MHD Heat Transfer Research Articles

Unsteady MHD Heat Transfer in Couette Flow of Water at 4°C in a Rotating System with Ramped Temperature via Finite Element Method

An unsteady magnetohydromagnetic natural convection on the Couette flow of electrically conducting water at <i>4°C</i> (Pr = <i>11.40</i>) in a rotating system has been considered. A Finite Element Method (FEM) was employed to find the numerical solutions of the dimensionless governing coupled boundary layer partial differential equations. The primary velocity, secondary velocity and temperature of water at <i>4°C</i> as well as shear stresses and rate of heat transfer have been obtained for both ramped temperature and isothermal plates. The results are independent of the mesh (grid) size and the present numerical solutions through the Finite Element Method (FEM) are in good agreement with the existing analytical solutions by the Laplace Transform Technique (LTT). These are shown in tabular and graphical forms.

MHD flow and heat transfer in model geometries for WCLL blankets

In the water cooled lead lithium (WCLL) blanket liquid lead lithium PbLi is used as breeder, neutron multiplier, and as heat transfer medium. The released heat is removed by water that flows at a pressure of 155bar through cooling pipes immersed in the liquid-metal pool. In order to withstand disruption-induced forces and water pressure in case of accidental conditions, the breeder zone is stiffened by internal plates that form rectangular ducts in which the liquid metal is confined. Numerical simulations have been performed to predict liquid metal flows in model geometries for WCLL blankets under the influence of external magnetic fields. In the analysis the flow is driven by an applied pressure gradient or by buoyancy due to the presence of volumetric heat sources in the fluid and heat removal at the water-cooled pipes. For strong magnetic fields the flow exhibits several quasi-2D cores with jumps in core velocity across thin internal layers tangent to the cooling pipes.

MHD Stokes flow and heat transfer in a lid‐driven square cavity under horizontal magnetic field

This study considers the steady flow of a viscous, incompressible and electrically conducting fluid in a lid‐driven square cavity under the effect of a uniform horizontally applied magnetic field. The governing equations are obtained from the Navier‐Stokes equations including buoyancy and Lorentz force terms and the energy equation including Joule heating and viscous dissipation terms. These equations are solved iteratively in terms of velocity components, stream function, vorticity, temperature, and pressure by using radial basis function approximation. Particular solution, which is approximated by radial basis functions to satisfy both differential equation and boundary conditions, becomes the solution of the differential equation itself. Vorticity boundary conditions are obtained from stream function equation using finite difference scheme. Normal derivative of pressure is taken as zero on the boundary. The numerical results are obtained for several values of Hartmann number and Grashof number for the Stokes approximation (Re << 1). The results show that when the viscous dissipation is present, the flow and isolines concentrate through the cold wall forming boundary layers as Grashof number increases. An increase in the magnetic field intensity retards the effect of buoyancy force in the square cavity, whereas the movement of the upper lid causes buoyancy force to be dominant. The solution is obtained in a considerably low computational expense through the use of radial basis function approximations for the MHD equations. Copyright © 2017 John Wiley & Sons, Ltd.

MHD heat and mass transfer flow of a nanofluid over an inclined vertical porous plate with radiation and heat generation/absorption

MHD boundary layer flow, heat and mass transfer analysis of nanofluid over an inclined vertical plate saturated by porous medium with thermal radiation, magnetic field and heat generation/absorption is investigated in the present article. By using similarity variables the governing non-linear partial differential equations are transformed into ordinary differential equations and these equations together with associated boundary conditions are solved numerically by using versatile, extensively validated, variational Finite element method. The sway of key parameters, such as, Magnetic parameter (M), buoyancy ratio parameter (Nr), Radiation parameter (An), Heat source/sink parameter (Q), Brownian motion parameter (Nb), thermophoretic parameter (Nt) and Lewis number (Le) on hydrodynamic, thermal and concentration boundary layers are examined in detail and the results are shown graphically. Furthermore, the impact of these parameters on local skin friction coefficient (Cf), rate of heat transfer (Nux) and rate of mass transfer (Shx) is also investigated. The results are compared with the works published previously and found to be excellent agreement.

