Steady mixed convection flow of Maxwell fluid over an exponentially stretching vertical surface with magnetic field and viscous dissipation

The steady mixed convection flow and heat transfer from an exponentially stretching vertical surface in a quiescent Maxwell fluid in the presence of magnetic field, viscous dissipation and Joule heating have been studied. The stretching velocity, surface temperature and magnetic field are assumed to have specific exponential function forms for the existence of the local similarity solution. The coupled nonlinear ordinary differential equations governing the local similarity flow and heat transfer have been solved numerically by Chebyshev finite difference method. The influence of the buoyancy parameter, viscous dissipation, relaxation parameter of Maxwell fluid, magnetic field and Prandtl number on the flow and heat transfer has been considered in detail. The Nusselt number increases significantly with the Prandtl number, but the skin friction coefficient decreases. The Nusselt number slightly decreases with increasing viscous dissipation parameter, but the skin friction coefficient slightly increases. Maxwell fluid reduces both skin friction coefficient and Nusselt number, whereas buoyancy force enhances them.     

Free convection heat and mass transfer with Hall current, Joule heating and thermal diffusion

A boundary layer analysis has been presented to study the combined effects of viscous dissipation, Joule heating, transpiration, heat source, thermal diffusion and Hall current on the hydromagnetic free convection and mass transfer flow of an electrically conducting, viscous, homogeneous, incompressible fluid past an infinite vertical porous plate. The governing partial differential equations of the hydromagnetic free convective boundary layer flow are reduced to non-linear ordinary differential equations and solutions for primary velocity, secondary velocity, temperature and concentration field are obtained for large suction. The expressions for the skin-friction, the heat transfer and the mass transfer are also derived. The results of the study are discussed through graphs and tables for different numerical values of the parameters entered into the equations governing the flow.     

Dufour and Soret effects on MHD flow of viscous fluid between radially stretching sheets in porous medium

The aim of this paper is to examine the Dufour and Soret effects on the two-dimensional magnetohydrodynamic (MHD) steady flow of an electrically conducting viscous fluid bounded by infinite sheets. An incompressible viscous fluid fills the porous space. The mathematical analysis is performed in the presence of viscous dissipation, Joule heating, and a first-order chemical reaction. With suitable transformations, the governing partial differential equations through momentum, energy, and concentration laws are transformed into ordinary differential equations. The resulting equations are solved by the homotopy analysis method (HAM). The convergence of the series solutions is ensured. The effects of the emerging parameters, the skin friction coefficient, the Nusselt number, and the Sherwood number are analyzed on the dimensionless velocities, temperature, and concentration fields.     

Slip effects on heat and mass transfer in MHD micropolar fluid flow over an inclined plate with thermal radiation and chemical reaction

The influence of partial slip, thermal radiation, chemical reaction and temperature‐dependent fluid properties on heat and mass transfer in hydro‐magnetic micropolar fluid flow over an inclined permeable plate with constant heat flux and non‐uniform heat source/sink is studied. The transverse magnetic field is assumed as a function of the distance from the origin. Also it is assumed that the fluid viscosity and the thermal conductivity vary as an inverse function and linear function of temperature, respectively. With the use of the similarity transformation, the governing system of non‐linear partial differential equations are transformed into non‐linear ordinary differential equations and are solved numerically using symbolic software MATHEMATICA 7.0 (Wolfram Research, Champaign, IL). The numerical values obtained for the velocity, microrotation, temperature, species concentration, skin friction coefficient and the Nusselt number are presented through graphs and tables for several sets of values of the parameters. The effects of various physical parameters on the flow and heat transfer characteristics are discussed.Copyright © 2011 John Wiley & Sons, Ltd.     

Irreversibility investigation of Casson fluid flow in an inclined channel subject to a Darcy-Forchheimer porous medium:a numerical study

The heat transfer and entropy generation characteristics of the magnetohydrodynamic Casson fluid flow through an inclined microchannel with convective boundary conditions are analyzed.Further,the effects of the viscous forces,Joule heating,heat source/sink,and radiation on the flow are taken into account.The non-dimensional transformations are used to solve the governing equations.Then,the reduced system is resolved by the fourth-fifth order Runge-Kutta-Fehlberg method along with the shooting technique.The effects of different physical parameters on the heat transfer and entropy generation are discussed in detail through graphs.From the perspective of numerical results,it is recognized that the production of entropy can be improved with the Joule heating,viscous dissipation,and convective heating aspects.It is concluded that the production of entropy is the maximum with increases in the Casson parameter,the angle of inclination,and the Hartmann number.Both the Reynolds number and the radiation parameter cause the dual impact on entropy generation.     

