The effects of chemical reaction,Hall and ion-slip currents on MHD flow with temperature dependent viscosity and thermal diffusivity

In this paper, the problem of magneto-micropolar fluid flow, heat and mass transfer with suction and blowing through a porous medium is analyzed numerically. This problem was studied under the effects of chemical reaction, Hall, ion-slip currents, variable viscosity and variable thermal diffusivity. The governing fundamental equations are approximated by a system of non-linear ordinary differential equation. This system is solved numerically by using the Chebyshev pseudospectral method. Details of the velocities, temperature and concentration fields as well as the local skin-friction, the local Nusselt number and the local Sherwood number for the various values of the parameters of the problem are presented. The numerical results indicate that, the concentration decreases as the permeability parameter, the chemical reaction parameter and Schmidt number increase and it increases as variable viscosity and variable thermal diffusivity increase. The local Nusselt number and the local Sherwood number decrease as the magnetic field and ion-slip current parameters increase, whereas they increase as Hall current parameter increases. Also, there is a (non-linear) strong dependency of the concentration gradient at the wall on both Schmidt number and the mass transfer parameter.     

Heat and mass transfer in MHD non-Darcian flow of a micropolar fluid over a stretching sheet embedded in a porous media with non-uniform heat source and thermal radiation

A mathematical analysis has been carried out to study magnetohydrodynamic boundary layer flow, heat and mass transfer characteristic on steady two-dimensional flow of a micropolar fluid over a stretching sheet embedded in a non-Darcian porous medium with uniform magnetic field. Momentum boundary layer equation takes into account of transverse magnetic field whereas energy equation takes into account of Ohmic dissipation due to transverse magnetic field, thermal radiation and non-uniform source effects. An analysis has been performed for heating process namely the prescribed wall heat flux (PHF case). The governing system of partial differential equations is first transformed into a system of non-linear ordinary differential equations using similarity transformation. The transformed equations are non-linear coupled differential equations which are then linearized by quasi-linearization method and solved very efficiently by finite-difference method. Favorable comparisons with previously published work on various special cases of the problem are obtained. The effects of various physical parameters on velocity, temperature, concentration distributions are presented graphically and in tabular form.     

Free convection heat and mass transfer in a power law fluid past an inclined surface with thermophoresis

The problem of heat and mass transfer in a power law, two-dimensional, laminar, boundary layer flow of a viscous incompressible fluid over an inclined plate with heat generation and thermophoresis is investigated by the characteristic function method. The governing non-linear partial differential equations describing the flow and heat transfer problem are transformed into a set of coupled non-linear ordinary differential equation which was solved using Runge–Kutta shooting method. Exact solutions for the dimensionless temperature and concentration profiles, are presented graphically for different physical parameters and for the different power law exponents 0 < n < 0.5 and for n > 0.5.     

Dead-core solutions for slightly non-isothermal diffusion-reaction problems with power-law kinetics

The paper deals with dead-core solutions to a non-isothermal reaction- diffusion problem with power-law kinetics for a single reaction that takes place in a catalyst pellet along with mass and heat transfer from the bulk phase to the outer pellet surface. The model boundary value problem for two coupled non-linear diffusion-reaction equations is solved using the semi-analytical method. The exact solutions are established under the assumption of a small temperature gradient in the pellet. The nonlinear algebraic expressions are derived for the critical Thiele modulus, dead-zone length, reactant concentration, and temperature profiles in catalyst pellets of planar geometry. The effects of the reaction order, Arrhenius number, energy generation function, Thiele modulus, and Biot numbers are investigated on the concentration and temperature profiles, dead-zone length, and critical Thiele modulus.     

Effect of double stratification on MHD free convection in a micropolar fluid

This paper analyzes the flow and heat and mass transfer characteristics of the free convection on a vertical plate with variable wall temperature and concentration in a doubly stratified micropolar fluid. A uniform magnetic field is applied normal to the plate. The governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Keller-box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The non-dimensional velocity, microrotation, temperature and concentration are presented graphically for various values of magnetic parameter, coupling number, thermal and solutal stratification parameters. In addition, the Nusselt number, the Sherwood number, the skin-friction coefficient, and the wall couple stress are shown in a tabular form.     

