MHD Natural Convection Flow Research Articles

MHD natural convection flow in a vertical micro-concentric-annuli in the presence of radial magnetic field: An exact solution

Abstract This paper deals with a theoretical investigation of steady fully developed MHD natural convection flow of viscous, incompressible, electrically conducting fluid in micro-concntric-annuli in the presence of radial magnetic field. The velocity slip and temperature jump at the micro-concentric annuli surface are taken into account. Exact solutions are derived for energy and momentum equations under relevant boundary conditions. The solution obtained is graphically represented and the effects of various controlling parameters such as the radius ratio (η), Hartmann number (M), rarefaction parameter (βvKn), and fluid-wall interaction parameter (F) on the flow formation are discussed. The significant result from the study is that as rarefaction parameter (βvKn) increases the velocity slip on the surface of cylinders increases while fluid wall interaction parameter (F) decreases the velocity inside the micro-concntric-annuli. Furthermore, it is found that increase in radius ratio leads to increase in the volume flow rate.

MHD Natural Convective Flow in an Isosceles Triangular Cavity Filled with Porous Medium due to Uniform/Non-Uniform Heated Side Walls

Abstract In this article, numerical simulations are carried out for fluid flow and heat transfer through natural convection in an isosceles triangular cavity under the effects of uniform magnetic field. The cavity is of cold bottom wall and uniformly/non-uniformly heated side walls and is filled with isotropic porous medium. The governing Navier Stoke's equations are subjected to Penalty finite element method to eliminate pressure term and Galerkin weighted residual method is applied to obtain the solution of the reduced equations for different ranges of the physical parameters. The results are verified as grid independent and comparison is made as a limiting case with the results available in literature, and it is shown that the developed code is highly accurate. Computations are presented in terms of streamlines, isotherms, local Nusselt number and average Nusselt number through graphs and tables. It is observed that, for the case of uniform heating side walls, strength of circulation of streamlines gets increased when Rayleigh number is increased above critical value, but increase in Hartmann number decreases strength of streamlines circulations. For non-uniform heating case, it is noticed that heat transfer rate is maximum at corners of bottom wall.

Unsteady MHD Natural Convective Flow over Vertical Plate in Thermally Stratified Media with Variable Viscosity and Thermal Conductivity

Unsteady MHD Natural Convective Flow over Vertical Plate in Thermally Stratified Media with Variable Viscosity and Thermal Conductivity

Effect of chemical reaction and radiation absorption on the unsteady MHD free convection Couette flow in a vertical channel filled with porous materials

This paper deals with effect of chemical reaction and radiation absorption on the unsteady MHD natural convection flow in a vertical channel filled with porous materials. One of the plate moves with a constant velocity in the direction of fluid flow while the other plate is stationary. A uniform magnetic field acts perpendicular to the porous plate, which absorbs the fluid with a suction velocity varying with time. The dimensionless governing equations for this problem are solved analytically using two-term harmonic and non-harmonic perturbation series method. The results of the analytical solutions for velocity, temperature and concentration profiles of both phases are graphically presented and discussed. It is noteworthy to mention that growing permeability and channel width parameter lead to increase in the fluid velocity profile. Results in the present work have been compared with other works in literature and an excellent agreement is found.

Effects of Stress Work on MHD Natural Convection Flow along a Vertical Wavy Surface with Joule Heating

Effects of Stress Work on MHD Natural Convection Flow along a Vertical Wavy Surface with Joule Heating

Radiation effects on an unsteady MHD natural convective flow of a nanofluid past a vertical plate

Numerical analysis is carried out on an unsteady MHD natural convective boundary layer flow of a nanofluid past an isothermal vertical plate in the presence of thermal radiation. The governing partial differential equations are solved numerically by an efficient, iterative, tri-diagonal, semi-implicit finite-difference method. In particular, we investigate the effects of radiation, magnetic field and nanoparticle volume fraction on the flow and heat transfer characteristics. The nanofluids containing nanoparticles of aluminium oxide, copper, titanium oxide and silver with nanoparticle volume fraction range less than or equal to 0.04 are considered. The numerical results indicate that in the presence of radiation and magnetic field, an increase in the nanoparticle volume fraction will decrease the velocity boundary layer thickness while increasing the thickness of the thermal boundary layer. Meanwhile, an increase in the magnetic field or nanoparticle volume fraction decreases the average skin-friction at the plate. Excellent validation of the present results has been achieved with the published results in the literature in the absence of the nanoparticle volume fraction.

Heat and Mass Transfer Effects on MHD Natural Convective Flow Past an Infinite Vertical Porous Plate with Thermal Radiation and Hall Current

The objective of the present study is to find both the analytical and numerical solutions of the unsteady hydromagnetic natural convective radiating fluid flow of an incompressible, viscous Boussinesq's fluid past an infinite vertical plate embedded in a porous medium with heat and mass transfer in presence of hall current. The Rosseland approximation for an optically thick fluid is invoked to describe the radiative flux. Mathematical model of this mechanism has been constructed in the form of partial differential equations and are solved by an efficient finite element method as well as by Perturbation technique. A parametric study of the physical parameters is made, and a representative set of numerical results for the velocity, temperature and concentration are presented graphically as well as local shear stress and local Nusselt and Sherwood numbers are presented in tabular forms. The comparison of the analytical and numerical results is very good indicating the correctness of the present analysis and its applicability.

