Hydromagnetic free-convection flow past an impulsively started vertical plate in a rotating fluid

The three dimensional flow of a viscous incompressible and electrically conducting fluid past an infinite vertical plate started impulsively in its own plane is discussed in a rotating system. The magnetic Reynolds number is taken small so that the induced magnetic field can be neglected. An exact solution is obtained for the axial and the transverse components of the velocity and the skin-friction by defining a complex velocity. It is observed that both velocity components of water (primary and secondary) decrease with rotation parameter in both cases, cooling and heating of the plate.     

Heat transfer in fluctuating flow past an infinite plate with suction and constant heat flux

An analysis of unsteady heat transfer in a two-dimensional flow past an infinite porous plate has been carried out under the following conditions: (1) constant or variable suction; (2) free-stream oscillating in time about a non-zero constant mean; and (3) constant heat flux at the plate. Approximate solutions to the temperature field have been derived. the transient temperature, the amplitude and phase of the Nusselt number are shown on graphs.     

Radiation and mass transfer effects on flow of an incompressible viscous fluid past a moving vertical cylinder

The interaction of free convection with thermal radiation of a viscous incompressible unsteady flow past a moving vertical cylinder with heat and mass transfer is analyzed. The fluid is a gray, absorbing-emitting but non-scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing equations are solved using an implicit finite-difference scheme of Crank-Nicolson type. Numerical results for the transient velocity, the temperature, the concentration, the local as well as average skin-friction, the rate of heat and mass transfer are shown graphically. It is found that at small values of the Prandtl number and radiation parameter N, the velocity and temperature of the fluid increases sharply near the cylinder as the time t increase, which is totally absent in the absence of radiation effects.     

Effects of free convection and mass transfer on the flow past an impulsively moving infinite vertical circular cylinder

The effects of free convection and mass transfer are taken into account for the Stokes' problem of the flow near an impulsively moving infinite vertical circular cylinder. Expressions of the velocity, temperature, concentration and skin friction of the fluid in closed form are obtained by the Laplace transform technique. The results based on various values of the parameters Gr (Grashof number), Gm (modified Grashof number), Sc (Schmidt number) and Pr (Prandtl number) are given in graphical form. It will be seen that there is a rise in the velocity due to the presence of a foreign mass. But higher Sc yields the lower velocity and skin friction. As the radius of the circular cylinder approaches to infinite, the results presented in this paper agree with those of V.M. Soundalgekar's and C.K. Chen's etc. for the flow past an impulsively moving infinite vertical plate.     

Soret and heat source effects on the unsteady radiative MHD free convection flow from an impulsively started infinite vertical plate

The heat and mass transfer characteristics of the unsteady electrically conducting fluid flow past a suddenly started vertical infinite flat plate are taken into account in this paper. The radiation and heat absorption/generation effects for two distinct types of thermal boundary conditions are accounted for. Derivation of exact analytical solutions are aimed under different physical properties. The velocity, concentration and temperature profiles, skin friction coefficient, Sherwood number and Nusselt number are easily examined and discussed via the closed forms obtained. In particular, the Sherwood and Nusselt numbers are found evolve into their steady state case in the large time limit. The results obtained here may be further used to verify the validity of obtained numerical solutions for more complicated transient free convection fluid flow problems.     

Heat and mass transfer effects on fluid past an exponentially accelerated vertical plate due to time-fractional MHD-free convection

This article focuses on the study of heat and mass transfer (HMT) fluid flow over an exponentially accelerated vertical plate, which is subjected to an applied magnetic field and viscous dissipation. The research has applications in various manufacturing processes such as wire/fiber drawing, hot rolling, continuous casting, and hot extrusion, where heat transfer to the ambient medium and the hot moving material are of utmost importance. The findings could also be relevant to aerospace engineering applications. The study investigates the time-fractional natural convection phenomenon and utilizes conservation laws to derive the flow guiding equations, which are then made nondimensional. Finite difference discretization is utilized to solve the dimensionless equations implicitly. Then the flow simulation results such as concentration, temperature, and velocity profiles are discussed based on the variation in parameters such as Prandtl number ($Pr$), thermal/mass Grashof number ($\mathit{Gr}/\mathit{Gc}$), Eckert number ($\mathit{Ec}$), magnetic parameter ($M$), time-fractional order ($\lambda$), and Schmidt number $\left(\mathit{Sc}\right)$. Also, the HMT rate is depicted using the Nusselt number and skin friction plots. It is noted that HMT increases when $\mathit{Sc}$ increases and $\lambda$ decreases. The change in time-fractional order affects the velocity profiles adjacent to the wall and is more significant in the case of lower values of the Prandtl number.     

Unsteady free convection flow past an infinite vertical plate with variable suction and mass transfer

The effects of variable suction on the unsteady two-dimensional free convective flow of a viscous incompressible fluid past an infinite vertical plate have been discussed on taking into consideration the presence of a foreign mass. Approximate solutions to transient flow, the amplitude and the phase of the skinfriction and the rate of heat transfer have been derived. During the course of discussion, the effects of Gr, Gc, Pr, Sc, ω and A (the suction parameter) have been discussed.     

