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.     

Magnetohydrodynamic non-Darcy mixed convection heat transfer from a vertical heated plate embedded in a porous medium with variable porosity

A numerical model is developed to study magnetohydrodynamics (MHD) mixed convection from a heated vertical plate embedded in a Newtonian fluid saturated sparsely packed porous medium by considering the variation of permeability, porosity and thermal conductivity. The boundary layer flow in the porous medium is governed by Forchheimer–Brinkman extended Darcy model. The conservation equations that govern the problem are reduced to a system of non-linear ordinary differential equations by using similarity transformations. Because of non-linearity, the governing equations are solved numerically. The effects of magnetic field on velocity and temperature distributions are studied in detail by considering uniform permeability (UP) and variable permeability (VP) of the porous medium and the results are discussed graphically. Besides, skin friction and Nusselt number are also computed for various physical parameters governing the problem under consideration. It is found that the inertial parameter has a significant influence in increasing the flow field and the rate of heat transfer for variable permeability case. The important finding of the present work is that the magnetic field has considerable effects on the boundary layer velocity and on the rate of heat transfer for variable permeability of the porous medium. Further, the results obtained under the limiting conditions were found to be in good agreement with the existing ones.     

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.     

The effect of variable viscosity on MHD viscoelastic fluid flow and heat transfer over a stretching sheet

An analysis has been carried out to study the momentum and heat transfer characteristics in an incompressible electrically conducting non-Newtonian boundary layer flow of a viscoelastic fluid over a stretching sheet. The partial differential equations governing the flow and heat transfer characteristics are converted into highly non-linear coupled ordinary differential equations by similarity transformations. The effect of variable fluid viscosity, Magnetic parameter, Prandtl number, variable thermal conductivity, heat source/sink parameter and thermal radiation parameter are analyzed for velocity, temperature fields, and wall temperature gradient. The resultant coupled highly non-linear ordinary differential equations are solved numerically by employing a shooting technique with fourth order Runge–Kutta integration scheme. The fluid viscosity and thermal conductivity, respectively, assumed to vary as an inverse and linear function of temperature. The analysis reveals that the wall temperature profile decreases significantly due to increase in magnetic field parameter. Further, it is noticed that the skin friction of the sheet decreases due to increase in the Magnetic parameter of the flow characteristics.     

Effect of variable viscosity on MHD non-Darcy mixed convective heat transfer over a stretching sheet embedded in a porous medium with non-uniform heat source/sink

An analysis has been presented to investigate the effect of temperature-dependent viscosity on non-Darcy MHD mixed convective heat transfer past a porous medium by taking into account of Ohmic dissipation and non-uniform heat source/sink. Thermal boundary layer equation takes into account of viscous dissipation and Ohmic dissipation due to transverse magnetic field and electric field. The governing fundamental equations are first transformed into system of ordinary differential equations using self-similarity transformation and are solved numerically by using the fifth-order Runge–Kutta–Fehlberg method with shooting technique for various values of the physical parameters. The effects of variable viscosity, porosity, Eckert number, Prandtl number, magnetic field, electric field and non-uniform heat source/sink parameters on velocity and temperature profiles are analyzed and discussed. Favorable comparisons with previously published work on various special cases of the problem are obtained. Numerical results on the development of the local skin-friction co-efficient and local Nusselt number with non-uniform heat source/sink are tabulated for various physical parameters to show the interesting aspects of the solution.     

Combined effect of magnetic field and heat absorption on unsteady free convection and heat transfer flow in a micropolar fluid past a semi-infinite moving plate with viscous dissipation using element free Galerkin method

The fully developed electrically conducting micropolar fluid flow and heat transfer along a semi-infinite vertical porous moving plate is studied including the effect of viscous heating and in the presence of a magnetic field applied transversely to the direction of the flow. The Darcy-Brinkman-Forchheimer model which includes the effects of boundary and inertia forces is employed. The differential equations governing the problem have been transformed by a similarity transformation into a system of non-dimensional differential equations which are solved numerically by element free Galerkin method. Profiles for velocity, microrotation and temperature are presented for a wide range of plate velocity, viscosity ratio, Darcy number, Forchhimer number, magnetic field parameter, heat absorption parameter and the micropolar parameter. The skin friction and Nusselt numbers at the plates are also shown graphically. The present problem has significant applications in chemical engineering, materials processing, solar porous wafer absorber systems and metallurgy.     

