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.     

On the analytical solution for MHD natural convection flow and heat generation fluid in porous medium

Homotopy analysis method (HAM) is employed to investigate the momentum, heat and mass transfer characteristics of MHD natural convection flow and heat generation fluid driven by a continuously moving permeable surface immersed in a fluid saturated porous medium. The solution is found to be dependent on several governing parameters, including the magnetic field strength parameter, Prandtl number, Darcy number, the dimensionless inertia coefficient, the dimensionless heat generation/absorption coefficient and the dimensionless suction/blowing coefficient. A parametric study of all governing parameters is carried out and representative results are illustrated to reveal a typical tendency of the solutions. Representative results are presented for velocity and temperature distributions as well as the local friction coefficient and local Nusselt number. Finally, a proper discussion is derived on the obtained results and some remarkable conclusions are mentioned.     

Effect of Hall currents and chemical reaction on hydromagnetic flow of a stretching vertical surface with internal heat generation/absorption

The problem of steady, laminar, hydromagnetic, simultaneous heat and mass transfer by laminar flow of a Newtonian, viscous, electrically conducting and heat generating/absorbing fluid over a continuously stretching surface in the presence of the combined effect of Hall currents and mass diffusion of chemical species with first and higher order reactions is investigated. The fluid is permeated by a strong transverse magnetic field imposed perpendicularly to the plate on the assumption of a small magnetic Reynolds number. Certain transformations are employed to transform the governing differential equations to a local similarity form which are solved numerically. Comparisons with previously published work have been conducted and the results are found to be in good agreement. A parametric study is performed to illustrate the influence of the magnetic field parameter, Hall parameter, the coefficients of space-dependent and temperature-dependent internal heat generation/absorption, the chemical reaction parameter and order of reaction on the fluid velocity, temperature and concentration distributions. Numerical data for the local skin-friction coefficient, the local Nusselt number and the local Sherwood number have been tabulated for various values of parametric conditions.     

Numerical investigation of transient heat transfer to hydromagnetic channel flow with radiative heat and convective cooling

This present study consists of a numerical investigation of transient heat transfer in channel flow of an electrically conducting variable viscosity Boussinesq fluid in the presence of a magnetic field and thermal radiation. The temperature dependent nature of viscosity is assumed to follow an exponentially model and the system exchanges heat with the ambient following Newton’s law of cooling. The governing nonlinear equations of momentum and energy transport are solved numerically using a semi-implicit finite difference method. Solutions are presented in graphical form and given in terms of fluid velocity, fluid temperature, skin friction and heat transfer rate for various parametric values. Our results reveal that combined effect of thermal radiation, magnetic field, viscosity variation and convective cooling have significant impact in controlling the rate of heat transfer in the boundary layer region.     

均匀自由流动的非牛顿流体中连续表面上的磁流体动力学流动和热传递

分析在平行自由流动的非牛顿黏弹性导电流体中,连续平展表面移动时的稳态流和热传递特性,该流动处于横向均匀磁场作用下.以二阶流体构建它的本构方程,得到了速度分布和温度断面图的数值结果.讨论了诸如黏弹性参数、磁场参数和Prandtl数等不同物理参数对诸种动量和热传递特性的影响,并给出相关图示.     

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.     

The influence of heat and mass transfer on MHD peristaltic flow through a porous space with compliant walls

The present study investigates the effects of heat and mass transfer on peristaltic transport in a porous space with compliant walls. The fluid is electrically conducting in the presence of a uniform magnetic field. Analytic solution is carried out under long-wavelength and low-Reynolds number approximations. The expressions for stream function, temperature, concentration and heat transfer coefficient are obtained. Numerical results are graphically discussed for various values of physical parameters of interest.     

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.     

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.     

Biomagnetic viscoelastic fluid flow over a stretching sheet

Of concern in this paper is an investigation of biomagnetic flow of a non-Newtonian viscoelastic fluid over a stretching sheet under the influence of an applied magnetic field generated owing to the presence of a magnetic dipole. The viscoelasticity of the fluid is characterised by Walter’s B fluid model. The applied magnetic field has been considered to be sufficiently strong to saturate the ferrofluid. The magnetization of the fluid is considered to vary linearly with temperature as well as the magnetic field intensity. The theoretical treatment of the physical problem consists of reducing it to solving a system of non-linear coupled differential equations that involve six parameters, which are solved by developing a finite difference technique. The velocity profile, the skin-friction, the wall pressure and the rate of heat transfer at the sheet are computed for a specific situation. The study shows that the fluid velocity increases as the rate of heat transfer decreases, while the local skin-friction and the wall pressure increase as the magnetic field strength is increased. It is also revealed that fluid viscoelasticity has an enhancing effect on the local skin-friction. The study will have an important bearing on magnetic drug targeting and separation of red cells as well as on the control of blood flow during surgery.     

