Unsteady Magnetohydrodynamic Free Convection Flow Research Articles

The impact silver nanoparticles on MHD free convection flow of Jeffrey fluid over an oscillating vertical plate embedded in a porous medium

This article studies the influence of copper nanoparticles (CuNPs) and silver nanoparticles (AgNPs) on the unsteady magnetohydrodynamic (MHD) free convection flow of Jeffrey fluid over an oscillating vertical plate embedded in a saturated porous medium. Nanoparticles (CuNPs and AgNPs) are suspended in Kerosene oil which is chosen as a conventional base fluid. Appropriate dimensionless variables are employed to the governing equations and the exact solutions are obtained for velocity and temperature fields using the Laplace transform technique. The results for various controlling parameters for both CuNPs and AgNPs are shown graphically and discussed in details. Expressions for skin friction and Nusselt number are also evaluated and presented in tabular forms. It has been observed that, an increase of volume fraction leads to the enhancement of velocity and temperature distributions. On the other hand, Hartmann number tends to resist the fluid flow due to the Lorentz force. A comparative study of the present results with the results from the earlier works provides an excellent agreement.

Hall effects on an unsteady magneto-convection and radiative heat transfer past a porous plate

Hall effects on an unsteady magnetohydrodynamic (MHD) free convective flow of a viscous incompressible electrically conducting optically thick radiating fluid past a vertical porous plate in the presence of a uniform transverse magnetic field are examined. The governing equations are solved numerically using the fourth-order Runge–Kutta–Fehlberg method with the shooting technique. Effects of the pertinent parameters on the flow field, temperature distribution, shear stresses and rate of heat transfer at the plate are presented in graphs and tables followed by a quantitative discussion. The results reveal that the flow field and the temperature distribution are greatly influenced by thermal radiation parameter. Hall currents moderate the flow field significantly. Suction (or injection) has a profound effect on the boundary layer thickness in which the suction reduces the thermal boundary layer thickness whereas injection thickens it.

Natural Convection Boundary Layer Flow of a Double Diffusive and Rotating Fluid Past a Vertical Porous Plate

An investigation is carried out for a fully developed unsteady magnetohydrodynamic free convection flow of a viscous incompressible and electrically conducting Newtonian fluid through porous medium bounded by an infinite vertical porous plate, in a rotating system in the presence of heat source and thermal diffusion. The porous plane and the porous medium are assumed to rotate in a solid body rotation. Whereas the vertical surface is subject to variable suction perpendicular to it and the temperature at this surface varies with respect to time about a nonzero constant mean. Analytical solutions for the distributions of velocity, temperature and concentration fields are obtained by using a regular perturbation technique. The effects of pertinent parameters on these distributions are studied numerically with the help of graphs. With the aid of the above flow quantities the expressions for skin friction, Nusselt number and Sherwood number are derived. Variations in these distributions are presented in tables. It is noticed that the velocity boundary layer condenses with the increasing values of Schmidt number. Flow reversal is prevented for low speed of rotation, high value of chemical reacting species and high value of magnetic parameter.

Influence of Thermal Radiation on Unsteady MHD Free Convection Flow of Jeffrey Fluid over a Vertical Plate with Ramped Wall Temperature

Influence of thermal radiation on unsteady magnetohydrodynamic (MHD) free convection flow of Jeffrey fluid over a vertical plate with ramped wall temperature is studied. The Laplace transform technique is used to obtain the analytical solutions. Expressions for skin friction and Nusselt number are also obtained. Results of velocity and temperature distributions are shown graphically for embedded parameters such as Jeffrey fluid parameterλ, Prandtl numberPr, Grashof numberGr, Hartmann numberHa, radiation parameterRd, and dimensionless timeτ. It is observed that the amplitude of velocity and temperature profile for isothermal are always higher than ramped wall temperature.

