Heat transfer in flow through a porous medium bounded by an infinite vertical plate under the action of a magnetic field

An analysis of steady two-dimensional flow, of an electrically conducting fluid through a porous medium, occupying a semi-infinite region of the space bounded by an infinite, vertical and porous limiting surface under the action of a transverse magnetic field is considered. Approximate solutions have been derived for the velocity and temperature fields and the rate of heat transfer (Nusselt number). The variations of the velocity and Nusselt number are shown on graphs.     

Unsteady flow through a porous medium in the presence of free convection

An analysis of the unsteady flow through a porous medium is considered when the porous medium is bounded by an infinite vertical plate. The free stream velocity and the temperature in the free stream are considered constant and the temperature of the plate varies with the time about a non-zero constant. Expressions for the velocity and the temperature are derived and the influence of the various parameters entering into the problem are discussed.     

Effects of hall current and wall temperature oscillation on free convective and mass transfer flow in a rotating porous medium with constant heat source

The combined effects of Hall current and a constant heat source on the hydromagnetic free convective and mass transfer flow past an infinite vertical porous plate in a rotating porous medium are considered, when the temperature of the plate varies with time about a nonzero constant mean and the temperature of the free stream is constant. The problem is solved analytically and the velocity profiles are shown on graphs. Effects of m (Hall parameter) and α (heat source parameter) on velocity are discussed extensively.     

Flow through a porous medium in the presence of a magnetic field

Unsteady free convective flow of an electrically conducting fluid through a porous medium bounded by an infinite vertical and porous plate is considered. The free stream velocity of the fluid vibrates about a mean constant value and the temperature of the plate is constant. The influences of the permeability parameter and the magnetic parameter on the velocity field are discussed.     

Hall current impacts on unsteady MHD free convective flow past an infinite vertical porous surface

In this paper, the magnetohydrodynamic free convective flow of an incompressible electrically conducting fluid over a vertical plate embedded in a porous medium is considered. A homogeneous transverse magnetic field is applied in the presence of a heat source and chemical reaction in a rotating frame, taking Hall current effects into account. The momentum equations for the fluid flow in a porous medium were determined by Brinkman modeling. At the undisturbed state, both the plate and fluid have an rigid body rotation due to the constant angular velocity, perpendicular to the infinite vertical plane surface. The vertical surface is subject to the homogeneous constant suction and the heat on the surface vary by time about a nonzero constant rate whereas the temperature of free stream is engaged to be constant. The accurate solutions for the velocity, temperature, and concentration distributions were acquired systematically using the perturbation method. The consequences of an assortment of governing flow parameters on the velocity, temperature, and concentration were analyzed through graphical profiles. The computational results for the skin friction, Nusselt number, and Sherwood number in a tabular format were also examined.     

Influence of chemical reaction and thermal radiation on the heat and mass transfer in MHD micropolar flow over a vertical moving porous plate in a porous medium with heat generation

An analysis is presented for the effects of chemical reaction and thermal radiation on hydromagnetic free convection heat and mass transfer for a micropolar fluid via a porous medium bounded by a semi-infinite vertical porous plate in the presence of heat generation. The plate moves with a constant velocity in the longitudinal direction and the free stream velocity follows an exponentially small perturbation law. A uniform magnetic field acts perpendicularly to the porous surface in which absorbs the micropolar fluid with a suction velocity varying with time. Analytical expressions are computed numerically. Numerical calculations are carried out the purpose of the discussion of the results which are shown on graphs and the effects of the various dimensionless parameters entering into the problem on the velocity, angular velocity, temperature, concentration. Also, the results of the skin-friction coefficient, the couple stress coefficient and the rates of the heat and mass transfers at the wall are prepared with various values of fluid properties and the flow conditions are studied.     

Effect of thermal radiation on unsteady mixed convection flow and heat transfer over a porous stretching surface in porous medium

An analysis is performed to investigate the effects of thermal radiation on unsteady boundary layer mixed convection heat transfer problem from a vertical porous stretching surface embedded in porous medium. The fluid is assumed to be viscous and incompressible. Numerical computations are carried out for different values of the parameters involved in this study and the analysis of the results obtained shows that the flow field is influenced appreciably by the unsteadiness parameter, mixed convection parameter, parameter of the porous medium and thermal radiation and suction at wall surface. With increasing values of the unsteadiness parameter, fluid velocity and temperature are found to decrease in both cases of porous and non-porous media. Fluid velocity decreases due to increasing values of the parameter of the porous medium resulting an increase in the temperature field in steady as well as unsteady case.     

