Thermophoresis and variable viscosity effects on MHD mixed convective heat and mass transfer past a porous wedge in the presence of chemical reaction

An analysis is presented to investigate the effects of thermophoresis and variable viscosity on MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid past a porous wedge in the presence of chemical reaction. The wall of the wedge is embedded in a uniform porous medium in order to allow for possible fluid wall suction or injection. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by using the R.K. Gill and shooting methods. Favorable comparison with previously published work is performed. Numerical results for the dimensionless velocity, temperature and concentration profiles as well as for the skin friction, heat and mass transfer and deposition rate are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.     

Effects of thermophoresis and radiation on laminar flow along a semi-infinite vertical plate

The present contribution deals with the thermophoresis particle deposition and thermal radiation effects on the flow, heat and mass transfer characteristics in a viscous fluid over a semi-infinite vertical porous plate. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by means of the fourth-order Runge–Kutta method with a shooting technique. The effects of different parameters on the dimensionless velocity, temperature, and concentration profiles are shown graphically. In addition, results for the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are tabulated and discussed.     

Unsteady natural convection Couette flow of heat generating/absorbing fluid between vertical parallel plates filled with porous material

The extended Brinkman Darcy model for momentum equations and an energy equation is used to calculate the unsteady natural convection Couette flow of a viscous incompressible heat generating/absorbing fluid in a vertical channel(formed by two infinite vertical and parallel plates) filled with the fluid-saturated porous medium.The flow is triggered by the asymmetric heating and the accelerated motion of one of the bounding plates.The governing equations are simplified by the reasonable dimensionless parameters and solved analytically by the Laplace transform techniques to obtain the closed form solutions of the velocity and temperature profiles.Then,the skin friction and the rate of heat transfer are consequently derived.It is noticed that,at different sections within the vertical channel,the fluid flow and the temperature profiles increase with time,which are both higher near the moving plate.In particular,increasing the gap between the plates increases the velocity and the temperature of the fluid,however,reduces the skin friction and the rate of heat transfer.     

Magnetohydrodynamic laminar boundary-layer flow over a porous wedge with thermophoresis particle deposition in the presence of variable stream conditions

An analysis is presented to investigate the effects of thermophoresis variable viscosity on MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid past a porous wedge in the presence of chemical reaction. The wall of the wedge is embedded in a uniform porous medium in order to allow for possible fluid wall suction or injection. The governing boundary layer equations are written into a dimensionless form by local non-similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by using the R.K. Gill and shooting methods. Favorable comparison with previously published work is performed. Numerical results for the dimensionless velocity, temperature and concentration profiles are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.     

Local nonsimilarity solution for the impact of the buoyancy force on heat and mass transfer in a flow over a porous wedge with a heat source in the presence of suction/injection

Combined heat and mass transfer in free, forced and mixed convection flows along a porous wedge with internal heat generation in the presence of uniform suction or injection is investigated. The boundary-layer analysis is formulated in terms of the combined thermal and solute buoyancy effect. The flow field characteristics are analyzed using the Runge-Kutta-Gill method, the shooting method, and the local nonsimilarity method. Due to the effect of the buoyancy force, power law of temperature and concentration, and suction/injection on the wall of the wedge, the flow field is locally nonsimilar. Numerical calculations up to third-order level of truncation are carried out for different values of dimensionless parameters as a special case. The effects of the buoyancy force, suction, heat generation, and variable wall temperature and concentration on the dimensionless velocity, temperature, and concentration profiles are studied. The results obtained are found to be in good agreement with previously published works.     