MHD Flow and Heat Transfer Analysis in the Wire Coating Process Using Elastic-Viscous

The most important plastic resins used for wire coating are polyvinyl chloride (PVC), nylon, polysulfone, and low-/high-density polyethylene (LDPE/HDPE). In this article, the coating process is performed using elastic-viscous fluid as a coating material for wire coating in a pressure type coating die. The elastic-viscous fluid is electrically conducted in the presence of an applied magnetic field. The governing non-linear equations are modeled and then solved analytically by utilizing an Adomian decomposition method (ADM). The convergence of the series solution is established. The results are also verified by Optimal Homotopy Asymptotic Method (OHAM). The effect of different emerging parameters such as non-Newtonian parameters α and β, magnetic parameter Mand the Brinkman number Br on solutions (velocity and temperature profiles) are discussed through several graphs. Additionally, the current results are compared with published work already available.

MHD liquid metal flow and heat transfer between vertical coaxial cylinders under horizontal magnetic field

Direct numerical simulations are presented of MHD liquid metal flow and heat transfer in vertical annuli. Three annular gaps and four ratios of annular height to annular gap are considered. The walls of the external and internal cylinders are isothermal with the temperature of the outer cylinder being higher and, thus, buoyancy is the driving force. The results show that the fluid motion increases as the aspect ratio and the annular gap become larger. The presence of the magnetic field results to fluid deceleration and, thus, to flow stabilization. Additionally, non symmetric flow patterns develop, due to the magnetic field, resulting in differently sized normal and parallel wall layers, namely the Hartmann and the Roberts layers, respectively. For all annular gaps considered, the highest spatially averaged heat transfer rates are obtained for aspect ratios equal to 1.

MHD flow and heat transfer in a nanofluid over a slender elastic sheet with variable thickness

MHD flow and heat transfer characteristics in a nanofluid over a slender elastic sheet with variable thickness in the presence of variable fluid properties are analyzed. The nonlinear governing equations with suitable boundary conditions are initially cast into dimensionless form by similarity transformations and then the resulting equations are solved via the optimal homotopy analysis method (OHAM). The influences of the fluid viscosity, wall thickness, power index, Brownian motion, and thermophoresis parameters on flow, temperature, and nanoparticle volume fraction fields are analyzed graphically. The analysis reveals quite an interesting and substantial influence of transpiration (wall suction or injection) on the flow and heat transfer characteristics. The flow decelerated with suction and accelerated noticeably with increasing injection (blowing).

Similarity Solution of Unsteady MHD Boundary Layer Flow and Heat Transfer past a Moving Wedge in a Nanofluid using the Buongiorno Model

The present work is focused on the unsteady MHD boundary layer flow and heat transfer over a wedge stretching surface moving in a nanofluid with the effects of various dimensionless parameters by using the Boungiorno model. The solution for the velocity, temperature and nanoparticle concentration depends on parameters like Prandtl number Pr, Brownian motion Nb, thermophoresis Nt, unsteadiness parameter A, velocity ratio parameter λ, pressure gradient parameter β and magnetic parameter M. The local similarity transformation is used to convert the governing partial differential equations into coupled higher order non-linear ordinary differential equations. These equations are numerically solved by using fourth order RungeKutta method along with shooting technique. Numerical results are obtained for distributions of velocity, temperature and nanoparticle concentration, as well as, for the skin friction, local Nusselt number and local Sherwood number for several values of governing parameters. The results are shown in graphically and as well as in a tabular form. From the graph the results indicate that the velocity increases for increasing values of magnetic parameter, unsteadiness parameter and pressure gradient parameter but decreases for velocity ratio parameter. The temperature profile increases for thermophoresis and Brownian motion parameter but reverse results arises for Prandtl number and velocity ratio parameter. On the other hand, nanoparticle concentration decreases for thermophoresis parameter, Lewis number and velocity ratio parameter. But in case of Brownian motion parameter the concentration decreases up to η < 1 and then increases. Besides, the present results are compared with previously published work and found to be in good agreement.

