Influence of viscous dissipation and radiation on unsteady MHD free-convection flow past an infinite heated vertical plate in a porous medium with time-dependent suction
01 Jun 2003-International Journal of Heat and Mass Transfer (Pergamon)-Vol. 46, Iss: 13, pp 2305-2311
TL;DR: In this article, the influence of viscous dissipation and radiation on the problem of unsteady magnetohydrodynamic free-convection flow past an infinite vertical heated plate in an optically thin environment with time-dependent suction was investigated.
About: This article is published in International Journal of Heat and Mass Transfer.The article was published on 2003-06-01. It has received 194 citations till now. The article focuses on the topics: Eckert number & Magnetohydrodynamic drive.
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TL;DR: In this article, the effects of Joule-heating, chemical reaction and thermal radiation on unsteady MHD natural convection from a heated vertical porous plate in a micropolar fluid are analyzed.
Abstract: The effects of Joule-heating, chemical reaction and thermal radiation on unsteady MHD natural convection from a heated vertical porous plate in a micropolar fluid are analyzed. The partial differential equations governing the flow and heat and mass transfer have been solved numerically using an implicit finite-difference scheme. The case corresponding to vanishing of the anti-symmetric part of the stress tensor that represents weak concentrations is considered. The numerical results are validated by favorable comparisons with previously published results. A parametric study of the governing parameters, namely the magnetic field parameter, suction/injection parameter, radiation parameter, chemical reaction parameter, vortex viscosity parameter and the Eckert number on the linear velocity, angular velocity, temperature and the concentration profiles as well as the skin friction coefficient, wall couple stress coefficient, Nusselt number and the Sherwood number is conducted. A selected set of numerical results is presented graphically and discussed.
139 citations
Cites background from "Influence of viscous dissipation an..."
...[14] researched the influence of viscous dissipation and radiation on unsteady MHD free-convection flow past an infinite heated vertical plate in a porous medium with time-dependent suction....
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TL;DR: In this paper, the influence of radiation on unsteady hydromagnetic natural convection transient flow near an impulsively moving vertical flat plate with ramped wall temperature in a porous medium is studied.
Abstract: Influence of radiation on unsteady hydromagnetic natural convection transient flow near an impulsively moving vertical flat plate with ramped wall temperature in a porous medium is studied. Exact solution of momentum and energy equations, under Boussinesq approximation, is obtained in closed form by Laplace transform technique. The variations in fluid velocity and temperature are shown graphically whereas numerical values of skin friction and Nusselt number are presented in tabular form.
127 citations
TL;DR: In this paper, the effect of viscous dissipation and thermal radiation on natural convection in a porous medium embedded within a vertical annular cylinder is investigated, where the inner surface of the cylinder was maintained at an isothermal temperature T w and the outer surface is maintained at ambient temperature T ∞.
124 citations
TL;DR: In this article, an analysis is performed to study the momentum, heat and mass transfer characteristics of MHD natural convection flow over a permeable, inclined surface with variable wall temperature and concentration, taking into consideration the effects of ohmic heating and viscous dissipation.
Abstract: An analysis is performed to study the momentum, heat and mass transfer characteristics of MHD natural convection flow over a permeable, inclined surface with variable wall temperature and concentration, taking into consideration the effects of ohmic heating and viscous dissipation. Power-law temperature and concentration variations are assumed at the inclined surface. The resulting governing equations are transformed using suitable transformations and then solved numerically by an implicit finite-difference method. The solution is found to be dependent on several governing parameters, including the magnetic field strength parameter, Eckert number, the buoyancy ratio between species and thermal diffusion, Prandtl number, Schmidt number, wall temperature and concentration exponent, the inclination angle from the vertical direction, and the injection parameter. A parametric study of all the governing parameters is carried out and representative results are illustrated to reveal a typical tendency of the solutions. Representative results are presented for the velocity, temperature, and concentration distributions as well as the local friction coefficient, local Nusselt number, and the local Sherwood number.
120 citations
Cites background from "Influence of viscous dissipation an..."
...Israel-Cookey et al. [ 10 ] investigated the influence of viscous dissipation and radiation on unsteady MHD free-convection flow past a heated vertical plate with time-dependent suction in an optically thin environment....
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TL;DR: In this article, the authors analyzed the heat transfer under the influence of radiation and viscous dissipation in a square cavity filled with saturated porous medium and found that the average Nusselt number at hot and cold wall increases with an increase in radiation parameter.
107 citations
References
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TL;DR: In this article, the phase lag in heat transfer from a heated circular wire in a fluctuating stream, in the range of Reynolds number for which a laminar boundary layer exists, is analyzed mathematically.