Unsteady MHD stagnation-point flow with heat and mass transfer in a micropolar fluid in the presence of thermophoresis and suction/injection

The effect of suction or injection on unsteady MHD flow with heat and mass transfer in a micropolar fluid near the forward stagnation point flow with thermophoresis has been investigated. The problem is reduced to a system of non-dimensional partial differential equations, which are solved numerically using the implicit finite-difference scheme. Profiles for velocity, microrotation, temperature and concentration as well as the skin friction, the rate of heat and mass transfer are determined and presented graphically for physical parameters. The results show that the suction increases the skin friction, the rate of heat and mass transfer while opposite trend is observed for the case of injection. It is also found that the effect of thermophoresis is decrease the concentration boundary layer thickness.     

Finite element analysis of hydromagnetic flow and heat transfer of a heat generation fluid over a surface embedded in a non-Darcian porous medium in the presence of chemical reaction

An analysis is carried out to study the flow, chemical reaction and mass transfer of a steady laminar boundary layer of an electrically conducting and heat generating fluid driven by a continuously moving porous surface embedded in a non-Darcian porous medium in the presence of a transfer magnetic field. The governing partial differential equations are converted into ordinary differential equations by similarity transformation and are solved numerically by using the finite element method. The results obtained are presented graphically for velocity, temperature and concentration profiles, as well as the Sherwood number for various parameters entering into the problem.     

Influence of heat and mass transfer on peristaltic flow of a third order fluid in a diverging tube

In the present investigation we have discussed the heat and mass transfer analysis on peristaltic flow of a third order fluid in a diverging tube. The assumption of low Reynolds number and long wavelength have been used to simplify the complicated problem into relatively simple problem. Two types of analytical solutions named as perturbation solution and solution have been evaluated for velocity, temperature and concentration field. The expression for pressure rise and frictional forces are calculated using numerical integration. In addition, the quantitative effects of pressure rise, frictional forces, temperature and concentration profile are displayed graphically. Trapping phenomena is also discussed at the end of the article.     

Numerical solution of the momentum and heat transfer equations for a hydromagnetic flow due to a stretching sheet of a non-uniform property micropolar liquid

A study of the hydromagnetic flow due to a stretching sheet and heat transfer in an incompressible micropolar liquid is made. Temperature-dependent thermal conductivity and a non-uniform heat source/sink render the problem analytically intractable and hence a numerical study is made using the shooting method based on Runge-Kutta and Newton-Raphson methods. The two problems of horizontal and vertical stretching are considered to implement the numerical method. The former problem involves one-way coupling between linear momentum and heat transport equations and the latter involves two-way coupling. Further, both the problems involve two-way coupling between the non-linear equations of conservation of linear and angular momentums. A similarity transformation arrived at for the problem using the Lie group method facilitates the reduction of coupled, non-linear partial differential equations into coupled, non-linear ordinary differential equations. The algorithm for solving the resulting coupled, two-point, non-linear boundary value problem is presented in great detail in the paper. Extensive computation on velocity and temperature profiles is presented for a wide range of values of the parameters, for prescribed surface temperature (PST) and prescribed heat flux (PHF) boundary conditions.     

Heat and mass transfer in MHD free convection from a moving permeable vertical surface by a perturbation technique

Numerical results are presented for heat and mass transfer effect on hydromagnetic flow of a moving permeable vertical surface. An analysis is performed to study the momentum, heat and mass transfer characteristics of MHD natural convection flow over a moving permeable surface. The surface is maintained at linear temperature and concentration variations. The non-linear coupled boundary layer equations were transformed and the resulting ordinary differential equations were solved by perturbation technique [Aziz A, Na TY. Perturbation methods in heat transfer. Berlin: Springer-Verlag; 1984. p. 1–184; Kennet Cramer R, Shih-I Pai. Magneto fluid dynamics for engineers and applied physicists 1973;166–7]. The solution is found to be dependent on several governing parameter, including the magnetic field strength parameter, Prandtl number, Schmidt number, buoyancy ratio and suction/blowing parameter, a parametric study of all the governing parameters is carried out and representative results are illustrated to reveal a typical tendency of the solutions. Numerical results for the dimensionless velocity profiles, the temperature profiles, the concentration profiles, the local friction coefficient and the local Nusselt number are presented for various combinations of parameters.     