Hall effects on the hydromagnetic free convective flow and mass transfer through a porous medium bounded by an infinite vertical porous plate with constant heat flux

Effects of Hall current on free convection and mass transfer flow through a porous medium bounded by a vertical surface when a uniform magnetic field acts in a plane which makes an angle x with the plane transverse to the plate have been analysed. An analytic solution of the problem is obtained and the effects of the Hall parameter and the permeability parameter, as well as the other parameters entering into the problem, are discussed and shown graphically.     

Mass transfer effects on MHD flow and heat transfer past a vertical porous plate through a porous medium under oscillatory suction and heat source

This paper considers the effect of mass transfer on free convective flow and heat transfer of a viscous incompressible electrically conducting fluid past a vertical porous plate through a porous medium with time dependant permeability and oscillatory suction in presence of a transverse magnetic field and heat source. The solutions for velocity field, temperature field and concentration distribution are obtained using perturbation technique. The effects of the flow parameters such as magnetic parameter M, Grashof number for heat and mass transfer G_r,G_c, porosity parameter K_p, Prandtl number P_r, Schmidt number S_c, frequency parameter ω and heat source parameter S on the velocity, temperature and concentration distribution of the flow field and the skin friction, heat flux and the rate of mass transfer are studied analytically and presented with the aid of figures and tables. It is observed that the magnetic parameter and the Schmidt number retard the velocity of the flow field while the Grashof number for heat and mass transfer, the porosity parameter and the heat source parameter have accelerating effect on the velocity of the flow field at all points. Further, the Prandtl number reduces the temperature and the Schmidt number diminishes the concentration distribution of the flow field at all points. The skin friction coefficients τ₀ and τ increase due to increase in G_r,G_c and K_p while decrease due to increase in S_c, M, ω and P_r. Further, the rate of mass transfer S_h increases due to increase in S_c while an increase in ω results a decrease in S_h.     

Radiation effect on the flow and heat transfer over an unsteady stretching sheet

The effect of radiation on the heat and fluid flow over an unsteady stretching surface is analyzed. Using a similarity transformation the governing time dependent boundary layer equations for momentum and thermal energy are reduced to a set of ordinary differential equations. The resulting three-parameter problem is solved numerically for some representative values of the unsteadiness parameter A, the radiation parameter R and Prandtl number Pr. It is shown that the heat transfer rate is increased with increasing R, A and Pr. Also the effect of radiation parameter on the heat transfer rate is found to be more noticeable at larger values of A and Pr.     

Transient free convection in cold water past an infinite vertical porous plate

A finite-difference solution of the transient free convection flow of water near 4°C past an infinite vertical porous plate has been carried out. The most appropriate relation for the density in terms of the temperature, as derived by Gebhart and Mollendorf, is employed. It has been observed that, when the buoyancy force is in the upward direction, the velocity profiles are positive and opposite to those in the case where the buoyancy force is in the downward direction. Also, the skin friction is more when the buoyancy force is in the upward direction than when the buoyancy force is in the downward direction.     

MHD convective rotating flow of viscoelastic fluid past an infinite vertical oscillating porous plate with Hall effects

It is considered the unsteady and incompressible magnetohydrodynamic rotating free convection flow of viscoelastic fluid with simultaneous heat and mass transfer near an infinite vertical oscillating porous plate under the influence of uniform transverse magnetic field and taking Hall current into account. The governing equations of the flow field are then solved by a regular perturbation method for a small elastic parameter. The expressions for the velocity, temperature, and concentration have been derived analytically and also its behavior is computationally discussed with reference to different flow parameters with the help of graphs. The skin friction on the boundary, the heat flux in terms of the Nusselt number, and the rate of mass transfer in terms of the Sherwood number are also obtained and their behavior discussed. The resultant velocity enhances with increasing Hall parameter and rotation parameter. The reversal behavior is observed with increasing viscoelastic parameters. The resultant velocity enhances and experiences retardation in the flow field with increasing radiation parameters, whereas the secondary velocity component increases with increasing rotation parameters. The temperature diminishes as the Prandtl number and/or the frequency of oscillations. The concentration reduces at all points of the flow field with the increase in the Schmidt number.     

Local similarity solution for combined free-forced convective and mass transfer flow past a semi-infinite vertical plate

An analysis is presented of the effects of buoyancy forces in a laminar uniform forced-convective flow with mass transfer along a semi-infinite vertical plate. A family of solutions to the coupled nonlinear equations is numerically obtained. The velocity, temperature and concentration profiles are shown for different values of the dimensionless parameters g_r =Gr/Re_x² and g_c =Gc/Ref_x² (Gr =Grashof number, Gc =modified Grashof number, Re_x =Local Reynolds number). The numerical values of the skin friction and the rate of heat transfer for different values of Gr and Gc are also tabulated. The flow field is greatly influenced by the dimensionless ratio Gr/Re_x², which means that the effects of the free convection currents and mass transfer flow on the flow field, are important.     