Abstract: The laminar boundary layer in two-dimensional flow about a cylindrical body, when the velocity of the oncoming flow relative to the body oscillates in magnitude but not in direction, is analyzed mathematically. It is found that the maxima of skin friction at any point anticipate the maxima of the stream velocity, because the pressure gradient needed to speed up the main stream locally produces a given percentage increase in the slow flow near the wall sooner than it can do so in the main stream itself. For each point on the body surface there is a critical frequency $\omega \_{0}$, such that for frequencies $\omega $ > $\omega \_{0}$ the oscillations are to a close approximation ordinary 'shear waves' unaffected by the mean flow; the phase advance in the skin friction is then 45 degrees. For frequencies $\omega $ < $\omega \_{0}$, on the other hand, the oscillations are closely approximated as the sum of parts proportional to the instantaneous velocity and acceleration of the oncoming stream; the phase advance in the skin friction is then tan$^{-1}$ ($\omega /\omega \_{0}$). The part depending on the instantaneous velocity may be called the quasi-steady part of the oscillations. The coefficient of the acceleration of the oncoming stream in the frictional drag of the body may be called the frictional component of the virtual mass. For a flat plate in a stream of speed V, $\omega \_{0}$ = 0$\cdot $6 V/x at a distance x from the leading edge. If c is the length of the plate, its transient motion parallel to itself is governed solely by quasi-steady forces and this added virtual mass provided that $\omega $c/V < 0$\cdot $6. The frictional component of the virtual mass of a flat plate or any thin obstacle is found to be approximately 0$\cdot $5 times the mass of the fluid in the boundary layer's 'displacement area'; it is suggested that the coefficient may need to be increased to about 0$\cdot $8 for turbulent layers. When the body surface is hot, the maxima in heat transfer from it tend to lag behind those of the stream velocity, as a result of thermal inertia, but this is counteracted to some extent by the effect of convection by the phase-advanced velocities near the wall. For layers with a favourable gradient in the mean flow, one finds that the tendency to lag predominates. For the Blasius layer, however, the two effects appear to cancel out fairly closely; and for layers with adverse pressure gradient in the main stream there seems to be phase advance at the lower frequencies. At frequencies well above $\omega \_{0}$ there is always a phase lag of 90 degrees, but the amplitude of heat-transfer fluctuations is then much reduced, even though that of the skin friction fluctuations is increased. Special attention is paid to the phase lag in the heat transfer from a heated circular wire in a fluctuating stream, in the range of Reynolds number for which a laminar boundary layer exists. Curves for the amplitude and phase of the heat-transfer fluctuations as a function of frequency are given in figure 4, from calculations for the layer of nearly uniform thickness, which covers the front quadrant of the wire, and across which most of the fluctuating part of the heat transfer is believed to occur. For frequencies small compared with $\omega _{0}$ = 20V/d (where d is the diameter), the departure of the heat-transfer fluctuations from their quasisteady form consists essentially of a time lag of the order of 0$\cdot $2d/V.
482 citations
346 citations
TL;DR: In this paper, the effects of material parameters on the velocity and temperature fields across the boundary layer are investigated, and the effect of increasing values of suction velocity parameter results in a slight increasing surface skin friction for lower values of plate moving velocity.
210 citations
TL;DR: In this article, free convection heat transfer due to the simultaneous action of buoyancy, radiation and transverse magnetic field was investigated for a semi-infinite vertical plate, and solutions were derived by expanding the stream function and the temperature into a series in terms of the parameter ζ = x 1/2 L 1/1/2, where L is the length of the plate Velocity and temperature functions are shown on graphs and the numerical values of functions affecting the shear stress and the rate of heat transfer are entered in a table.
Abstract: Free convection heat transfer due to the simultaneous action of buoyancy, radiation and transverse magnetic field is investigated for a semi‐infinite vertical plate Solutions are derived by expanding the stream function and the temperature into a series in terms of the parameter ζ = x1/2 L–1/2, where L is the length of the plate Velocity and temperature functions are shown on graphs and the numerical values of functions affecting the shear stress and the rate of heat transfer are entered in a table The effects of the magnetic field parameter λ and the radiation parameter F on these functions are discussed
186 citations
TL;DR: In this paper, an exact solution of the Navier-Stokes equations for incompressible flow is derived under the conditions: (i) the flow is two-dimensional and is bounded by an infinite, plane, porous wall; (ii) flow is independent of the distance parallel to the wall, (iii) the component of velocity parallel to a large distance from it fluctuates in time about a constant mean; (iv) the components of velocity normal to a wall is constant.
Abstract: An exact solution of the Navier-Stokes equations for incompressible flow is derived under the conditions: (i) the flow is two-dimensional and is bounded by an infinite, plane, porous wall; (ii) the flow is independent of the distance parallel to the wall; (iii) the component of velocity parallel to the wall at a large distance from it fluctuates in time about a constant mean; (iv) the component of velocity normal to the wall is constant. It is found that the skin-friction fluctuations illustrate Lighthill’s (1954) theory of the behaviour of boundary layers subject to fluctuating pressure gradients. The amplitude of the skin-friction fluctuations rises with frequency, while the phase lead of the skin-friction over the main-stream-velocity fluctuation rises from zero at zero frequency to 7r/4 at very high frequencies. The velocity profile in the boundary layer fluctuates, and under certain transient conditions resembles that of a separated boundary layer, that is, a boundary layer with reverse flow close to the wall. With viscous dissipation of kinetic energy taken into account, the corresponding exact solution of the energy equation for an incompressible fluid with constant physical properties is derived under a condition of zero heat transfer between the fluid and the wall—the so-called ‘thermometer’ or ‘kinetic temperature’ problem. Whereas the velocity field consists of a mean flow and a first-harmonic fluctuation, the temperature field contains additionally a second-harmonic fluctuation. It is found that the mean temperature of the wall rises with frequency, and is ultimately proportional to the square root of the frequency. The first-harmonic fluctuation of the wall temperature lags behind the main-stream-velocity fluctuation by an amount which rises from zero at zero frequency to 1/4n at high frequencies, while the phase lag of the second-harmonic rises from zero at zero frequency but drops again to zero at high frequencies. The amplitude of the first-harmonic fluctuation tends to zero at high frequencies, whereas the amplitude of the second-harmonic fluctuation tends to a non-zero limit. Thus the residual temperature fluctuation of the wall at high frequencies has a frequency which is twice that of the fluctuating stream.
132 citations