Magnetohydrodynamic Natural Convection Flow Research Articles

Radiation and heat generation effects on viscous Joule heating MHD-conjugate heat transfer for a vertical flat plate

Conjugate heat transfer formed by the coupling effect of conduction inside and free convection flow along the flat plate is analyzed. The Joule heating effect because of considered magnetohydrodynamics (MHD) along with viscous dissipation, heat generation, and radiation phenomena are included in the investigation. The converted dimensionless partial differential equations representing the aforementioned flow characteristics are transformed into nonlinear equations with the help of a stream function with similarity variable. Finally, a numerical solution is carried out using the implicit finite difference method to analyze the flow behaviors in terms of velocity, temperature, skin friction coefficient, heat transfer rate, and surface temperature. A complete parametric analysis is done on the numerical results to show the effects of the radiation parameter, magnetic parameter, Eckert number, heat generation parameter, conjugate conduction parameter, and Prandtl number. It is found that thermal radiation, viscous Joule heating, and internal heat generation in the presence of axial conduction effects have a significant effect on MHD natural convection flow and thermal fields.

Lattice Boltzmann simulation of natural convection heat transfer in an open enclosure filled with Cu–water nanofluid in a presence of magnetic field

In this paper magneto hydrodynamic (MHD) natural convection flow of Cu–water nanofluid in an open enclosure is investigated numerically using lattice Boltzmann method (LBM) scheme. The effective thermal conductivity and viscosity of nanofluid are calculated by the Maxwell–Garnetts (MG) and Brinkman models, respectively. In addition, the MDF model was used for simulating the effect of uniform magnetic field. The influence of pertinent parameters such as Hartmann number, nanoparticle volume fraction, Rayleigh number and the inclination of magnetic field on the flow and heat transfer characteristics have been examined. The results indicate that the absolute values of stream function decline significantly by increasing Hartmann numbers while these values rise by increasing Rayleigh numbers. Moreover, the results show that the solid volume fraction has a significant influence on stream function and heat transfer, depending on the value of Hartmann and Rayleigh numbers.

Effects of Viscous Dissipation and Heat Generation on Magneto Hydrodynamics Natural Convection Flow along a Vertical Wavy Surface

In this paper we consider the combined effects of viscous dissipation and heat generation on MHD natural convection flow along a vertical wavy surface are studied. The governing Navier-Stokes equations with associated boundary conditions are transformed into non-dimensional boundary layer equations using appropriate variables. Implicit finite difference method based on Keller-box scheme is used to solve these governing equations. The numerical results in terms of the skin friction coefficient, the rate of heat transfer in terms of local Nusselt number, the streamlines as well as the isotherms are discussed and shown graphically for different values of viscous dissipation parameter N, heat generation parameter Q and magnetic parameter M.

General Solutions for Magnetohydrodynamic Natural Convection Flow with Radiative Heat Transfer and Slip Condition over a Moving Plate

General solutions for the magnetohydrodynamic (MHD) natural convection flow of an incompressible viscous fluid over a moving plate are established when thermal radiation, porous effects, and slip condition are taken into consideration. These solutions, obtained in closed-form by Laplace transform technique, depend on the slip coefficient and the three essential parameters Gr, Preff, and Keff. They satisfy all imposed initial and boundary conditions and can generate a large class of exact solutions corresponding to different fluid motions with technical relevance. For illustration, two special cases are considered and some interesting results from the literature are recovered as limiting cases. The influence of pertinent parameters on the fluid motion is graphically underlined.

Natural Convection Flow on a Vertical Cylinder with Sinusoidal Temperature Oscillation Under The Effect of Magneto Hydrodynamic

The present work investigates the effect of magneto hydrodynamic (MHD) laminar natural convection flow on a vertical cylinder subjected to sinusoidal temperature oscillation. The governing equations which used are continuity, momentum and energy equations. These equations are transformed to dimensionless equations using vortices-stream function method and the resulting nonlinear system of partial differential equations are then solved numerically using finite difference approximation. A computer program was built to calculate the rate of heat transfer in terms of average Nussle number, velocity distribution as well as temperature distribution for a selection of magneto hydrodynamic parameter range , dimensionless amplitude and dimensionless time τ΄ (0.2 – 0.8). Numerical solution have been considered for a fluid Prenatal 542 number fixed at (Pr=0.7), Rayleigh number . Generally, the results show that Nu increase as Ra, M and a increase and decrease with τ΄. The effect of Ra and M on the rate of heat transfer is concluded by a correlation. The results are found to be in good agreement compared with the results of [Adams, 1954] for the case of no MHD.