Perturbation analysis of unsteady magnetohydrodynamic convective heat and mass transfer in a boundary layer slip flow past a vertical permeable plate with thermal radiation and chemical reaction

An analytical study for the problem of unsteady mixed convection with thermal radiation and first-order chemical reaction on magnetohydrodynamics boundary layer flow of viscous, electrically conducting fluid past a vertical permeable plate has been presented. Slip boundary condition is applied at the porous interface. The classical model is used for studying the effect of radiation for optically thin media. The non-linear coupled partial differential equations are solved by perturbation technique. The results obtained show that the velocity, temperature and concentration fields are appreciably influenced by the presence of chemical reaction, thermal stratification and magnetic field. It is observed that the effect of thermal radiation and magnetic field decreases the velocity, temperature and concentration profiles in the boundary layer. Also, the effects of the various parameters on the skin-friction coefficient and the rate of heat transfer at the surface are discussed.     

Buoyancy and chemical reaction effects on MHD mixed convection heat and mass transfer in a porous medium with thermal radiation and Ohmic heating

The combined effect of mixed convection with thermal radiation and chemical reaction on MHD flow of viscous and electrically conducting fluid past a vertical permeable surface embedded in a porous medium is analyzed. The heat equation includes the terms involving the radiative heat flux, Ohmic dissipation, viscous dissipation and the internal absorption whereas the mass transfer equation includes the effects of chemically reactive species of first-order. The non-linear coupled differential equations are solved analytically by perturbation technique. The results obtained show that the velocity, temperature and concentration fields are appreciably influenced by the presence of chemical reaction, thermal stratification and magnetic field. It is observed that the effect of thermal radiation and magnetic field is to decrease the velocity, temperature and concentration profiles in the boundary layer. There is also considerable effect of magnetic field and chemical reaction on skin-friction coefficient and Nusselt number.     

Non-Darcy unsteady mixed convection flow near the stagnation point on a heated vertical surface embedded in a porous medium with thermal radiation and variable viscosity

The unsteady mixed convection boundary layer flow near the stagnation point on a heated vertical plate embedded in a fluid saturated porous medium is studied. It is assumed that the unsteadiness is caused by the impulsive motion of the free stream velocity and by sudden increase in the surface temperature. Both the buoyancy assisting and the buoyancy opposing flow situations are considered with combined effects of the first and second order resistance of solid matrix of non-Darcy porous medium, variable viscosity and radiation. The problem is reduced to a system of non-dimensional partial differential equations, which is solved numerically using the Keller-box method. The features of the flow and the heat transfer characteristics for different values of the governing parameters are analyzed and discussed. The surface shear stress and the heat transfer of the present study are compared with the available results and a good agreement is found.     

Effects of radiation and variable viscosity on unsteady MHD flow of a rotating fluid from stretching surface in porous medium

This work is focused on the study of unsteady magnetohydrodynamics boundary-layer flow and heat transfer for a viscous laminar incompressible electrically conducting and rotating fluid due to a stretching surface embedded in a saturated porous medium with a temperature-dependent viscosity in the presence of a magnetic field and thermal radiation effects. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. With appropriate transformations, the unsteady MHD boundary layer equations are reduced to local nonsimilarity equations. Numerical solutions of these equations are obtained by using the Runge–Kutta integration scheme as well as the local nonsimilarity method with second order truncation. Comparisons with previously published work have been conducted and the results are found to be in excellent agreement. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity in primary and secondary flows as well as the local skin-friction coefficients and the local Nusselt number are illustrated graphically to show interesting features of Darcy number, viscosity-variation, magnetic field, rotation of the fluid, and conduction radiation parameters.     