Magnetohydrodynamic Free Convective Flow of Nanofluids Past an Oscillating Porous Flat Plate in A Rotating System with Thermal Radiation and Hall Effects

ABSTRACTThe unsteady magnetohydrodynamic free convective flow due to an oscillating porous flat plate in a rotating frame of reference are studied when thermal radiation and Hall currents are taken into consideration. The entire system rotates with a uniform angular velocity about an axis normal to the plate. A uniform magnetic field is applied along the normal to the plate directed into the fluid region. Copper, alumina and titania water nanofluids are considered. The governing equations are solved analytically by employing the small perturbation approximation. The numerical results for fluid velocity and temperature are presented graphically for the pertinent parameters and discussed in details.

Unsteady MHD Free Convection Flow of a Kuvshinski Fluid Past a Vertical Porous Plate in the Presence of Chemical Reaction and Heat Source/Sink

Unsteady magneto hydrodynamic (MHD) free convection flow of a viscous, incompressible and electrically conducting, well known non-Newtonian fluid named as Kuvshinski fluid past an infinite vertical porous plate in the presence of homogeneous chemical reaction, radiation absorption and heat source/sink is studied analytically. The plate is assumed to move with a constant velocity in the direction of fluid flow. A magnetic field of uniform strength is applied perpendicular to the plate, which absorbs the fluid with a suction that varies with time. The dimensionless governing equations are solved analytically using two terms harmonic and non-harmonic functions. The expressions for the fields of velocity, temperature and concentration are obtained. With the aid of these the expressions for skin friction, Nusselt number and Sherwood number are derived. The effects of various physical parameters on the flow quantities are studied through graphs and tables. For the validity, we have checked our results with previously published work and found in good agreement. Velocity decreases for an increase in visco elastic parameter α2, heat absorption coefficient φ, the chemical reaction parameter γ , the magnetic field parameter M, the Prandtl number Pr, the Schmidt number Sc, and increases for increase in Grashof number Gm, the radiation absorption parameter Q1

Unsteady magnetohydrodynamic free convection flow of a second grade fluid in a porous medium with ramped wall temperature.

Magnetic field influence on unsteady free convection flow of a second grade fluid near an infinite vertical flat plate with ramped wall temperature embedded in a porous medium is studied. It has been observed that magnitude of velocity as well as skin friction in case of ramped temperature is quite less than the isothermal temperature. Some special cases namely: (i) second grade fluid in the absence of magnetic field and porous medium and (ii) Newtonian fluid in the presence of magnetic field and porous medium, performing the same motion are obtained. Finally, the influence of various parameters is graphically shown.

MHD double diffusion flow by free convection past an infinite inclined plate with ramped wall temperature in a porous medium

The combined effects of heat and mass transfer on unsteady magnetohydrodynamic (MHD) free convection flow in a porous medium past an infinite inclined plate with ramped wall temperature have been investigated. The closed form analytical solutions have been obtained for the velocity, temperature and concentration fields by using Laplace transforms method. The analytical expressions for non-dimensional skin-friction, Nusselt number and Sherwood number have been computed. The effects of the embedded flow parameters such as inclination angle, radiation parameter, magnetic field parameter, and Grashof number on flow fields are shown graphically. It is found that increasing the inclination angle and radiation parameters, the fluid velocity along an inclined plate will be decreased.

Unsteady boundary layer MHD free convection flow in a porous medium with constant mass diffusion and Newtonian heating

In this article, the unsteady boundary layer magnetohydrodynamic (MHD) free convection flow past an oscillating vertical plate embedded in a porous medium with constant mass diffusion and Newtonian heating condition is analysed. By considering the effects of thermal radiation in the energy equation, the problem is first modeled and then written in dimensionless form, which is then solved by using the Laplace transform technique. The expressions for velocity, temperature and concentration fields are obtained and plotted graphically to see the influence of embedded parameters. The results for skin friction, Nusselt number and Sherwood number are also shown in tables. Further a table is included for the comparison of our results with those present in the literature.