MHD NATURAL CONVECTION FLOW ALONG A VERTICAL WAVY SURFACE IN PRESENCE OF HEAT GENERATION/ABSORPTION WITH VISCOSITY DEPENDENT ON TEMPERATURE

The present numerical simulation is analyzed the Magnetohydrodynamic natural convection flow andheat transfer along a uniformly heated vertical wavy surface in presence of heat generation/absorption withtemperature dependent variable viscosity. Using the appropriate transformations the governing boundary layerequations are reduced to non-dimensional forms. The resulting nonlinear system of partial differentialequations are mapped into the domain of a vertical flat plate and then solved numerically applying implicitfinite difference method together with Keller-box scheme. The solutions are expressed in terms of the skinfriction coefficient, the rate of heat transfer, the streamlines as well as the isotherms over the whole boundarylayer. The implications of heat generation/absorption parameter (Q) and viscosity parameter (?) on the flowstructure and heat transfer characteristics are investigated in detail while, Prandtl number (Pr), magneticparameter (M) and the amplitude-to-length ratio of the wavy surface (?) are considered fixed. Comparison withpreviously published work is performed and is found to be in good agreement.DOI: http://dx.doi.org/10.3329/jme.v42i1.15944

Hall current effects on magnetohydrodynamic natural convection flow with strong cross magnetic field

A boundary layer analysis has been presented to study the effect of Hall current on the MHD natural convection flow of a viscous incompressible fluid along a semi-infinite uniformly heated vertical plate in the presence of a strong cross magnetic field. The governing equations are expressed in terms of local non-similar boundary layer equations. Solutions are obtained for small and large values of local Hartmann parameter, ξ. For small ξ solutions are obtained through power series method and for large ξ analytical solutions are obtained via matched asymptotic expansion method. Numerical solutions are also obtained by implicit finite difference method together with Thompson's algorithm, over the entire range of ξ. The boundary layer structure is investigated in terms of shear stress, τw, rate of heat transfer, qw, and rate of mass transfer, mw, for low Prandtl number (i.e. Pr << 1). Comprehensive interpretation of energy distribution is also given in terms of heatlines.

Unsteady MHD Flow of a Visco-Elastic Fluid Along Vertical Porous Surface with Chemical Reaction

An unsteady magneto hydrodynamic natural convection flow of a visco-elastic (Walters’ fluid (Model B′)) incompressible electrically conducting fluid along an infinite hot vertical porous surface with fluctuating free stream as well as suction velocity in the presence of chemical reaction has been studied. The solutions of momentum, energy, and species concentration equations under Boussinesq approximation are obtained analytically by employing successive perturbation technique. The expressions for the skin friction, Nusselt number and Sherwood number are also derived. The variations in the fluid velocity, temperature and concentration are shown graphically whereas numerical values of skin-friction, Nusselt number and Sherwood number are presented in a tabular form for various values of pertinent flow parameters.

Radiation Effects on MHD Free Convection Flow along Vertical Flat Plate in Presence of Joule Heating and Heat Generation

Abstract In this paper, the effect of radiation on magnetohydrodynamic (MHD) free convection flow along a vertical flat plate in presence of Joule heating and heat generation have been investigated. The governing equations associated with the conduction based boundary conditions are transformed into dimensionless form employing the appropriate transformations and then solved numerically using the implicit finite difference method with Keller box scheme. The numerical solutions are obtained in terms of velocity profiles, temperature distributions, skin friction coefficient and heat transfer rate and then presented graphically and discussed. A complete parametric analysis is done on these numerical results to show the effects of the magnetic parameter, radiation parameter, Joule heating parameter and heat generation parameter. It is found that radiation, Joule heating and heat generation play significant role on MHD natural convection flow during heat transfer. To illustrate the accuracy of the results, the present results for the local skin friction and surface temperature distribution excluding the effects of magnetic field parameter, radiation parameter, Joule heating parameter and heat generation parameter are compared with the results of Merkin and Pop designed for the fixed value of Prandtl number and an excellent agreement were found.

Conjugate Effect of Radiation and Thermal Conductivity Variation on MHD Free Convection Flow for a Vertical Plate

A numerical investigation is performed to study the effect of thermal radiation on magnetohydrodynamic (MHD) free convection flow along a vertical flat plate in presence of variable thermal conductivity in this paper. The governing equations of the flow and the boundary conditions are transformed into dimensionless form using appropriate similarity transformations and then solved employing the implicit finite difference method with Keller-box scheme. Results for the details of the velocity profiles, temperature distributions as well as the skin friction, the rate of heat transfer and surface temperature distributions are shown graphically. Results reveal that the thermal radiation is more significant in MHD natural convection flow during thermal conductivity effect is considered. To illustrate the accuracy of the present results, the results for the local skin fraction and surface temperature distribution excluding the extension effects are compared with results of Merkin and Pop designed for the fixed value of Prandtl number and a good agreement were found.