Group method analysis of combined heat and mass transfer by MHD non-Darcy non-Newtonian natural convection adjacent to horizontal cylinder in a saturated porous medium

The group theoretic method is applied for solving problem of combined magneto-hydrodynamic heat and mass transfer of non-Darcy natural convection about an impermeable horizontal cylinder in a non-Newtonian power law fluid embedded in porous medium under coupled thermal and mass diffusion, inertia resistance, magnetic field, thermal radiation effects. The application of one-parameter groups reduces the number of independent variables by one and consequently, the system of governing partial differential equations with the boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions. The ordinary differential equations are solved numerically for the velocity using shooting method. The effects of magnetic parameter M, Ergun number Er, power law (viscosity) index n, buoyancy ratio N, radiation parameter R_d, Prandtl number Pr and Lewis number Le on the velocity, temperature fields within the boundary layer, heat and mass transfer are presented graphically and discussed.     

Effects of chemical reaction and radiation on an unsteady MHD flow past an accelerated infinite vertical plate with variable temperature and mass transfer

This paper deals with the study of the effects of first order chemical reaction and radiation on an unsteady MHD flow of an incompressible viscous electrically conducting fluid past an accelerated infinite vertical plate with variable temperature and mass transfer. The resulting approximate dimensionless system of governing partial differential equations are integrated in closed form by the Laplace transform technique A uniform magnetic field is assumed to be applied transversely to the direction of the flow. Rosseland model of radiation has been chosen in the investigation, the expressions for the velocity field, temperature field and concentration field and skin-friction in the direction of the flow, coefficient of heat transfer and mass flux at the plate have been obtained in non-dimensional form and these are illustrated graphically for various physical parameters involved in the study. Investigation reveals that the fluid velocity is decelerated in the region adjacent to the plate, due to the effect of first order chemical reaction and the rate of heat transfer (from plate to the fluid) decreases due to the absorption of thermal radiation. The results obtained in this work are consistent with physical situation of the problem.     

Magnetohydrodnamics nanofluid flow of shaped nanoparticles over a porous stretching wall and slip effect

In this study, we analyze the magnetohydrodynamic flow of magnetite-engine oil nanofluid in the presence of nonidentical shaped nanoparticles subject to the porous medium and velocity slip effect. Energy analysis is carried out with the Ohmic heating and thermal radiation impacts. The system of partial differential equations are transformed into the system of ordinary differential equations using similarity variable. The Hamilton–Crosser model is used. The exact solutions for the momentum and heat transport analysis are found. The impact of various emerging parameters on the velocity and temperature profiles are analyzed by graphs. Furthermore, the local skin friction and heat transfer rate are examined graphically. It is examined that the velocity field increases with an increment in the magnitude of ϕ and L. An increase in the value of Hartman number enhancing the temperature profile.     

Nonsimilar boundary layer analysis of double-diffusive convection from a vertical truncated cone in a porous medium with variable viscosity

This work presents a boundary layer analysis about variable viscosity effects on the double-diffusive convection near a vertical truncated cone in a fluid-saturated porous medium with constant wall temperature and concentration. The viscosity of the fluid is assumed to be an inverse linear function of the temperature. A boundary layer analysis is employed to derive the nondimensional nonsimilar governing equations, and the transformed boundary layer governing equations are solved by the cubic spline collocation method to yield computationally efficient numerical solutions. The obtained results are found to be in good agreement with previous papers on special cases of the problem. Results for local Nusselt and Sherwood numbers are presented as functions of viscosity-variation parameter, buoyancy ratio, and Lewis number. For a porous medium saturated with a Newtonian fluid with viscosity proportional to an inverse linear function of temperature, higher value of viscosity-variation parameter leads to the decrease of the viscosity in fluid flow, thus increasing the fluid velocity as well as the local Nusselt number and the local Sherwood number.     

MHD non-Darcy mixed convective diffusion of species over a stretching sheet embedded in a porous medium with non-uniform heat source/sink, variable viscosity and Soret effect

The effects of temperature dependent viscosity and non-uniform heat source/sink on non-Darcy MHD mixed convection boundary layer flow over a vertical stretching sheet embedded in a fluid-saturated porous media is studied in this paper. Boundary layer equations are transformed into ordinary differential equations using self-similarity transformation which are then solved numerically using fifth-order Runge-Kutta-Fehlberg method with shooting technique for various values of the governing parameters. The effects of variable viscosity, porosity, electric field parameter, non-uniform heat source/sink parameters, Soret number and Schmidt number on concentration profiles are analyzed and discussed. Favorable comparisons with previously published work on various special cases of the problem are obtained. Numerical results for variation of the local Sherwood number with buoyancy parameter, Schmidt number, and Soret number are reported graphically to show some interesting aspects of the physical parameters.     