Combined influence of wall conductance,pressure work,viscous dissipation and joule heating on MHD channel flow heat transfer

To investigate the combined influence of viscous dissipation, pressure work, Joule heating, arbitrary voltage ratio, unequal wall conductances and wall heat fluxes on the fully developed laminar MHD channel flow heat transfer, the exact solution of the energy equations for fluid and channel walls are derived assuming the Hartmann velocity profile. It is concluded that there can be a substantial difference, depending upon Hartmann number, electric field and Brinkman number, between the Nusselt number considering the wall conductance and that neglecting it. Representative results are presented in diagrams.     

Flow and heat transfer over a generalized stretching/shrinking wall problem—Exact solutions of the Navier-Stokes equations

In this paper, we investigate the steady momentum and heat transfer of a viscous fluid flow over a stretching/shrinking sheet. Exact solutions are presented for the Navier-Stokes equations. The new solutions provide a more general formulation including the linearly stretching and shrinking wall problems as well as the asymptotic suction velocity profiles over a moving plate. Interesting non-linear phenomena are observed in the current results including both exponentially decaying solution and algebraically decaying solution, multiple solutions with infinite number of solutions for the flow field, and velocity overshoot. The energy equation ignoring viscous dissipation is solved exactly and the effects of the mass transfer parameter, the Prandtl number, and the wall stretching/shrinking strength on the temperature profiles and wall heat flux are also presented and discussed. The exact solution of this general flow configuration is a rare case for the Navier-Stokes equation.     

Effects of viscous dissipation and heat generation (absorption) in a thermal boundary layer of a non-Newtonian fluid over a continuously moving permeable flat plate

The problem of boundary-layer flow and heat transfer of a non-Newtonian power-law fluid over a moving porous infinite flat plate in the presence of viscous dissipation and heat generation or absorption is investigated analytically. It is assumed that both the momentum and the energy equations are coupled by the stress friction factor, and an assumption is introduced regarding the heat-transfer index. It is found that exact analytical solutions for velocity and temperature exist only for pseudoplastic fluids in the presence of suction at the surface. The effects of the suction parameter, Eckert number, and the heat generation or absorption parameter on the velocity and temperature profiles, as well as on the skin-friction coefficient and Nusselt number are discussed.     

Effects of thermophoresis particle deposition and of the thermal conductivity in a porous plate with dissipative heat and mass transfer

Network simulation method(NSM) is used to solve the laminar heat and mass transfer of an electricallyconducting,heat generating/absorbing fluid past a perforated horizontal surface in the presence of viscous and Joule heating problem. The governing partial differential equations are non-dimensionalized and transformed into a system of nonlinear ordinary differential similarity equations,in a single independent variable,η. The resulting coupled,nonlinear equations are solved under appropriate transformed boundary conditions. Computations are performed for a wide range of the governing flow parameters,viz Prandtl number,thermophoretic coeffcient(a function of Knudsen number),thermal conductivity parameter,wall transpiration parameter and Schmidt number. The numerical details are discussed with relevant applications. The present problem finds applications in optical fiber fabrication,aerosol filter precipitators,particle deposition on hydronautical blades,semiconductor wafer design,thermo-electronics and problems including nuclear reactor safety.     

DSMC (direct simulation Monte Carlo) analysis of microchannel flow with gas–liquid boundary

High heat capacity and constant operation temperature make a 2-phase heat remover tool promising for solving high heat dissipation problems in MEMS devices. However, microscale analysis of the flow with the conventional Navier–Stokes equation is inadequate, because the non-continuum effect is important when the characteristic dimension is comparable to the local mean free path. DSMC is a direct, particle-based numerical simulation method that uses no continuum assumption. In this paper, the gas–liquid boundary effects in microchannel flow are studied using this method. Modified DSMC code is used to simulate low-speed flow—under which viscous heating produces no significant temperature change—and MD results are incorporated into the DSMC boundary condition. Steady Couette flow simulation results show that the gas–liquid boundary affects the density distribution and the temperature dependence of the slip velocity. Unsteady simulation results show that mass transfer by diffusion is faster than momentum transfer by collision.     