Local Nonsimilarity Solution for the Impact of a Chemical Reaction in an MHD Mixed Convection Heat and Mass Transfer Flow over a Porous Wedge in the Presence Of Suction/Injection

Combined heat and mass transfer in free, forced, and mixed convection flows along a porous wedge with a magnetic effect in the presence of a chemical reaction is investigated. The flow field characteristics are analyzed with the Runge—Kutta—Gill method in conjunction with the shooting method, and local nonsimilarity method. The governing boundary-layer equations are written in a dimensionless form with the use of the Falkner—Skan transformations. Owing to the effect of the buoyancy force, the power law of temperature and concentration, and suction/injection on the wall of the wedge, the flow field is locally nonsimilar. Numerical calculations up to the third-order level of truncation are carried out for different values of dimensionless parameters as a special case. Effects of the magnetic field strength in the presence of a chemical reaction with a variable wall temperature and concentration on the dimensionless velocity, temperature, and concentration profiles are shown graphically. Comparisons with previously published works are performed, and excellent agreement between the results is obtained.     

On heat transfer effects of a viscous fluid squeezed and extruded between two parallel plates

The unsteady squeezing and extrusion of a viscous fluid between two parallel plates of constant temperature is examined. The dimensionless extrusion parameter,=U/V, is introduced to represent the effects of the extrusion on the squeezing velocities. The squeezing parameter=VH/, represents the effect of the inertial forces on heat and fluid flow characteristics. It is found that increasing the extrusion parameter will increase both the velocity and the heat transfer rates to the viscous fluid. Increasing the squeezing parameter had also decreased the fluid velocity and enhanced heat transfer rates. Increasing the viscous effects or the Eckert number E=U²/c_p (T_E – T_s) heated the fluid and consequently decreased the heat transfer rates. Different velocity profiles, temperature profiles, and Nusselt numbers against various dimensionless groups are drawn.     

Magneto-hydrodynamic mixed convection of a power-law fluid past a stretching surface in the presence of thermal radiation and internal heat generation/absorption

The problem of magneto-hydrodynamic mixed convective flow and heat transfer of an electrically conducting, power-law fluid past a stretching surface in the presence of heat generation/absorption and thermal radiation has been analyzed. After transforming the governing equations with suitable dimensionless variables, numerical solutions are generated by an implicit finite-difference technique for the non-similar, coupled flow. The solution is found to be dependent on the governing parameters including the power-law fluid index, the magnetic field parameter, the modified Richardson number, the radiation parameter, the heat generation parameter, and the generalized Prandtl number. To reveal the tendency of the solutions, typical results for the velocity and temperature profiles, the skin-friction coefficient, and the local Nusselt number are presented for different values of these controlling parameters.     

Natural convection of non-Newtonian power-law fluid over axisymmetric and two-dimensional bodies of arbitrary shape in fluid-saturated porous media

Numerical analysis of the free convection coupled heat and mass transfer is presented for non-Newtonian power-law fluids with the yield stress flowing over a two-dimensional or axisymmetric body of an arbitrary shape in a fluid-saturated porous medium. The governing boundary layer equations and boundary conditions are cast into a dimensionless form by the similarity transformation. The resulting system of equations is solved by a finite difference method. The parameters studied are the rheological constants, the buoyancy ratio, and the Lewis number. Representative velocity, temperature, and concentration profiles are presented and discussed. It is found that the results depend strongly on the values of the yield stress parameter and the power-law index of the non-Newtonian fluid.     

3D Casson nanofluid flow over slendering surface in a suspension of gyrotactic microorganisms with Cattaneo-Christov heat flux

A mathematical model is proposed to execute the features of the non-uniform heat source or sink in the chemically reacting magnetohydrodynamic (MHD) Casson fluid across a slendering sheet in the presence of microorganisms and Cattaneo-Christov heat flux. Multiple slips (diffusion, thermal, and momentum slips) are applied in the modeling of the heat and mass transport processes. The Runge-Kutta based shooting method is used to find the solutions. Numerical simulation is carried out for various values of the physical constraints when the Casson index parameter is positive, negative, or infinite with the aid of plots. The coefficients of the skin factors, the local Nusselt number, and the Sherwood number are estimated for different parameters, and discussed for engineering interest. It is found that the gyrotactic microorganisms are greatly encouraged when the dimensionless parameters increase, especially when the Casson fluid parameter is negative. It is worth mentioning that the velocity profiles when the Casson fluid parameter is positive are higher than those when the Casson fluid parameter is negative or infinite, whereas the temperature and concentration fields show exactly opposite phenomena.     