Influence of temperature-dependent viscosity and thermal radiation on MHD forced convection over a non-isothermal wedge

An analysis has been carried out to study heat transfer characteristics of an incompressible Newtonian electrically conducting and heat generating/absorbing fluid having temperature-dependent viscosity over a non-isothermal wedge in the presence of thermal radiation. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The wedge surface is assumed to be permeable so as to allow for possible wall suction or injection. The effects of viscous dissipation, Joule heating, stress work and thermal radiation are included in the model. The governing differential equations are derived and transformed using a non-similarity transformation. The transformed equations are solved numerically by applying a fifth-order Runge-Kutta-Fehlberg scheme with shooting technique. Favorable comparisons with previously published work on various special cases of the problem are obtained. Numerical results for the velocity and temperature profiles for a prescribed magnetic field parameter as well as the development of the local skin-friction coefficient and local Nusselt number with the magnetic field and radiation parameters are presented graphically and in tabulated form to elucidate the influence of the various physical parameters.     

Hydromagnetic non-Darcy flow and heat transfer over a stretching sheet in the presence of thermal radiation and Ohmic dissipation

Non-Darcy flow and heat characteristics over a stretching sheet is presented here by taking into account of Ohmic dissipation and thermal radiation effects. The governing fundamental equations are first transformed into system of ordinary differential equations using self-similarity transformation and they are then solved numerically by using the fifth-order Runge–Kutta–Fehlberg method with shooting technique for some values of the physical parameters. Important features of the flow and heat transfer characteristic for different values of thermal radiation, magnetic and electric fields are analyzed and discussed. Favorable comparisons with previously published work on various special cases of the problem are obtained. Numerical results for the velocity and temperature profiles for a prescribed magnetic field and electric field parameter as well as the development of the local skin-friction coefficient and local Nusselt number with radiation parameters are reported graphically for various parametric conditions to show interesting aspects of the numerical solution.     

Soret and Dufour effects on MHD slip flow with thermal radiation over a porous rotating infinite disk

In this investigation, thermal radiation effect over an electrically conducting, Newtonian fluid in a steady laminar magnetohydrodynamic convective flow over a porous rotating infinite disk with the consideration of heat and mass transfer in the presence of Soret and Dufour diffusion effects is investigated. The partial differential equations governing the problem under consideration are transformed by a similarity transformation into a system of ordinary differential equations which are solved numerically using fourth order Runge–Kutta based shooting method. The effects of the magnetic interaction parameter, slip flow parameter, Soret number, Dufour number, Schmidt number, radiation parameter, Prandtl number and suction parameter on the fluid velocity, temperature and concentration distributions in the regime are depicted graphically and are analyzed in detail. The corresponding skin-friction coefficients, the Nusselt number and the Sherwood number are also calculated and displayed in tables showing the effects of various parameters on them.     

Lie group analysis of unsteady MHD three dimensional by natural convection from an inclined stretching surface saturated porous medium

Lie group method is investigated for solving the problem of heat transfer in an unsteady, three-dimensional, laminar, boundary-layer flow of a viscous, incompressible and electrically conducting fluid over inclined permeable surface embedded in porous medium in the presence of a uniform magnetic field and heat generation/absorption effects. A uniform magnetic field is applied in the y-direction and a generalized flow model is presented to include the effects of the macroscopic viscous term and the microscopic permeability of porous medium. The infinitesimal generators accepted by the equations are calculated and the extension of the Lie algebra for the problem is also presented. The restrictions imposed by the boundary conditions on the generators are calculated. The investigation of the three-independent-variable partial differential equations is converted into a two-independent-variable system by using one subgroup of the general group. The resulting equations are solved numerically with the perturbation solution for various times. Velocity, temperature and pressure profiles, surface shear stresses, and wall-heat transfer rate are discussed for various values of Prandtl number, Hartmann number, Darcy number, heat generation/absorption coefficient, and surface mass-transfer coefficient.