The Study of Heat Generation and Viscous Dissipation on Mhd Heat And Mass Diffusion Flow Past A Surface

The present work is devoted to the numerical study of magneto hydrodynamic (MHD) natural convection flow of heat and mass transfer past a plate taking into account viscous dissipation and internal heat generation. The governing equations and the associated boundary conditions for this analysis are made non dimensional forms using a set of dimensionless variables. Thus, the non dimensional governing equations are solved numerically using finite difference method Crank-Nicolson's scheme. Numerical outcomes are found for different values of the magnetic parameter, Modified Grashof number, Prandtl number, Eckert number, heat generation parameter and Schmidt number for the velocity and the temperature within the boundary layer as well as the skin friction coefficients and the rate of heat and mass transfer along the surface. Results are presented graphically with detailed discussion.

MHD natural convection flow from an isothermal horizontal circular cylinder under consideration of temperature dependent viscosity

PurposeThe purpose of this paper is to discuss, with numerical simulations, magnetohydrodynamic (MHD) natural convection laminar flow from an isothermal horizontal circular cylinder immersed in a fluid with viscosity proportional to a linear function of temperature.Design/methodology/approachThe governing boundary layer equations are transformed into a non‐dimensional form and the resulting nonlinear system of partial differential equations are reduced to convenient form, which are solved numerically by two very efficient methods: implicit finite difference method together with Keller box scheme; and direct numerical scheme.FindingsNumerical results are presented by velocity and temperature distributions of the fluid as well as heat transfer characteristics, namely the shearing stress and the local heat transfer rate in terms of the local skin‐friction coefficient and the local Nusselt number for a wide range of MHD parameter, viscosity‐variation parameter and viscous dissipation parameter.Originality/valueMHD flow in this geometry with temperature dependent viscosity is absent in the literature. IN this paper, the results obtained from the numerical simulations have been verified by two methodologies.

Joule heating effect on magnetohydrodynamic natural convection flow along a vertical wavy surface

In this paper, the effect of Joule heating on magnetohydrodynamic natural convection flow of viscous incompressible fluid along a uniformly heated vertical wavy surface has been investigated. The governing boundary layer equations with associated boundary conditions for this phenomenon are converted to nondimensional form using a suitable transformation. The equations are mapped into the domain of a vertical flat plate and then solved numerically employing the implicit finite difference method, known as the Keller-box scheme. Effects of pertinent parameters, such as the Joule heating parameter (J), Prandtl number (Pr), magnetic parameter (M) and the amplitude of the wavy surface ? on the surface shear stress in terms of the skin friction coefficient (Cfx), the rate of heat transfer in terms of local Nusselt number (Nux), the streamlines and the isotherms are discussed. A comparison with previously published work is performed and the results show excellent agreement. DOI: http://dx.doi.org/10.3329/jname.v9i1.5954 Journal of Naval Architecture and Marine Engineering 9(2012) 11-24

Lie symmetry group transformation for MHD natural convection flow of nanofluid over linearly porous stretching sheet in presence of thermal stratification

The magnetohydrodynamics (MHD) convection flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the presence of thermal stratification are examined. The partial differential equations governing the problem under consideration are transformed by a special form of the Lie symmetry group transformations, i.e., a one-parameter group of transformations into a system of ordinary differential equations which are numerically solved using the Runge-Kutta-Gill-based shooting method. It is concluded that the flow field, temperature, and nanoparticle volume fraction profiles are significantly influenced by the thermal stratification and the magnetic field.

Radiation effects on transient magnetohydrodynamic natural convection flow with heat generation

In the present investigation, we have considered the radiation effects on a transient two-dimensional natural convection laminar boundary-layer flow of viscous incompressible electrically conducting and optically dense fluid along a vertical flat surface with heat generation. Using a method of transformed coordinates, the boundary-layer equations are transformed into a new form. The transformed equations can then be solved straight forwardly by any numerical methods designed for regular and stationary geometries. In this paper, an implicit finite difference scheme is used. The governing equations have been reduced in the form that are valid for small and large time regimes, by using stream-function formulation. The results obtained for the above mentioned three time regimes are compared and found in excellent agreement. Moreover, the solutions are also obtained in terms of transient local shear stress, transient local rate of heat transfer, transient velocity and temperature distribution for a wide range of parameters Plank constant Rd, surface temperature variation parameter θw, Hartman number M and heat generation parameter λ for the liquid metals having Prandtl number Pr=0.005, 0.05 and 0.1.