Solution of Falkner- Skan Unsteady MHD Boundary Layer Flow and Heat Transfer Past a Moving Porous Wedge in a Nanofluid

The present problem deals with the effect of various dimensionless parameters on the forced convection unsteady MHD boundary layer flow and heat transfer over a permeable wedge stretching surface in a nanofluid. The effects of Brownian motion and thermophoresis are considered. The solution for the velocity, temperature and nanoparticle concentration depends on various dimensionless parameters like Prandtl number Pr, velocity ratio parameter λ, permeability parameter K*, unsteady parameter A, pressure gradient parameter β, magnetic parameter M. The local similarity transformation is used to convert the governing partial differential equations into coupled third order non-linear ordinary differential equations. These equations are numerically solved using suitable method along with shooting technique. Numerical results are obtained for distributions of velocity, temperature and nanoparticle concentration, as well as, for the skin friction, local Nusselt number and local Sherwood number for several values of governing parameters. The numerical results are shown graphically and also in a tabular form. The velocity decreases for increasing values of velocity ratio parameter but increases for magnetic parameter, unsteady parameter, permeability parameter and pressure gradient parameter. The temperature profiles decreases for thermophoresis parameter Prandtl number and velocity ratio parameter whereas the temperature remains unchanged for Brownian motion parameter. Again, nanoparticle concentration profiles increases for Brownian motion parameter but decreases for thermophoresis parameter, Lewis number and velocity ratio parameter. Besides, the results of rate of velocity and rate of heat transfer are compared with previously published work for the validity and accuracy and found to be in good agreement.

Time-space dependent fractional viscoelastic MHD fluid flow and heat transfer over accelerating plate with slip boundary

The MHD flow and heat transfer of viscoelastic fluid over an accelerating plate with slip boundary are investigated. Different from most classical works, a modified time-space dependent fractional Maxwell fluid model is proposed in depicting the constitutive relationship of the fluid. Numerical solutions are obtained by explicit finite difference approximation and exact solutions are also presented for the limiting cases in integral and series forms. Furthermore, the effects of parameters on the flow and heat transfer behavior are analyzed and discussed in detail.

Analysis of MHD boundary layer slip flow and heat transfer along a stretching cylinder

Analysis of MHD boundary layer slip flow and heat transfer along a stretching cylinder

Numerical computation of steady buoyancy driven MHD heat and mass transfer past an inclined infinite flat plate with sinusoidal surface boundary conditions

Numerical computation of steady buoyancy driven MHD heat and mass transfer past an inclined infinite flat plate with sinusoidal surface boundary conditions

A new numerical method for investigation of thermophoresis and Brownian motion effects on MHD nanofluid flow and heat transfer between parallel plates partially filled with a porous medium

Numerical investigation the problem of nanofluid heat and mass transfer in a channel partially filled with a porous medium in the presence of uniform magnetic field is carried out by a new computational iterative approach known as the spectral local linearization method (SLLM). The similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations which are then solved by SLLM and validity of our solutions is verified by the numerical results (fourth-order Runge-Kutta scheme with the shooting method). In modeling the flow in the channel, the effects of flow inertia, Brinkman friction, nanoparticles concentration and thickness of the porous region are taken into account. The results are obtained for velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number. Also, effects of active parameters such as viscosity parameter, Hartmann number, Darcy number, Prandtl number, Schmidt number, Eckert number, Brownian motion parameter, thermophoresis parameter and the thickness of porous region on the hydrodynamics, heat and mass transfer behaviors are investigated.

MHD convective boundary layer slip flow and heat transfer over nonlinearly stretching cylinder embedded in a thermally stratified medium

This article presents a numerical method of solution to laminar axisymmetric hydro magnetic flow of incompressible, electrically conducting and viscous fluid moving over the circular cylinder embedded in a thermally stratified medium. Fluid over the cylinder moves due to the stretching of cylindrical surface. Different physical conditions at the boundary are also considered. With the help of suitable similarity transformation the boundary layer equations are transformed into ordinary differential equations. The resulting nonlinear ordinary differential equations were solved by Runge-Kutta technique with shooting method. Obtained numerical results for different pertinent parameters are graphically shown for velocity distribution and temperature distribution. Due to the industrial applications point of view, it is evaluated that local Nusselt number at the surfaces increases due to the influence of thermal stratification. The skin-friction and heat transfer coefficients have presented in the form of table. Comparison of heat transfer coefficient is also illustrated.