Natural convection of non-Newtonian power-law fluid over axisymmetric and two-dimensional bodies of arbitrary shape in fluid-saturated porous media

Numerical analysis of the free convection coupled heat and mass transfer is presented for non-Newtonian power-law fluids with the yield stress flowing over a two-dimensional or axisymmetric body of an arbitrary shape in a fluid-saturated porous medium. The governing boundary layer equations and boundary conditions are cast into a dimensionless form by the similarity transformation. The resulting system of equations is solved by a finite difference method. The parameters studied are the rheological constants, the buoyancy ratio, and the Lewis number. Representative velocity, temperature, and concentration profiles are presented and discussed. It is found that the results depend strongly on the values of the yield stress parameter and the power-law index of the non-Newtonian fluid.     

Local non-similarity solution to impact of chemical reaction on MHD mixed convection heat and mass transfer flow over porous wedge in the presence of suction / injection

Combined heat and mass transfer on free, forced, and mixed convection flow along a porous wedge with magnetic effect in the presence of chemical reaction is investigated. The flow field characteristics are analyzed by the Runge-Kutta-Gill scheme with the shooting method as well as the local non-similarity method up to the third level of truncation, which are used to reduce the governing partial differential equations into nine ordinary differential equations. The governing boundary layer equations are converted to a dimensionless form by Falkner-Skan transformations. Because of the effect of suction/injection on the wall of the wedge with buoyancy force and variable wall temperature, the flow field is locally non-similar. Numerical calculations up to the third order level of truncation are carried out as a special case for different values of dimensionless parameters. Effects of the magnetic field strength in the presence of chemical reaction with variable wall temperature and concentration on the dimensionless velocity, temperature and concentration profiles are shown graphically.     

TEMPERATURE PROFILES OF LOCAL THERMAL NONEQUILIBRIUM FOR THERMAL DEVELOPING FORCED CONVECTION IN POROUS MEDIUM PARALLEL PLATE CHANNEL

Based on the two-energy equation model, taking into account viscous dissipation due to the interaction between solid skeleton and pore fluid flow, temperature expressions of the solid skeleton and pore fluid flow are obtained analytically for the thermally developing forced convection in a saturated porous medium parallel plate channel, with walls being at constant temperature. It is proved that the temperatures of the two phases for the local thermal nonequilibrium approach to the temperature derived from the one-energy equation model for the local thermal equilibrium when the heat exchange coefficient goes to infinite. The temperature profiles are shown in figures for different dimensionless parameters and the effects of the parameters on the local thermal nonequilibrium are revealed by parameter study.     

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 magnetohydro-dynamics(MHD) double-diffusive free convective flow of an electrically conducting fluidpast a vertical plate embedded in a non-Darcy porous medium are investigated numeri-cally.The governing non-linear dimensionless equations are solved by an implicit finitedifference scheme of the Crank-Nicolson type with a tridiagonal matrix manipulation.The effects of various parameters entering into the problem on the unsteady dimension-less velocity,temperature,and concentration profiles are studied in detail.Furthermore,the time variation of the skin friction coefficient,the Nusselt number,and the Sherwoodnumber is presented and analyzed.The results show that the unsteady velocity,tem-perature,and concentration profiles are substantially influenced by the Dufour and Soreteffects.When the Dufour number increases or the Soret number decreases,both the skinfriction and the Sherwood number decrease,while the Nusselt number increases.It isfound that,when the magnetic parameter increases,the velocity and the temperaturedecrease in the boundary layer.     