Aligned Magnetic Field Effect on Unsteady MHD Natural Convection Flow of a Chemically Reacting, Radiative and Dissipative Fluid Past a Porous Vertical Plate in the Presence of Constant Heat and Mass Flux

Aligned Magnetic Field Effect on Unsteady MHD Natural Convection Flow of a Chemically Reacting, Radiative and Dissipative Fluid Past a Porous Vertical Plate in the Presence of Constant Heat and Mass Flux

Fully developed MHD natural convection flow in a vertical annular microchannel: An exact solution

An exact solution of steady fully developed natural convection flow of viscous, incompressible, electrically conducting fluid in a vertical annular micro-channel with the effect of transverse magnetic field in the presence of velocity slip and temperature jump at the annular micro-channel surfaces is obtained. Exact solution is expressed in terms of modified Bessel function of the first and second kind. The solution obtained is graphically represented and the effects of radius ratio (η), Hartmann number (M), rarefaction parameter (βvKn), and fluid–wall interaction parameter (F) on the flow are investigated. During the course of numerical computations, it is found that an increase in Hartmann number leads to a decrease in the fluid velocity, volume flow rate and skin friction. Furthermore, it is found that an increase in curvature radius ratio leads to an increase in the volume flow rate.

MHD natural convection flow in a vertical parallel plate microchannel

The fully developed steady natural convection flow of conducting fluid in a vertical parallel plate micro-channel in the presence of transverse magnetic field is considered. The velocity slip and temperature jump at the plates are taken in to consideration. The effect of various flow parameters entering into the problem such as Hartmann number, rarefaction parameter, fluid-wall interaction parameter and wall-ambient temperature difference ratio are discussed with the aid of line graphs. During the course of computation, it is found that increase in the effects of rarefaction and fluid wall interaction leads to increase in volume flow rate while the volume flow rate decreases with increase in Hartmann number.

MHD natural convection flow in cavities filled with square solid blocks

Purpose – The purpose of this paper is to study the influence of magnetic field on natural convection inside the enclosures partially filled with conducting square solid obstacles. Also, the effect of thermal conductivity ratio between the solid and fluid materials is investigated for different number of solid blocks. Design/methodology/approach – The dimensionless governing equations are transformed into sets of algebraic equations using finite volume method and momentum equations are solved by the SIMPLE algorithm with the hybrid scheme. The validation of the numerical code was conducted by comparing the results of average Nusselt number with previously published works. Findings – The results indicate that both the magnetic field and solid blocks can significantly affect the flow and temperature fields. It is shown that for a given Rayleigh number, variation of Nusselt number might be increasing or decreasing with change in solid-to-fluid thermal conductivity ratio depending on magnetic field strength and number of solid blocks. Originality/value – No work has been reported previously on the effect of magnetic field on natural convection flow in a cavity partially filled with square solid blocks. The numerical analysis of conductivity ratio between the solid and fluid materials under the effect of magnetic field have been carried out for the first time.

MHD natural-convection flow in an inclined square enclosure filled with a micropolar-nanofluid

Abstract Transient, laminar, natural-convection flow of a micropolar-nanofluid (Al2O3/water) in the presence of a magnetic field in an inclined rectangular enclosure is considered. A meshless point collocation method utilizing a velocity-correction scheme has been developed. The governing equations in their velocity–vorticity formulation are solved numerically for various Rayleigh (Ra) and Hartman (Ha) numbers, different nanoparticles volume fractions (φ) and considering different inclination angles and magnetic field directions. The results show that, both, the strength and orientation of the magnetic field significantly affect the flow and temperature fields. For the cases considering herein, experimentally given forms of dynamic viscosity, thermal conductivity and electrical conductivity are utilized.

Analytical and numerical study of MHD natural convection in a horizontal shallow cavity with heat generation

A study is presented of two-dimensional MHD natural convection flow in an internally heated horizontal shallow cavity in the presence of an external uniform vertical magnetic field. The main feature of the present flow is a symmetric double-cell Hadley circulation with the fluid ascending in the center of the cavity and descending near the vertical cold walls. All walls are electrically insulated, with the horizontal being adiabatic and the vertical isothermal. The method of the matched asymptotic expansions is used to obtain solutions of the flow and heat transfer problem. This analysis which is valid for large cavity aspect ratios and for any magnetic field strength is particularly helpful for the inexpensive determination of the flow and heat transfer characteristics. In addition, numerical simulations are performed for a range of Hartmann, Prandtl and Rayleigh numbers in order to verify the accuracy and validity of the analytical results, to calculate the constants arising by the analytical approach and to obtain details of the flow in the vicinity of the vertical side walls. The comparison of the analytical and numerical results is very good indicating the correctness of the present analysis and its applicability.