The Effect of Temperature Dependent Viscosity on MHD Natural Convection Flow from an Isothermal Sphere

Laminar magnetohydrodynamic (MHD) natural convection flow from an isothermal sphere immersed in a fluid with viscosity proportional to linear function of temperature has been studied. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations are reduced to convenient form which are solved numerically by two very efficient methods, namely, (i) Implicit finite difference method together with Keller box scheme and (ii) Direct numerical scheme. Numerical results are presented by velocity and temperature distribution, streamlines and isotherms of the fluid as well as heat transfer characteristics, namely the local skin-friction coefficients and the local heat transfer rate for a wide range of magnetohydrodynamic paramagnet and viscosity-variation parameter.

Numerical investigation of Dufour and Soret effects on unsteady MHD natural convection flow past vertical plate embedded in non-Darcy porous medium

The Dufour and Soret effects on the unsteady two-dimensional magnetohydrodynamics (MHD) double-diffusive free convective flow of an electrically conducting fluid past a vertical plate embedded in a non-Darcy porous medium are investigated numerically. The governing non-linear dimensionless equations are solved by an implicit finite difference scheme of the Crank-Nicolson type with a tridiagonal matrix manipulation. The effects of various parameters entering into the problem on the unsteady dimensionless velocity, temperature, and concentration profiles are studied in detail. Furthermore, the time variation of the skin friction coefficient, the Nusselt number, and the Sherwood number is presented and analyzed. The results show that the unsteady velocity, temperature, and concentration profiles are substantially influenced by the Dufour and Soret effects. When the Dufour number increases or the Soret number decreases, both the skin friction and the Sherwood number decrease, while the Nusselt number increases. It is found that, when the magnetic parameter increases, the velocity and the temperature decrease in the boundary layer.

Heat Generation Effects on MHD Natural Convection Flow along a Vertical Wavy Surface with Variable Thermal Conductivity

The heat generation effects on magnetohydrodynamic(MHD) natural convection flow along a vertical wavy surface with variable thermal conductivity have been investigated. The governing boundary layer equations are first transformed into a non-dimensional form using suitable set of dimensionless variables. The resulting nonlinear system of partial differential equations are mapped into the domain of a vertical flat plate and then solved numerically employing the implicit finite difference method, known as Keller-box scheme. The numerical results of the surface shear stress in terms of skin friction coefficient and the rate of heat transfer in terms of local Nusselt number, the stream lines as well as the isotherms are shown graphically for a selection of parameters set consisting of thermal conductivity variation parameter, heat generation parameter Q, magnetic parameter M and Prandtl number Pr. Comparison of numerical results of present work with other published data has been shown in table.

Homotopy Peturbation Method for Heat andMass Transfer in Magnetohydrodynamic Flow

In this study, an approximate analytical solution of the magnetohydrodynamic natural convection flow and heat generation fluid driven by a continuously moving permeable surface immersed in a fluid-saturated porous medium is obtained using the homotopy perturbation method. The homotopy perturbation method produces analytical expressions for the solution of nonlinear differential equations. The obtained analytic solution is in the form of an infinite power series. In this work, the analytical solution is obtained by a special version of the homotopy perturbation method called the single-parameter homotopy perturbation method. In this method, only two terms of the homotopy perturbation method solution are used. The results reveal that the proposed method is very effective and simple, and it can be applied to other nonlinear problems. Also, it is shown that this method coincides with the perturbation method for the studied problem.

Effect of a Partition on Hydro-Magnetic Convection in an Enclosure

We deal with the effect of an adiabatic partition and magnetic field on magneto-hydrodynamic natural convection flow and heat transfer in a partitioned enclosure. The horizontal walls of the enclosure are adiabatic and the vertical walls are isothermal. The adiabatic partition is attached to either the bottom adiabatic wall or hot isothermal wall of the enclosure. The governing equations are discretized by the finite-volume method and are solved by iteration. We discuss transient and steady-state cases for different combinations of parameters in the study. The results are obtained for different values of the Hartmann, Grashof and Prandtl numbers and different positions of the partition, and presented graphically. The heat transfer and fluid flow characteristics inside the enclosure are affected by the partition and magnetic field. We find that the heat transfer rate is enhanced when the partition is attached to the adiabatic wall. The heat transfer rate is suppressed when the Hartmann number is increased. In the presence of the magnetic force, the heat transfer rate is increased by 1 and 2% when the Prandtl number is increased from 0.015 to 0.054 for the vertical and horizontal partition cases, respectively.