Heat and mass transport on MHD flow over semi-infinite moving porous plate with chemical reaction effect

The consequences of chemical reaction, on unsteady magnetohydrodynamic heat and mass transport laminar flows of a viscous, electrically conducting with heat-generating or absorbing fluid enclosed through a semi-infinite absorbent plate has been premeditated. The plate is assumed to be in motion with a constant velocity within the path of fluid flow. A homogeneous magnetic field performs at right angles to the absorbent surface; it is absorbing the fluid with a suction velocity varying with a certain instant of time. The nondimensional governing equations for the present configuration are solved systematically utilizing harmonic and nonharmonic terms. Graphical consequences for the velocity, temperature, and concentration profiles together supported by the investigative solutions are displayed and discussed computationally. The resulting velocity is reducing by an augment in the strength of the magnetic field and Prandtl number, whereas it is enhancing by growing in the permeability of the porous medium. The temperature delivery is reduces by an escalating heat source parameter and occurrence of fluctuation. It is significant to note that the temperature increases notably with growing the radiation absorption parameter. The influences of the chemical reaction and Schmidt number reduced the concentration in the entire fluid medium.     

Mass transfer and free convection through a porous medium by the presence of a rotating fluid

Steady free convection and mass transfer through a porous medium bounded by an infinite vertical porous plate is considered for a fluid rotating with a constant angular velocity when the heat flux at the plate is constant. The influence of the various parameters entering into the problem on the velocity field is discussed.     

Entropy Analysis of a Coupled‐Convection Flow through a Vertical Channel Partially Filled by a Porous Medium with Injection/Suction and Slip Boundary Conditions

Flow fields, thermal fields, and entropy generation have been investigated for fully developed mixed convection flow between two vertical porous plates. The vertical channel is partially filled by a porous medium, and channel walls are subjected to a constant injection velocity at the left wall and constant suction velocity at the right wall. The viscous dissipation effects and velocity slip for the longitudinal component of the velocity at the channel walls are also taken into account. The momentum and energy equations for the mixed convection problem in the vertical channel are solved by means of the perturbation series method, by taking perturbation parameter proportional to the Brinkman number. For the present problem, numerical solution is also obtained and compared with the analytical solution. The effects of various pertinent parameters on the velocity distribution, temperature distribution, entropy generation rate, and Bejan number are investigated and discussed graphically.     

An exact analysis of radiative heat transfer and unsteady MHD convective flow of a second‐grade fluid with ramped wall motion and temperature

The influence of simultaneously applied ramped boundary conditions on unsteady magnetohydrodynamic natural convective motion of a second‐grade fluid is investigated and analyzed in this study. The motion of the fluid is considered near an infinite upright plate that is nested in a porous medium subject to nonlinear thermal radiation effects. The Laplace transformation technique is utilized to acquire the exact solutions of momentum and energy equations. To effectively examine the rate of heat transfer and shear stress, the Nusselt number and skin friction coefficient are also established. The outcomes of mathematical computations are elucidated through tables and figures to highlight some physical aspects of the problem. Some limiting models of the present problem are also deduced and presented. On comparison, it is observed that the fluid exhibits lower temperature and velocity profiles under ramped boundary conditions. It is also found that wall shear stress can be controlled by choosing large values of the magnetic parameter (M) and Prandtl number (Pr). In addition, the heat transfer rate specifies inverse trends for growing values of radiation parameter (Nr) and Prandtl number (Pr), while it increases rapidly under a ramped surface condition and decreases slowly under a constant surface condition.     

Non-Darcy mixed convection from a horizontal plate embedded in a nanofluid saturated porous media

The problem of steady mixed convection boundary-layer flow over an impermeable horizontal flat plate embedded in a porous medium saturated by a nanofluid is numerically studied. The model used for the nanofluid incorporates only the effect of the volume fraction parameter. The surface of the plate is maintained at a constant temperature and a constant nano-particle volume fraction. The resulting governing partial differential equations are transformed into a set of two ordinary (similar) equations, which are solved using the bvp4c function from Matlab. A comparison is made with the available results in the literature, and the present results are in very good agreement with the known results. A representative set of numerical results for the reduced heat transfer from the plate, dimensionless velocity and temperature profiles is graphically and tabularly presented. Also, the salient features of the results are analyzed and discussed.     

Hot Dates

For this article, an analytical study has been conducted on the flow and energy transfer of unsteady compressible oscillating flow through channels filled with porous medium representing stack in thermoacoustic engines/refrigerators. The flow in the porous material is described by the Darcy momentum equation. Analytical expressions for oscillating velocity, temperature in the porous layer, complex Nusselt number, and energy flux density are obtained after simplifying and solving the governing differential equations with reasonable approximations (such as long wave, short stack, small amplitude oscillation, etc.). The result for heat transfer between the porous medium and the channel wall is expressed as a dimensionless Nusselt number. For the limiting case of nonporous medium, the Nusselt number obtained in the present study matches quantitatively with the expression available in the existing literature. The results reveal that the Nusselt number in oscillating flow is significantly enhanced (almost an order of magnitude) by employing sufficiently large thermal conductivity of porous media in a channel. The system of equations developed in the present study is a helpful tool for thermal engineers to design porous stacks for thermoacoustic devices.     

