly journals Darcy-Brinkman free convection about a wedge and a cone subjected to a mixed thermal boundary condition

1992 ◽  
Vol 15 (4) ◽  
pp. 789-794 ◽  
Author(s):  
G. Ramanaiah ◽  
V. Kumaran
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Porous Medium ◽  
Heat Transfer Coefficient ◽  
Free Convection ◽  
Transformation Group ◽  
Darcy Number ◽  
Thermal Boundary Condition ◽  
High Porosity

The Darcy-Brinkman free convection near a wedge and a cone in a porous medium with high porosity has been considered. The surfaces are subjected to a mixed thermal boundary condition characterized by a parameterm;m=0,1,∞correspond to the cases of prescribed temperature, prescribed heat flux and prescribed heat transfer coefficient respectively. It is shown that the solutions for differentmare dependent and a transformation group has been found, through which one can get solution for anymprovided solution for a particular value ofmis known. The effects of Darcy number on skin friction and rate of heat transfer are analyzed.

Unsteady Natural Convection Heat Transfer Past a Vertical Flat Plate Embedded in a Porous Medium Saturated With Fractional Oldroyd-B Fluid

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Jinhu Zhao ◽  
Liancun Zheng ◽  
Xinxin Zhang ◽  
Fawang Liu ◽  
Xuehui Chen
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Natural Convection ◽  
Prandtl Number ◽  
Fractional Derivative ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Elastic Effect

This paper investigates natural convection heat transfer of generalized Oldroyd-B fluid in a porous medium with modified fractional Darcy's law. Nonlinear coupled boundary layer governing equations are formulated with time–space fractional derivatives in the momentum equation. Numerical solutions are obtained by the newly developed finite difference method combined with L1-algorithm. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Results indicate that, different from the classical result that Prandtl number only affects the heat transfer, it has remarkable influence on both the velocity and temperature boundary layers, the average Nusselt number rises dramatically in low Prandtl number, but increases slowly with the augment of Prandtl number. The maximum value of velocity profile and the thickness of momentum boundary layer increases with the augment of porosity and Darcy number. Moreover, the relaxation fractional derivative parameter accelerates the convection flow and weakens the elastic effect significantly, while the retardation fractional derivative parameter slows down the motion and strengthens the elastic effect.

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