Unsteady Magnetohydrodynamic Free Convection Flow of a Radiative Fluid Past an Infinite Vertical Plate with Constant Heat and Mass Flux

Theoretical analysis of unsteady magnetohydrodynamic free convection flow of a viscous incompressible radiative fluid past an infinite vertical plate with constant heat and mass flux is presented. The dimensionless governing linear partial differential equations have been solved using the Laplace transform technique. The exact solutions for the velocity, temperature and concentration fields are derived. The effects of radiation, magnetic field and buoyancy ratio parameters on the velocity and temperature fields are discussed through graphs. It is found that the velocity increases with increasing radiation parameter whereas it decreases with increasing magnetic field parameter for buoyancy assisted flows.

Unsteady Magnetohydrodynamic Free Convective Flow Past a Vertical Porous Plate

A numerical solution to the problem of unsteady magnetohydrodynamic free convective flow past a vertical porous plate has been analyzed. The dimensionless governing equations are solved using finite element method. The velocity, temperature and concentration fields are studied for different physical parameters.

Finite element solution of heat and mass transfer flow with Hall current, heat source, and viscous dissipation

The aim of the paper is to investigate the effect of heat and mass transfer on the unsteady magnetohydrodynamic free convective flow with Hall current, heat source, and viscous dissipation. The problem is governed by the system of coupled non-linear partial differential equations whose exact solution is difficult to obtain. Therefore, the problem is solved by using the Galerkin finite element method. The effects of the various parameters like Hall current, Eckert number, heat source parameter, Prandtl number, and Schmidt number on the velocity components, the temperature, and the concentration are also examined through graphs.

The Effects of Thermal Radiation and Heat Source on an Unsteady MHD Free Convection Flow Past an Infinite Vertical Plate with Thermal Diffusion and Diffusion Thermo

In this paper, we investigate the effects of thermal radiation and heat source on an unsteady magnetohydrodynamic free convection flow past an infinite vertical plate in a porous medium in presence of thermal diffusion and diffusion thermo. The dimensionless governing equations are solved numerically using finite element method. The numerical results for some special cases were compared with Shanker et al. and were found to be in good agreement. Graphical results for velocity, temperature and concentration profiles based on the numerical solutions are presented and discussed within the boundary layer. And also the skin-friction at the plate due to velocity field, rate of heat transfer due to temperature field and mass transfer due to concentration field are obtained in non-dimensional form. The effects of the different physical flow parameters on these respective flow fields are discussed through graphs and results are physically interpreted.

RADIATION AND CHEMICAL REACTION EFFECTS ON UNSTEADY MHD FREE CONVECTION FLOW OF A DISSIPATIVE FLUID PAST AN INFINITE VERTICAL PLATE WITH NEWTONIAN HEATING

This paper focuses on the study of the effects of radiation and chemical reaction on unsteady magnetohydrodynamic free convection flow of a dissipative fluid past an impulsively started infinite vertical plate in the presence of Newtonian heating and uniform mass diffusion. The dimensionless governing equations are unsteady, coupled, and nonlinear partial differential equations. An analytical method fails to give a closed-form solution. Hence, the implicit finite difference scheme of the Crank-Nicolson method is employed. The influence of the magnetic field parameter, radiation parameter, and chemical reaction parameter on the velocity field and skin friction for both air (Pr = 0.71) and water (Pr = 7) are extensively discussed with the help of graphs.

Unsteady Magnetohydrodynamic Free Convection Flow Past a Semi-Infinite Permeable Moving Plate Through Porous Medium With Chemical Reaction and Radiation Absorption

The effect of the chemical reaction and radiation absorption on the unsteady free convective flow of an incompressible viscous fluid through porous medium past a semi-infinite vertical permeable moving plate is studied. The system is stressed by a uniform transverse magnetic field. The system equations are derived for the flow over a vertical plate and the resulting nonlinear coupled differential equations are solved numerically by finite difference technique. Also, the case of the flow over a horizontal plate was studied analytically by using the perturbation technique. A comparison between the case of vertical and horizontal flow was illustrated graphically to access the accuracy of our numerical calculations, and the results show an excellent agreement. The effects of various parameters on the velocity, temperature and concentration profiles are presented graphically and the physical aspects of the problem are highlighted and discussed.