MHD Convection Fluid Flow and Heat Transfer in an Inclined Microchannel with Heat Generation

The problem of fully developed free convection flow of electrically conducting fluid in an inclined microchannel in the presence of transverse magnetic field and internal heat generation is investigated. The analytical solution for velocity profile and temperature profile have been obtained, considering the velocity slip and temperature jump conditions at the wall of the microchannel. The effect of different parameters involved in the problem on the velocity and temperature profile along with the skin friction parameter and Nusselt number has been discussed graphically.

MHD Laminar Flows and Heat Transfer Adjacent to Permeable Stretching Sheets with Partial Slip Condition

MHD Laminar Flows and Heat Transfer Adjacent to Permeable Stretching Sheets with Partial Slip Condition

Steady MHD Heat and Mass Transfer Flow Over a Permeable Stretching Surface with Velocity, Thermal, and Mass Slip Conditions

Steady MHD Heat and Mass Transfer Flow Over a Permeable Stretching Surface with Velocity, Thermal, and Mass Slip Conditions

Boundary layer flow of dusty fluid over a radiating stretching surface embedded in a thermally stratified porous medium in the presence of uniform heat source

AbstractNumerical investigation for the effect of thermal stratification on MHD flow and heat transfer of dusty fluid over a vertical stretching sheet embedded in a thermally stratified porous medium in the presence of uniform heat source and thermal radiation. The governing equations for the problem were reduced in to dimensionless ordinary differential equations using suitable similarity transformations. The transformed nonlinear ordinary differential equations are numerically solved by applying efficient RungeKutta Fehlberg-45 Method with shooting technique. The effects of various flow controlling parameters such as Prandtl number, heat source/sink parameter, fluid particle interaction parameter, heat source parameter, radiation parameter on velocity and temperature distributions of both fluid and dust phases are depicted graphically. Finally, the numerical results are compared and found to be in good agreement with previously published results under special cases. The results indicate that the fluid phase velocity is always greater than that of the particle phase and thermal stratification significantly affects the surface shear stress as well as the surface heat transfer.

Numerical Investigation on MHD Flow and Heat Transfer over an Exponentially Stretching Sheet with Viscous Dissipation and Radiation Effects

This study is to examine the steady two dimensional laminar flow of a viscous incompressible electrically conducting fluid over a continuous surface. In this study DTM-Pade method is used to solve which is a combination of differential transform method (DTM) and Pade approximant. Comparisons between the solutions obtained by DTM and DTM-Pade and are shown that DTM-Pade is the completely powerful method then DTM for solving the problems in which boundary conditions at infinity. Also in this study the effect of Magnetic and Radiation parameters, Prandtl number and Eckert number for velocity and temperature distributions are investigated.

MHD flow and heat transfer of Casson nanofluid over a wedge

Heat transfer characteristics of a steady, two dimensional, magnetohydrodynamic boundary layer flow of Casson nanofluid over a wedge have been investigated by incorporating the effects of Brownian motion and thermophoresis. The flux of volume fraction of nanoparticles is taken zero on the boundary. Using suitable similarity transformation, the governing partial differential equations for the modelling of boundary layer flow are reduced to ordinary differential equations. The resulting coupled non-linear ordinary differential equations are successfully solved numerically with the help of variational finite element method. To validate the present analysis the numerical results are compared with previously published work available in the literature and they found to be in good agreement. The effects of the flow controlling parameters on velocity, temperature and nanoparticle volume fraction profiles are investigated. The skin-friction co-efficient, Nusselt number and Sherwood number presented for several set of values of the physical parameters and salient features are analyzed.