Effects of variable thermal conductivity,viscous dissipation on steady MHD natural convection flow of low Prandtl fluid on an inclined porous plate with Ohmic heating

Abstract Aim of the paper is to investigate the effects of linearly varying thermal conductivity, viscous dissipation and Ohmic heating on steady free convection flow of a viscous incompressible electrically conducting liquid having low Prandtl number along an inclined isothermal non-conducting porous plate in the presence of transverse magnetic field. The governing equations of continuity, momentum and energy are transformed into ordinary differential equations using similarity transformation. The resulting coupled and non-linear ordinary differential equations are solved using Runge-Kutta fourth order method and shooting technique. The velocity and temperature distributions are discussed numerically and presented through graphs. Skin-friction coefficient and Nusselt number at the plate are derived, discussed and their numerical values for various values of physical parameters are presented through tables.     

Exact solutions for the incompressible viscous magnetohydrodynamic fluid of a rotating disk flow

The main interest of the present investigation is to generate exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow motion due to a disk rotating with a constant angular speed. For an external uniform magnetic field applied perpendicular to the plane of the disk, the governing equations allow an exact solution to develop taking into account of the rotational non-axisymmetric stationary conducting flow.Making use of the analytic solution, exact formulas for the angular velocity components as well as for the wall shear stresses are extracted. It is proved analytically that for the specific flow the properly defined thicknesses decay as the magnetic field strength increases in magnitude. Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation. The temperature field is shown to accord with the dissipation and the Joule heating. According to Fourier's heat law, a constant heat transfer from the disk to the fluid occurs, though decreases for small magnetic fields because of the dominance of Joule heating, it eventually increases for growing magnetic field parameters.     

Carreau fluid flow due to nonlinearly stretching sheet with thermal radiation,heat flux,and variable conductivity

A sophisticated theoretical and mathematical model is proposed. It is verified that this model can estimate and monitor the detailed behavior for the steady Carreau fluid flow past a nonlinear stretching surface and the predicted phenomena due to the presence of heat flux, thermal radiation, and viscous dissipation. Despite the fact that some properties of the fluid do not depend on the temperature, the fluid thermal conductivity is assumed to depend on the temperature. Based on accelerating the fluid elements, some of the kinetic energy for the fluid can be turned to the internal heating energy in the form of viscous dissipation phenomena. The contribution in this study is that a similar solution is obtained, in spite of the high nonlinearity of the Carreau model,especially, with the heat flux, variable conductivity, and viscous dissipation phenomena.Some of the major significant findings of this study can be observed from the reduction in the fluid velocity with enhancing the Weissenberg number. Likewise, the increase in the sheet temperature is noted with increasing the Eckert number while the reverse behavior is observed for increasing both the radiation parameter and the conductivity parameter.Finally, the accuracy and trust in the proposed numerical method are validated after benchmarking for our data onto the earlier results.     

Effect of viscous dissipation on mixed convection heat transfer in a vertical tube with uniform wall heat flux

 The laminar and parallel flow of a Newtonian fluid in a vertical cylindrical duct with circular cross section has been analysed. Both the viscous dissipation effect and the buoyancy effect have been taken into account. The momentum balance equation and the energy balance equation have been solved by means of a perturbation method, in the case of a uniform heat flux prescribed at the wall of the duct. The velocity distribution, the temperature distribution, the Nusselt number and the Fanning friction factor have been evaluated analytically. Moreover, the velocity and temperature of the fluid have been compared with those obtained in two special cases: forced convection with viscous dissipation (i.e. negligible buoyancy effect); mixed convection with negligible effects of viscous dissipation. Received on 26 June 2000     

Heat and Mass Transfer in MHD Micropolar Flow Over a Vertical Moving Porous Plate in a Porous Medium

An analysis is presented for the problem of free convection with mass transfer flow for a micropolar fluid via a porous medium bounded by a semi-infinite vertical porous plate in the presence of a transverse magnetic field. The plate moves with constant velocity in the longitudinal direction, and the free stream velocity follows an exponentially small perturbation law. A uniform magnetic field acts perpendicularly to the porous surface in which absorbs the micropolar fluid with a suction velocity varying with time. Numerical results of velocity distribution of micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid. Also, the results of the skin-friction coefficient, the couple stress coefficient, the rate of the heat and mass transfers at the wall are prepared with various values of fluid properties and flow conditions.     