Unsteady flow through a porous medium with the presence mass transfer

Unsteady flow through a very porous medium with the presence mass transfer is considered. The porous medium is bounded by a vertical plate and this plate absorbs the fluid with a constant velocity. Also the free stream velocity of the fluid vibrates about a mean constant value. The influences of the permeability parameter and the modified Grashof number on the velocity field are discussed.     

Transpiration-induced buoyancy effect around a horizontal cylinder embedded in a porous medium

Laminar free convection around a long porous limiting cylindrical surface arising from the buoyancy forces created by temperature as well as by transpiration-induced concentration gradients is investigated. All the fluid properties except for the temperature and concentration-dependent body forces are assumed to be constant in the analysis. The dimensionless non-linear coupled boundary-layer equations embody the following parameters: (1) Pr, the Prandtl number, (2) Sc, the Schmidt number and (3) R, the ratio of the concentration to the thermal buoyancy forces. Numerical results for the local Nusselt number, the local wall shear stress and the local Sherwood number are displayed graphically for the transpiration-induced convective diffusion of hydrogen, water vapour and naphthalene into an air-saturated porous medium. The dimensionless thermal, concentration and momentum boundary layer thicknesses, along with the cumulative tangential mass flow rate are given in tabular form. The analysis covers a wide range of blowing rates.     

Couette flow through a porous medium of a high prandtl number fluid with temperature-dependent viscosity

The velocity and temperature profiles for an impulsively started Couette flow have been derived for a fluid with a high and strongly temperature-dependent viscosity when the flow takes place through a porous medium. The steady as well as the transient state flows are discussed and the influence of the medium permeability is assessed. In the steady state the presence of the porous medium causes higher maximum temperatures only for sufficiently low permeabilities and in all cases significantly lower velocity profiles. The flow development times tend to be higher for the low permeabilities only for high Nahme numbers. For the transient state it is noticeable that, in all cases, the velocity develops much more rapidly than the temperature and that the presence of the porous medium accelerates this tendency. Finally the medium permeability produces skew temperature profiles and higher temperature time gradients at all times.     

Mass transfer and free convection flow through A porous medium

A theoretical analysis of the steady free convective and mass transfer flow is presented, when a viscous and incompressible fluid flows through a porous medium occupying a semi-infinite region of the space bounded by an infinite vertical porous plate. The fluid is subjected to a normal suction velocity, and the heat flux at the plate is constant. The free-stream velocity is assumed constant.     

HYDROMAGNETIC FLOW AND HEAT TRANSFER OF A HEAT-GENERATING FLUID OVER A SURFACE EMBEDDED IN A POROUS MEDIUM

Similarity solutions for the laminar boundary-layer equations describing steady hydromagnetic two-dimensional flow and heat transfer in a stationary electrically-conducting and heat-generating fluid driven by a continuously moving porous surface immersed in a fluid-saturated porous medium are obtained. The flow is exposed to a transverse magnetic field and the surface is moving with a constant velocity. Fluid suction or injection is imposed at the wall. The dimensionless similar equations are solved numerically by an implicit finite-difference method. The numerical flow and heat transfer results are illustrated graphically for various parametric conditions to show special features of the solutions. Favorable comparisons with previously published work confirm the correctness of the numerical results. © 1997 Elsevier Science Ltd     

Heat and mass transfer on MHD convective flow over an infinite vertical porous plate with the heat source and chemical reaction

It is considered that the magnetohydrodynamic free convective flow of an incompressible electrically conducting fluid through a porous medium past a vertical absorbent surface. The homogeneous transverse magnetic field is considered in the existence of heat source and chemical reaction in the rotating frame. The accurate solutions of the velocity, temperature, and concentration are acquired systematically making use of the perturbation method. The consequences of a variety of governing flow parameters on the velocity, temperature, and concentration are analyzed through graphical profiles. Computational outcomes for the skin friction, Nusselt number, and Sherwood number through the tabular format were also examined.     

Combined radiation and convection heat transfer in a porous channel bounded by isothermal parallel plates

Combined radiation and convection heat transfer in a porous medium confined between gray isothermal parallel plates is investigated. The medium is absorbing, emitting and scattering. Cases of boundaries at temperatures higher or lower than the medium are considered. In the porous medium, the boundary effect on the fully developed laminar velocity field as proposed by Kaviany is accounted for. For various values of the extinction coefficient, the scattering albedo, the conduction-radiation parameter and the boundary emissivity, Nusselt number, temperature and heat flux distributions are found for the range of values including the extreme limits of the porous medium shape parameter (PMSP), γ=(W²φ/K)^1/2, where W is the channel width, φ the porosity and K the permeability. For the lower limiting value of the PMSP γ, the effect of the porous medium is negligible and the situation approaches that of Poiseuille flow. For this limiting case, results from the present work are compared with those available in the literature. For medium to high values of the PMSP γ, for the purpose of comparison, some results are presented in tabular form. Radiation is found to have a significant effect on various parameters studied. The discrete transfer method was used for the solution of the radiative part of the energy equation. An iterative finite difference scheme was used to solve the energy equation.