Unsteady boundary layer flow of a Casson fluid due to an impulsively started moving flat plate

This paper discusses the unsteady flow and heat transfer of a Casson fluid over a moving flat plate with a parallel free stream. The analytic solutions of the system of nonlinear partial differential equations valid for all times in the whole spatial domain are constructed in the series form by a homotopic approach. The influences of the governing parameters on the velocity, temperature, skin friction coefficient, and local Nusselt number are thoroughly investigated. It is revealed that an increase in the dimensionless time decreases the velocity and enhances the temperature. The surface shear stress and surface heat transfer are enhanced by increasing the Casson fluid parameter (β) and Eckert number (Ec), respectively. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20358     

Effects of slip on sheet-driven flow and heat transfer of a third grade fluid past a stretching sheet

The entrained flow and heat transfer of an electrically conducting non-Newtonian fluid due to a stretching surface subject to partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). The constitutive equation of the non-Newtonian fluid is modeled by that for a third grade fluid. The heat transfer analysis has been carried out for two heating processes, namely, (i) with prescribed surface temperature (PST case) and (ii) prescribed surface heat flux (PHF case). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective second order numerical scheme has been adopted to solve the obtained differential equations. The important finding in this communication is the combined effects of the partial slip, magnetic field and the third grade fluid parameter on the velocity, skin-friction coefficient and the temperature field. It is interesting to find that slip decreases the momentum boundary layer thickness and increases the thermal boundary layer thickness, whereas the third grade fluid parameter has an opposite effect on the thermal and velocity boundary layers.     

Finite element Soret Dufour effects on an unsteady MHD heat and mass transfer flow past an accelerated inclined vertical plate

The present study is focused on the Soret and Dufour effects on magnetohydrodynamics unsteady fluid flow over an accelerated inclined vertical plate with thermal radiation and heat source. Solution of the nondimensional governing differential equations are worked out by the efficient Galerkin finite element method. The influence of several relevant flow parameters on velocity, temperature, and concentration distributions, as well as the numerical results, are studied and graphically displayed. The nondimensional skin friction and the rate of heat and mass transfer parameters are presented in the Tables 1-3 below. Raising the Soret number results in growing concentrations, but the converse is true for the Schmidt number. Skin friction reduces when Soret and Dufour numbers increase. The present simulations apply to the processing of magnetic materials in the chemical and metallurgical industries.     

Transient two-dimensional model of heat and mass transfer in a PEM fuel cell membrane

In the present work, a numerical study of heat and mass transfer within the membrane of a proton exchange membrane fuel cell is presented. The electrolyte membrane is considered an isotropic porous medium and ideal insulator for electrons and reactants. The adopted model in this study is based on the assumption of single-phase and multi-spices flow, supposed two-dimensional and unsteady. For the water transport, the major considered forces are; the convective force, resulting from the pressure gradient, the osmotic force, due to the concentration gradient and the electric force caused by the proton migration from the anode to the cathode. Based on a one-dimensional model, found in the literature, a transient two-dimensional one was proposed. The set of governing equations, written in velocity–pressure formulation, is solved by the implicit finite difference method. An alternating Direct Implicit scheme was used for the calculation. The numerical resolution gives the time- and space-dependent temperature and water concentration. The main focus lies on the influence of different cases of boundary conditions on water concentration and heat transfer variation with the intention of testing the reliability of the proposed computational fluid dynamic (CFD) code.     

Slip flow and temperature jump on the impulsively started plate

The unsteady compressible boundary layer equations over an impulsively started flat plate are firstly solved subjected to velocity slip and temperature jump conditions. Comparisons are carried out with existing solutions. Then the conjugate problem for a slab of finite thickness is dealt, when the fluid dynamic field is coupled with the thermal field in the solid.     

Effect of arc-shaped vertical control plate on heat and mass transfer in uniform flow past an isothermally heated circular cylinder

The current work investigates the effect of an arc-shaped vertical control plate on the heat and mass transfer in uniform flow past an isothermally heated circular cylinder. The control plate is positioned downstream at various distances from the circular cylinder's surface. The governing equations are discretized by the higher order compact (HOC) finite difference scheme, and then this system of discretized equations is solved by using a bi-conjugate gradient stabilized iterative method for Prandtl number $Pr=0.7$, Reynolds number $Re=150$. To investigate the effect of an arc-shaped control plate on heat and mass transfer, we consider a range of nondimensional distances between the circular cylinder and the control plate, $0.5\le d∕R_0\le 8$, where $d$ is the control plate's distance and $R_0$ is the cylinder's radius. The exact timing and location of the bifurcation points are calculated by using topological aspect-based structural bifurcation analysis. Significant effects of various locations of the control plate on periodic wake and heat transfer are observed. It is found that the increasing distance of the control plate from the cylinder delays the occurrence of the structural bifurcation and shifts the bifurcation points upwards in the upper half and downwards in the lower half of the cylinder. Our study shows that the specific location of the control plate can fully suppress the vortex shedding. Time-averaged total Nusselt number can be drastically reduced by increasing the distance between the control plate and the cylinder. With proper positioning, the vertical control plate can lessen the time-averaged drag force by up to $22.5\%$ when compared to a cylinder without a control plate. Overall, this work presents many new phenomena that have not been reported before.