Electrohydrodynamic linear stability of finitely conducting flows through porous fluids with mass and heat transfer

In this work, a linear stability analysis is used to investigate a capillary surface waves between two horizontal finite fluid layers. The system is acted upon by a vertical periodic electric field. The problem examines few representatives of porous media. It is also includes finite conductivity, mass and heat transfer. It is assumed that the basic flow is two-dimensional streaming flow. A general dispersion relation governing the linear stability is derived. In contrast with our previous work [23], the present problem shows that the stability criterion depends on the mass and heat transfer parameter. The present study recovers some special cases upon appropriate data choices. The presence of finite conductivity’s together with the dielectric permeability’s make the uniform electric field plays a dual role in the stability criterion. This shows some analogy with the nonlinear stability theory. In addition, the mass and heat transfer parameter as well as the Darcy’s coefficients play a stabilizing role in the stability picture. In case of the Rayleigh–Taylor instability, by means of the Whittaker technique, the parametric excitation of the electrohydrodynamic surface waves is obtained. The transition curve equations are calculated up to the fourth order for a small dimensionless parameter. The analytical results are numerically confirmed.     

Multi-Fracture Reservoir Simulations for Long Time Physical Processes

Reservoirs with multi-fracture techniques are developed and frequently used for oil and gas industry. Recently, they are also used for deep geothermal reservoirs especially for Hot Dry Rock (HDR). The analysis of the reservoir is generally interested in long time physical properties (10–100 years), e.g. fluid flow, heat transport etc. Typical CFD simulations are limited in this context. Here we developed a fluid flow and heat transport modeling in a multi-fracture reservoir based on the so-called Mixed Dimensional Model (MDM), which describes the different characteristic flows and the heat transport in different dimensions. In the mathematical point of view, these models are discretized based on the Cellular Automaton (CA) method combined with other necessary numerical techniques. The different cases of fluid flow and heat transport in multi-fracture reservoirs have been simulated and shown physical results very reasonably with less computational time. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the effectiveness of viscous dissipation and Joule heating on steady Magnetohydrodynamic heat and mass transfer flow over an inclined radiate isothermal permeable surface in the presence of thermophoresis

The combined effect of viscous dissipation and joule heating on steady Magnetohydrodynamic heat and mass transfer flow of viscous incompressible fluid over an inclined radiate isothermal permeable surface in the presence of thermophoresis is studied. Numerical results for the dimensionless velocity, temperature and concentration profiles as well as the local skin-friction coefficient, the local Nusselt number and the local Stanton number are displayed graphically for various physical parameters. Comparisons with previously published work are performed and the results are found to be in very good agreement. Results show that rate of heat transfer is sensitive for increasing angle of inclination parameter for the case of fluid injection and it decreases with the increase of magnetic field parameter and Eckert number.     

Finite element modeling of a leaking third component migration from a heat source buried into a fluid saturated porous medium

A finite element model for a leaking species migration from a heat source buried into a fluid saturated porous medium is demonstrated. A semi-implicit algorithm is coupled with the velocity correction procedure to solve the transient equations of the generalised porous medium model. A parametric study is carried out for different Darcy and Rayleigh numbers and size of the leaking hole. The results show that the leaking hole size has a significant effect on migration of the third component into the porous medium.     

Effect of Second Order Chemical Reaction on MHD Free Convective Radiating Flow over an Impulsively Started Vertical Plate

An attempt has been made to study laminar convective heat and mass transfer flow of an incompressible, viscous and electrically conducting fluid over an impulsively started vertical plate with conduction-radiation embedded in a porous medium in presence of transverse magnetic field. The influence of both second order chemical reaction and heat generation are taken into account. The governing coupled partial differential equations are solved by Crank-Nicolson method. The effects of important physical parameters on the velocity, temperature and concentration have been analyzed through graphs. The results of the present study agree well with the previous solutions. Applications of the present study are shown in material processing systems and different industries. The important findings of present study are: chemical reaction parameter acts as resistive force to reduce the velocity whereas heat source parameter enhances the velocity.     

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.     

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.     

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.     

Some exact solutions for fractional generalized Burgers’ fluid in a porous space

This work is concerned with deriving the equation for describing the magnetohydrodynamic (MHD) flow of a fractional generalized Burgers’ fluid in a porous space. Modified Darcy's law has been taken into account. Closed form solutions for velocity are obtained in three problems. The solutions for Navier–Stokes, second grade, Maxwell, Oldroyd-B and Burgers’ fluids appear as the limiting cases of the obtained solutions. A parametric study of some physical parameters involved in the problems is performed to illustrate the influence of these parameters on the velocity profiles.     

The effects of heat exchange and fluid production on the ignition of a porous solid

In this paper we study a system of nonlinear parabolic equations representing the evolution of small perturbations in a model describing the combustion of a porous solid. The novelty of this system rests on allowing the fluid and solid phases to assume different temperatures, as opposed to the well-studied single-temperature model in which heat is assumed to be exchanged at an infinitely rapid rate. Moreover, the underlying model incorporates fluid creation, as a result of reaction, and this property is inherited by the perturbation system. With respect to important physico-chemical parameters we look for global and blowing-up solutions, both with and without heat loss and fluid production. In this context, blowup can be identified with thermal runaway, from which ignition of the porous solid is inferred (a self-sustaining combustion wave is generated). We then proceed to study the existence and uniqueness of a particular class of steady states and examine their relationship to the corresponding class of time-dependent problems. This enables us to extend the global-existence results, and to indicate consistency between the time-independent and time-dependent analyses. In order to better understand the effects of distinct temperatures in each phase, a number of our results are then compared with those of a corresponding single-temperature model. We find that the results coincide in the appropriate limit of infinite heat-exchange rate. However, when the heat exchange is finite the blowup results can be altered substantially.