Effects of Thermal Diffusion and Radiation on Unsteady MHD Free Convection Flow Past an Infinite Heated Vertical Plate in a Porous Medium

We have explored the influence of thermal diffusion and radiation on unsteady magnetohydrodynamic free convection flow past an infinite heated vertical plate in a porous medium. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed nonlinear differential equations are solved numerically with finite element methods. Numerical calculations are carried out for different values of dimensionless parameters. The results are presented graphically for velocity, temperature, and concentration profiles and show that the flow field and other quantities of physical interest are significantly influenced by these parameters.

Unsteady magnetohydrodynamic free convection flow past an accelerated vertical plate with constant heat flux and heat generation or absorption

AbstractThe unsteady free convection flow of an electrically conducting fluid past an accelerated infinite vertical plate with constant heat flux is investigated under the influence of uniform transverse magnetic field fixed relative to the fluid or to the plate in the presence of heat generation or absorption. Two important cases, (i) exponentially accelerated plate (EAP) and (ii) uniformly accelerated plate (UAP), have been considered. The governing partial differential equations have been solved analytically using the Laplace transform technique and closed form solutions are obtained for the velocity and temperature fields without any restriction. The effects of system parameters such as the Prandtl number, heat generation or absorption, Grashof number, and magnetic field parameter on the flow fields are analyzed through graphs and tables. Further, the solution of the problem involves inverse Laplace transforms of some new exponential forms and these formulas are provided.

Magnetohydrodynamic Transient Free-Convective Flow in a Vertical Annulus With Thermal Boundary Condition of the Second Kind

A theoretical analysis of an unsteady magnetohydrodynamic free-convective flow of a viscous incompressible and electrically conducting fluid between two concentric vertical cylinders is carried out considering thermal boundary condition of the second kind at the outer surface of the inner cylinder. The governing equations of motion and energy are transformed into ordinary differential equations using the Laplace transform technique. The ordinary differential equations are then solved analytically and the Riemann-sum approximation method is used to invert the Laplace domain into time domain. A parametric study depicting the effect of the various parameters on the temperature, velocity, and their related quantities is conducted. On the outer surface of the inner cylinder, the skin friction is seen to decrease with the Hartmann number and increase with time. An opposite behavior is seen on the inner surface of the outer cylinder.

Effects of Thermophoresis on Unsteady MHD Free Convective Heat and Mass Transfer along an Inclined Porous Plate with Heat Generation in Presence of Magnetic Field

An analysis of Thermophoresis effect on unsteady magneto-hydrodynamic free convection flow over an inclined porous plate with time dependent suction in presence of magnetic field with heat generation has been considered by employing Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. Resulting non-dimensional velocity, temperature and concentration profiles are then presented graphically for different values of the parameters entering into the problem. Finally, the effects of the pertinent parameters on the skin-friction coefficient, the rate of heat transfer (Nusselt number) and wall deposition flux (Stanton number), which are of physical interest, are exhibited in tabular form.

An Exact Solution of Unsteady MHD Free Convection Flow of a Radiating Gas Past an Infinite Inclined Isothermal Plate

The effect of thermal radiation on unsteady magnetohydrodynamic free convection flow of an optically thin gray gas past an infinite inclined plate with constant temperature has been investigated. The governing coupled partial differential equations are solved analytically using the Laplace transform technique. The dimensionless velocity and temperature profiles are shown in graphs and the numerical values of the non-dimensional skin-friction and Nusselt number are presented in tables. The influence of the system parameters such asPrandtl number, inclination angle, magnetic field parameter, Grashof number, radiation parameter and time on flow fields have been discussed in detail. The results indicate that the inclination angle, magnetic field parameter and radiation parameter effects were to decrease the fluid velocity along an inclined plate.