Influence of Chemical Reaction, Heat Source, Soret and Dufour Effects on Separation of a Binary Fluid Mixture in MHD Natural Convection Flow in Porous Media

Separation of a heat absorbing or generating binary fluid mixture of incompressible viscous fluids in MHD natural convection flow about a vertical surface embedded in a saturated porous medium subjected to a chemical reaction is numerically analyzed, by taking into account the Soret and Dufour effects. The temperature and concentration profiles are drawn and the effects of magnetic, Lewish, Dufour, Soret, heat source, sustention parameter, order of the chemical reaction and chemical reaction parameter are exhibited graphically. The Nusselt and local Sherwood numbers are tabulated for various values of the above mentioned parameters. It is observed from the table that the Nusselt and local Sherwood numbers are effected significantly due to the presence of the chemical reaction and the magnetic field.

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.

Computational analysis of viscous dissipation and joule-heating effects on non-Darcy MHD natural convection flow from a horizontal cylinder in porous media with internal heat generation

In the present paper we examine the effects of viscous dissipation, Joule heating and heat source/sink on non-Darcy MHD natural convection heat transfer flow over permeable horizontal circular cylinder in a porous medium. The boundary layer equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite difference scheme. A parametric study illustrating the influence of Darcy parameter (Da), Forchheimer parameter (?), Grashof number(Gr), heat source/sink parameter (?) and viscous dissipation parameter (Ec) on the fluid velocity, temperature as well as local skin-friction and Nusselt numbers is conducted Increasing Forchheimer inertial drag parameter (?) retards the flow considerably but enhances temperatures. Increasing viscous dissipation parameter(Ec) is found to elevate velocities i.e. accelerate the flow and increase temperatures. Increasing heat source/sink parameter (?) is found to elevate velocities and increase temperatures. Increasing the Grashof number (Gr) is found to elevate the velocity and decrease the temperatures. Local skin friction number is found to be increases with increasing heat source/sink parameter (?) where as Local Nusselt number is found to decrease with increasing heat source/sink parameter (?).

Coupled heat and mass transfer by MHD natural convection of micropolar fluid about a truncated cone in the presence of radiation and chemical reaction

An analysis is performed to study the thermal radiation and chemical reaction effects on coupled heat and mass transfer by MHD natural convective boundary-layer flow of a micropolar fluid over a permeable truncated cone with variable surface temperature and concentration. A suitable set of dimensionless variables is used to transform the governing equations of the problem into a non-similar form. The resulting non-similar equations have the property that they reduce to various special cases previously considered in the literature. An adequate and efficient implicit, tri-diagonal finite difference scheme is employed for the numerical solution of the obtained equations. Various comparisons with previously published work are performed and the results are found to be in excellent agreement. A representative set of numerical results for the velocity, microrotation, temperature and concentration profiles as well as the local skin-friction coefficient, local wall couple stress, local Nusselt number and the local Sherwood number is presented graphically for various parametric conditions and discussed.DOI: http://dx.doi.org/10.3329/jname.v10i2.15898

MHD natural convection flow with radiative heat transfer past an impulsively moving vertical plate with ramped temperature in the presence of hall current and thermal diffusion

An investigation on an unsteady MHD natural convection flow with radiative heat transfer of a viscous, incompressible, electrically conducting and optically thick fluid past an impulsively moving vertical plate with ramped temperature in a porous medium in the presence of a Hall current and thermal diffusion is carried out. An exact solution of momentum and energy equations, under Boussinesq and Rosseland approximations, is obtained in a closed form by the Laplace transform technique for both ramped temperature and isothermal plates. Expressions for the skin friction and Nusselt number for both ramped temperature and isothermal plates are also derived. The numerical values of fluid velocity and fluid temperature are displayed graphically versus the boundary layer coordinate y for various values of pertinent flow parameters for both ramped temperature and isothermal plates. The numerical values of the skin friction due to primary and secondary flows are presented in tabular form for various values of pertinent flow parameters.

The Effect of Radiation on MHD Natural Convection Flow of Fluid with Variable Viscosity from a Porous Vertical Plate

This paper presents a new extension for the effect of Radiation on MHD Natural Convection Flow with Variable Viscosity from a Porous Vertical Plate. The governing boundary layer equations are first transformed into a non dimensional form and the resulting non linear system of partial differential equations are then solved numerically using finite difference method together with Keller-Box scheme. The numerical results show that the variable viscosity affects the surface shear stress and the rate of heat transfer which are here in terms of skin friction coefficient and local Nusselt number. It affects velocity as well as temperature profiles also. These are shown graphically and tabular form for a selection of parameters set of consisting of viscosity variation parameter , magnetohydrodynamic parameter M, radiation effect Rd, Prandtl number Pr.

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.