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Journal ArticleDOI

A non-linear study of fluctuating fluid flow on MHD mixed convection through a vertical permeable plate

01 Nov 2017-Vol. 263, Iss: 6, pp 062029
TL;DR: In this article, an analytical solution for an unsteady (independent of time), MHD mixed convection, two-dimensional (x and y), laminar, viscous flow of an incompressible fluid through a vertical permeable plate in a porous medium was developed with these assumptions: the suction velocity (which is normal to the plate) and the free stream velocity both fluctuate with respect to time with a fixed mean.
Abstract: In this paper, an analytical solution for an unsteady (independent of time), MHD mixed convection, two-dimensional (x and y), laminar, viscous flow of an incompressible fluid through a vertical permeable plate in a porous medium was developed with these assumptions:(i) the suction velocity (which is normal to the plate)and the free stream velocity both fluctuate with respect to time with a fixed mean; (ii) the wall temperature is constant;(iii) difference between the temperature of the plate and the free stream is moderately large due to the free convection currents. Based on the physical configuration of the model, the governing equations are derived and are non-dimensionalize using dimensionless parameters. The resultant nonlinear partial differential equations are solved using double regular perturbation technique analytically. The results are computed numerically to understand the behaviour of the fluid (i.e., effects of MHD, viscosity, body force etc.) for various non-dimensional parameters involving like Grashof number Gr, Prandtl number Pr, Hartmann number M, Eckert number E, the Viscous ratio λ and so on for velocity and temperature. These results are found to be in good agreement with known results available in the literature in the absence of few physical parameters. The numerical values of the above said flow is discussed through graphs on velocity and temperature.
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Journal ArticleDOI
TL;DR: In this article , the effects of fluctuating free stream and suction velocities on unsteady mixed convective flow over a vertical permeable plate in the occurrence of an unvarying porous medium with a thin environment, time-dependent suction, and viscous dissipation were analyzed.
Abstract: In this article, we analytically investigated the effects of fluctuating free stream and suction velocities on unsteady mixed convective flow over a vertical permeable plate in the occurrence of an unvarying porous medium with a thin environment, time-dependent suction, and viscous dissipation. The governing equations of the physical phenomena give rise to a bunch of extremely non-linear coupled PDE's involving various non-dimensional parameters. An analytical solution has been obtained through the plots for distinct chief physical parameters like Grashof number, the amplitude of the fluctuating suction velocity parameter, amplitude of fluctuating free stream velocity parameter, Prandtl number, permeability parameter, solutal Grashof number, and Eckert number, which are involved in the solution. Also, a comparison has been made with published results in the absence of some non-dimensional parameters for a particular case and found in good agreement. The study results that the fluctuating free stream velocity increases the velocity, temperature increases, and a reverse tendency is observed in the Eckert number.
References
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Book
01 Oct 1991
TL;DR: In this article, the authors identify the principles of transport in porous media and compare the available predicted results, based on theoretical treatments of various transport mechanisms, with the existing experimental results, and the theoretical treatment is based on the volume-averaging of the momentum and energy equations with the closure conditions necessary for obtaining solutions.
Abstract: Although the empirical treatment of fluid flow and heat transfer in porous media is over a century old, only in the last three decades has the transport in these heterogeneous systems been addressed in detail. So far, single-phase flows in porous media have been treated or at least formulated satisfactorily, while the subject of two-phase flow and the related heat-transfer in porous media is still in its infancy. This book identifies the principles of transport in porous media and compares the available predicted results, based on theoretical treatments of various transport mechanisms, with the existing experimental results. The theoretical treatment is based on the volume-averaging of the momentum and energy equations with the closure conditions necessary for obtaining solutions. While emphasizing a basic understanding of heat transfer in porous media, this book does not ignore the need for predictive tools; whenever a rigorous theoretical treatment of a phenomena is not available, semi-empirical and empirical treatments are given.

2,551 citations

Journal ArticleDOI
TL;DR: In this article, the effects of a solid boundary and the inertial forces on flow and heat transfer in porous media were analyzed, and a new concept of the momentum boundary layer central to the numerical routine was presented.

1,427 citations

Journal ArticleDOI
TL;DR: In this article, an analysis is made for steady free convection about a vertical flat plate embedded in a saturated porous medium at high Rayleigh numbers, where boundary layer thickness, local and overall surface heat flux, and local and average heat transfer coefficients are derived for an isothermal dike intruded in an aquifer.
Abstract: An analysis is made for steady free convection about a vertical flat plate embedded in a saturated porous medium at high Rayleigh numbers. Within the framework of boundary layer approximations, similarity solutions are obtained for a class of problems where wall temperature varies as xλ, i.e., a power function of distance from the origin where wall temperature begins to deviate from that of the surrounding fluids. Analytical expressions are obtained for boundary layer thickness, local and overall surface heat flux, and local and average heat transfer coefficients. Application to convective heat transfer about an isothermal dike intruded in an aquifer is discussed.

811 citations

Book
23 Feb 2001
TL;DR: Free and mixed convection boundary-layer flow on non-Newtonian fluids in porous media has been studied in this article for convective flow in buoyant plumes and jets.
Abstract: Chapter Headings. I Convective flows: viscous fluids. Free convection boundary-layer over a vertical flat plate. Mixed convection boundary-layer flow along a vertical flat plate. Free and mixed convection boundary-layer flow past inclined and horizontal plates. Double-diffusive convection. Convective flow in buoyant plumes and jets. Conjugate heat transfer over vertical and horizontal flat plates. Free and mixed convection from cylinders. Free and mixed convection boundary-layer flow over moving surfaces. Unsteady free and mixed convection. II Convective flows: porous media. Free and mixed convection boundary-layer flow on non-Newtonian fluids. Free and mixed convection boundary-layer flow over vertical surfaces in porous media. Free and mixed convection past horizontal and inclined surfaces in porous media. Conjugate free and mixed convection over vertical surfaces in porous media. Free and mixed convection from cylinders and spheres in porous media. Unsteady free and mixed convection in porous media. Non-Darcy free and mixed convection boundary-layer flow in porous media.

664 citations

Journal ArticleDOI
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