Combined heat and mass transfer by mixed convection MHD flow along a porous plate with chemical reaction in presence of heat source

An exact and a numerical solutions to the problem of a steady mixed convective MHD flow of an incompressible viscous electrically conducting fluid past an infinite vertical porous plate with combined heat and mass transfer are presented.A uniform magnetic field is assumed to be applied transversely to the direction of the flow with the consideration of the induced magnetic field with viscous and magnetic dissipations of energy.The porous plate is subjected to a constant suction velocity as well as a uniform mixed stream velocity.The governing equations are solved by the perturbation technique and a numerical method.The analytical expressions for the velocity field,the temperature field,the induced magnetic field,the skin-friction,and the rate of heat transfer at the plate are obtained.The numerical results are demonstrated graphically for various values of the parameters involved in the problem.The effects of the Hartmann number,the chemical reaction parameter,the magnetic Prandtl number,and the other parameters involved in the velocity field,the temperature field,the concentration field,and the induced magnetic field from the plate to the fluid are discussed.An increase in the heat source/sink or the Eckert number is found to strongly enhance the fluid velocity values.The induced magnetic field along the x-direction increases with the increase in the Hartmann number,the magnetic Prandtl number,the heat source/sink,and the viscous dissipation.It is found that the flow velocity,the fluid temperature,and the induced magnetic field decrease with the increase in the destructive chemical reaction.Applications of the study arise in the thermal plasma reactor modelling,the electromagnetic induction,the magnetohydrodynamic transport phenomena in chromatographic systems,and the magnetic field control of materials processing.     

Low-speed peristaltic transport in a vertical channel subject to the Soret and Dufour effects

Simultaneous effects of heat and mass transfer in peristaltic transport of a viscous fluid are considered. Mathematical modeling is provided in the presence of the Joule heating and the Soret and Dufour effects. The analysis is performed using the long wavelength and low Reynolds number considerations. Perturbation solutions are obtained for a small Brinkman number.     

Numerical solutions of free convection boundary layer flow on a solid sphere with Newtonian heating in a micropolar fluid

In this paper, the problem of free convection boundary layer flow on a solid sphere in a micropolar fluid with Newtonian heating, in which the heat transfer from the surface is proportional to the local surface temperature, is considered. The transformed boundary layer equations in the form of partial differential equations are solved numerically using an implicit finite-difference scheme. Numerical solutions are obtained for the local wall temperature, the local skin friction coefficient, as well as the velocity, angular velocity and temperature profiles. The features of the flow and heat transfer characteristics for different values of the material or micropolar parameter K, the Prandtl number Pr and the conjugate parameter γ are analyzed and discussed.     

Transient free convection flow of an incompressible viscous dissipative fluid

A finite-difference solution of transient free convection flow of a viscous dissipative fluid past an infinite vertical plate, on taking into account viscous dissipative heat is presented. Velocity profiles, temperature profiles are shown for different values of Pr, the Prandtl number and E, the Eckert number. The numerical values of the skin-friction and the rate of heat transfer are entered in a Table. It is observed that greater viscous dissipative heat causes a rise in the velocity, temperature and the skin-friction and a fall in the rate of heat transfer. An increase in Pr leads to a fall in the velocity, temperature and the skin-friction but the rate of heat transfer increases with increasing Pr.     

Molybdenum disulfide and magnesium oxide nanoparticle performance on micropolar Cattaneo-Christov heat flux model

This article intends to illustrate the Darcy flow and melting heat transmission in micropolar liquid.The major advantage of micropolar fluid is the liquid particle rotation through an independent kinematic vector named the microrotation vector.The novel aspects of the Cattaneo-Christov(C-C)heat flux and Joule heating are incorporated in the energy transport expression.Two different nanoparticles,namely,MoS2 and MgO,are suspended into the base-fluid.The governing partial differential equations(PDEs)of the prevailing problem are slackening into ordinary differential expressions(ODEs)via similarity transformations.The resulting mathematical phenomenon is illustrated by the implication of fourth-fifth order Runge-Kutta-Fehlberg(RKF)scheme.The fluid velocity and temperature distributions are deliberated by using graphical phenomena for multiple values of physical constraints.The results are displayed for both molybdenum disulphide and magnesium oxide nanoparticles.A comparative benchmark in the limiting approach is reported for the validation of the present technique.It is revealed that the incrementing material constraint results in a higher fluid velocity for both molybdenum disulphide and magnesium oxide nanoparticle situations.