Partial slip effects on the flow and heat transfer characteristics in a third grade fluid

This article looks at the slip effects on the flow and heat transfer of a third grade fluid past a porous plate. The resulting equations and boundary conditions are non-linear. The non-linear boundary condition is reduced into a linear one and a series solution of the problem is obtained using the homotopy analysis method (HAM). Variations of interesting parameters are seen on the velocity and temperature profiles.     

Flow,heat, and species transfer over a stretching plate considering coupled Stefan blowing effects from species transfer

In this paper, we investigate the flow, heat and mass transfer of a viscous fluid flow over a stretching sheet by including the blowing effects of mass transfer under high flux conditions. Mass transfer in this work means species transfer and is different from mass transpiration for permeable walls. The new contribution from this work is, for the first time, to consider the coupled blowing effects from massive species transfer on flow, heat, and species transfer for a stretching plate. Based on the exact solutions of the momentum equations, which are valid for the whole Navier–Stokes equations, the energy and mass transfer equations are solved exactly and the effects of the blowing parameter, the Schmidt number, and the Prandtl number on the flow, heat and mass transfer are presented and discussed. The solution is given in terms of an incomplete Gamma function. It is found the coupled blowing effects due to mass transfer can have significant influences on velocity profiles, drag, heat flux, as well as temperature and concentration profiles. These solutions provide rare results with closed form analytical expressions and can be used as benchmark problem for numerical code validation.     

Effects of thermophoresis on hydromagnetic mixed convection and mass transfer flow past a vertical permeable plate with variable suction and thermal radiation

The present paper deals with the effect of surface mass transfer on MHD mixed convection flow past a heated vertical flat permeable surface in the presence of thermophoresis, radiative heat flux and heat source/sink. Usual similarity transformations are introduced to obtain similarity solution, using regular perturbation technique. To observe physical insight and interesting aspects of the problem in the presence of thermophoresis, the non-dimensional velocity, temperature and concentration field are numerically studied and displayed graphically for pertinent parameters. It is observed that the thermophoresis has dominant effect on mass transfer mechanism in particle deposition process. The model finds applications in studying particulate deposition on turbine blades, removing small particles from gas streams and determining chemical vapor deposition rate in chemical industries.     

Free magnetohydrodynamic flow and convection from a vertical spinning cone with cross-diffusion effects

A study of cross-diffusion effects on convection from a vertically spinning cone under the influence of an external magnetic field is considered. The non-linear two-point boundary value problem governing the flow is solved numerically. Two different types of surface heating, namely linear surface temperature (LST) and linear surface heat flux (LSHF) are considered. A parametric study addressing the effects of various flow parameters on the fluid properties, the skin friction, heat and mass transfer coefficients is given.     

Mixed convection magnetohydrodynamic heat and mass transfer past a stretching surface in a micropolar fluid-saturated porous medium under the influence of Ohmic heating,Soret and Dufour effects

A numerical model is developed to examine the combined effects of Soret and Dufour on mixed convection magnetohydrodynamic heat and mass transfer in micropolar fluid-saturated Darcian porous medium in the presence of thermal radiation, non-uniform heat source/sink and Ohmic dissipation. The governing boundary layer equations for momentum, angular momentum (microrotation), energy and species transfer are transformed to a set of non-linear ordinary differential equations by using similarity solutions which are then solved numerically based on shooting algorithm with Runge–Kutta–Fehlberg integration scheme over the entire range of physical parameters with appropriate boundary conditions. The influence of Darcy number, Prandtl number, Schmidt number, Soret number and Dufour number, magnetic parameter, local thermal Grashof number and local solutal Grashof number on velocity, temperature and concentration fields are studied graphically. Finally, the effects of related physical parameters on local Skin-friction, local Nusselt number and local Sherwood number are also studied. Results showed that the fields were influenced appreciably by the Soret and Dufour effects, thermal radiation and magnetic field, etc.     