Lie group analysis for thermophoretic and radiative augmentation of heat and mass transfer in a Brinkman-Darcy flow over a flat surface with heat generation

A boundary layer analysis is presented to investigate numerically the effects of radiation,thermophoresis and the dimensionless heat generation or absorption on hydromagnetic flow with heat and mass transfer over a flat surface in a porous medium.The boundary layer equations are transformed to non-linear ordinary differential equations using scaling group of transformations and they are solved numerically by using the fourth order Runge-Kutta method with shooting technique for some values of physical parameters.Comparisons with previously published work are performed and the results are found to be in very good agreement.Many results are obtained and a representative set is displayed graphically to illustrate the influence of the various parameters on the dimensionless velocity,temperature and concentration profiles as well as the local skin-friction coefficient,wall heat transfer,particle deposition rate and wall thermophoretic deposition velocity.The results show that the magnetic field induces acceleration of the flow,rather than deceleration(as in classical magnetohydrodynamics(MHD) boundary layer flow) but to reduce temperature and increase concentration of particles in boundary layer.Also,there is a strong dependency of the concentration in the boundary layer on both the Schmidt number and mass transfer parameter.     

Developing laminar forced convection in eccentric annuli

The paper presents a boundary-layer model describing the laminar forced convection heat transfer in the entry region of eccentric annuli. A finite-difference numerical algorithm is developed for solving this model. Numerical results are presented for the developing velocity profiles and the pressure drop in annuli of radius ratio 0.5 and 0.9 over a dimensionless eccentricity ranged from 0.1 to 0.8. Heat transfer parameters are presented for a fluid of Pr=0.7 under the conditions of an isothermally heated inner wall while the outer wall is kept at the inlet fluid temperature. Received on 18 March 1997     

Heat and mass transfer in a visco–elastic fluid flow over an accelerating surface with heat source/sink and viscous dissipation

 In this paper we present a mathematical analysis of heat and mass transfer phenomena in a visco–elastic fluid flow over an accelerating stretching sheet in the presence of heat source/sink, viscous dissipation and suction/blowing. Similarity transformations are used to convert highly non-linear partial differential equations into ordinary differential equations. Several closed form analytical solutions for non-dimensional temperature, concentration, heat flux, mass flux profiles are obtained in the form of confluent hypergeometric (Kummer's) functions for two different cases of the boundary conditions, namely, (i) wall with prescribed second order power law temperature and second order power law concentration (PST), and (ii) wall with prescribed second order power law heat flux and second order power law mass flux (PHF). The effect of various physical parameters like visco–elasticity, Eckert number, Prandtl number, heat source/sink, Schmidt number and suction/blowing parameter on temperature and concentration profiles are analysed. The effects of all these parameters on wall temperature gradient and wall concentration gradient are also discussed. Received on 23 March 2000 / Published online: 29 November 2001     

The influence of thermal radiation on MHD station-point flow past a stretching sheet with heat generation

This letter is concerned with the plane and axisymmetric stagnation-point flows and heat transfer of an electrically-conducting fluid past a stretching sheet in the presence of the thermal radiation and heat generation or absorption. The analytical solutions for the velocity distribution and dimensionless temperature profiles are obtained for the various values of the ratio of free stream velocity and stretching velocity, heat source parameter, Prandtl number, thermal radiation parameter, the suction and injection velocity parameter and magnetic parameter and dimensionality index in the series form with the help of homotopy analysis method (HAM). Convergence of the series is explicitly discussed. In addition, shear stress and heat flux at the surface are calculated.     

Entropy analysis for viscoelastic magnetohydrodynamic flow over a stretching surface

This paper presents the application of the second law analysis of thermodynamics to viscoelastic magnetohydrodynamic flow over a stretching surface. The velocity and temperature profiles are obtained analytically using the Kummer's functions and used to compute the entropy generation number. The effects of the magnetic parameter, the Prandtl number, the heat source/heat sink parameter and the surface temperature parameter on velocity and temperature profiles are presented. The influences of the same parameters, the Hartmann number, the dimensionless group parameter and the Reynolds number on the entropy generation are also discussed.     

传热传质对有抽吸的收缩薄片上的非线性磁流体动力学边界层流动的影响

This work is concerned with Magnetohydrodynamic viscous flow due to a shrinking sheet in the presence of suction. The cases of two dimensional and axisymmetric shrinking are discussed. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are numerically solved by using an advanced numeric technique. Favorability comparisons with previously published work are presented. Numerical results for the dimensionless velocity, temperature and concentration profiles as well as for the skin friction, heat and mass transfer and deposition rate are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.