An implicit-Chebyshev pseudospectral method for the effect of radiation on power-law fluid past a vertical plate immersed in a porous medium

An implicit-Chebyshev collocation spectral method is employed in this study. This method was used to compute the problem of unsteady free convection with heat transfer from an isothermal vertical flat plate to a non-Newtonian fluid saturated porous medium, which is modeled as a power-law fluid. Boundary layer and Boussinesq approximations have been incorporated. The Darcy–Brinkman–Forchheimer model is applied to describe the flow field, where the magnetic field and the radiation effects are taken into account. Because of the non-Newtonian rheology, these problems are non-linear and must be solved numerically. The domain of the problem is discretized according to the implicit-Chebyshev spectral collocation scheme. In this study, the spatial derivatives are computed with a differentiation matrix and the time derivatives are computed with Crank–Nicolson implicit finite-difference method. Numerical calculations are carried out for the various parameters entering into the problem. Velocity and temperature profiles are shown in tables and graphically. It is found that as time approaches infinity, the values of friction factor and heat transfer coefficients approach the steady state values.     

粘性导电流体在磁场作用下流过多孔通道时传热传质振荡流的数值解——用于病理状态动脉中血液的流动

当血管内壁出现多孔性结构时,流过多孔性血管的血液将作不稳定的MHD流动.研究血液在其中的传热传质问题,考虑了与时间相关的渗透率和振荡引起的吸入速度,并数值地求解该问题.对分析中出现的参数取不同数值时,图形给出了速度、温度、浓度场,以及表面摩擦因数、Nusselt数和Sherwood数的计算结果.研究表明,血液流动受磁场和Grashof数的影响明显.     

Effect of viscous dissipation on natural convection heat and mass transfer from vertical cone in a non-Newtonian fluid saturated non-Darcy porous medium

In this paper we investigate the influence of viscous dissipation and Soret effect on natural convection heat and mass transfer from vertical cone in a non-Darcy porous media saturated with non-Newtonian fluid. The surface of the cone and the ambient medium are maintained at constant but different levels of temperature and concentration. The Ostwald-de Waele power law model is used to characterize the non-Newtonian fluid behavior. The governing equations are non-dimensionalized into non-similar form and then solved numerically by local non-similarity method. The effect of non-Darcy parameter, viscous dissipation parameter, Soret parameter, buoyancy ratio, Lewis number and the power-law index parameter on the temperature and concentration field as well as on the heat and mass transfer coefficients is analyzed.     

Effects of chemical reaction and variable viscosity on hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media with radiation

The effect of chemical reaction and variable viscosity on hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media has been studied in the presence of radiation and magnetic field. The plate surface is embedded in a uniform Darcian porous medium in order to allow for possible fluid wall suction or blowing and has a power-law variation of both the wall temperature and concentration. The similarity solution is used to transform the system of partial differential equations, describing the problem under consideration, into a boundary value problem of coupled ordinary differential equations, and an efficient numerical technique is implemented to solve the reduced system. Numerical calculations are carried out, for various values of the dimensionless parameters of the problem, which include a variable viscosity, chemical reactions, radiation, magnetic field, porous medium and power index of the wall temperature parameters. Comparisons with previously published works are performed and excellent agreement between the results is obtained. The results are presented graphically and the conclusion is drawn that the flow field and other quantities of physical interest are significantly influenced by these parameters.     

Effect of suction/injection on free convection along a vertical plate in a nanofluid saturated non-Darcy porous medium with internal heat generation

The effect of internal heat generation on free convection along a vertical plate embedded in a nanofluid saturated non-Darcy porous medium in the presence of suction/injection is analyzed. The non-linear governing equations and their associated boundary conditions are initially cast into dimensionless forms by non-dimensional variables. The resulting equations are solved numerically by an accurate, implicit, iterative finite-difference methodology and the obtained results are compared favorably with previously published work. A parametric study is performed to illustrate influence of the temperature exponent, non-Darcy, suction/injection, Brownian motion and thermophoresis parameters on the profiles of the velocity components, temperature and nanoparticle volume fraction. The numerical data for the heat and nanoparticle mass transfer rates have been tabulated for various parametric conditions.