Thermal radiation effect on mixed convection heat and mass transfer of a non-Newtonian fluid over a vertical surface embedded in a porous medium in the presence of thermal diffusion and diffusion-thermo effects

Thermal radiation, thermal diffusion, and diffusion-thermo effects on heat and mass transfer by mixed convection of non-Newtonian power-law fluids over a vertical permeable surface embedded in a saturated porous medium are investigated. The governing equations describing the problem are non-dimensionalized and transformed into a non-similar form. The transformed equations are solved by using the local non-similarity method combined with the shooting technique. The effects of the physical parameters of the problem on the fluid temperature and concentration are illustrated graphically and analyzed. Also, the effects of the pertinent parameters on the local Nusselt number and the local Sherwood number are presented.     

Transient free convection with mass transfer MHD micropolar fluid in a porous plate by the network method

The transient problem of coupled heat and mass transfer of a micropolar fluid in magneto‐hydrodynamic free convection from a vertical infinite porous plate with an exponentially decaying heat generating considering the viscous dissipation and ohmic heating effects is studied. Joule heating must be considered when the viscous dissipation and the Prandtl number are large. The non‐dimensional equations for the conservation of mass, momentum, energy and concentration are solved by means a numerical technique based on electric analogy (network simulation method). This method provides the numerical response of the system by running the network in circuit resolution software with the solution to both transient and steady‐state problems at the same time, and its programming does not require manipulation of the sophisticated mathematical software that is inherent in other numerical methods. The effects of the material parameters, viscous dissipation, internal generation and Joule heating on velocity, angular momentum and temperature fields across the boundary layer are investigated. In addition, the skin‐friction coefficient, couple stress coefficient, Nusselt number and Sherwood number are shown in tabular form. The numerical results for velocity and temperature distributions of micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid. Copyright © 2007 John Wiley & Sons, Ltd.     

Free convection boundary layer flow of a micropolar fluid past slender cones

Using the theory of micropolar fluids developed by Eringen, the transverse curvature effects on axisymmetric free convection boundary layer flow of a micropolar fluid past slender vertical cones are investigated. The case of constant surface heat flux is considered in this paper. Using perturbation techniques, the governing equations for momentum, angular momentum and energy have been solved numerically. Graphical representations for the velocity, angular velocity and thermal functions are presented for various physical and fluid property parameters.     

Convection from a stretching surface with suction and power-law variation in species concentration

The problem of laminar natural convection flow from a permeable semi-infinite accelerating vertical surface that is coated with a reacting chemical species is studied. The plate velocity and the species concentration vary as power laws. The fundamental parameters of the problem are the Schmidt number, the surface permeability and the reaction rate. The governing equations were transformed to a non-similar form and then solved analytically and numerically using the Keller box method. A parametric study illustrating the effects of the flow parameters on the velocity and the concentration fields was conducted and the physical aspects of the problem discussed. The study found, inter alia, that the fluid motion is decelerated by increases in the permeability of the accelerating surface and that the rate of mass transfer increases with Schmidt numbers but reduces with increasing reaction rates and the porosity of the accelerating surface.     

Effects of surface mass transfer on unsteady mixed convection flow over a vertical cone with chemical reaction

The unsteady mixed convection boundary layer flow over a vertical cone is considered to investigate the combined effects of the buoyancy force, thermal and mass diffusion in the presence of the first order chemical reaction and surface mass transfer. The unsteadiness is caused by the time dependent free stream velocity varying arbitrarily with time. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting system of coupled non-linear partial differential equations is solved numerically by the combination of quasi-linearization technique and an implicit finite difference scheme. Numerical computations are performed for different values of the parameters to display the velocity, temperature and concentration profiles graphically. Both accelerating and decelerating free stream velocities are considered. Numerical results are presented for the velocity, temperature and concentration profiles as well as for the skin-friction coefficient, local Nusselt number and local Sherwood number. The obtained results are compared with previously reported ones and are found to be in excellent agreement.     

MHD Flow and heat transfer of non-Newtonian power-law fluid with diffusion and chemical reaction on a moving cylinder

The problem of flow and heat transfer of an electrically conducting non-Newtonian fluid over a continuously moving cylinder in the presence of a uniform magnetic field is analyzed for the case of power-law variation in the temperature and concentration at the cylinder surface. A diffusion equation with a chemical reaction source term is taken into account. The governing non-similar partial differential equation are solved numerically by employing shooting method. The effects of various parameters on the velocity, temperature and concentration profiles as well as the heat and mass transfer rate from the cylinder surface to the surrounding fluid are presented graphically and in tabulated form.     

Effect of thermo‐solutal stratification on recirculation flow patterns in a backward‐facing step channel flow

This paper presents results on the combined effect of thermo‐solutal buoyancy forces on the recirculatory flow behavior in a horizontal channel with backward‐facing step and the ensuing impact on heat and mass transfer phenomena. The governing equations for double diffusive mixed convection are represented in velocity–vorticity form of momentum equations, velocity Poisson equations, energy and concentration equations. Galerkin's finite‐element method has been employed to solve the governing equations. Recirculatory flow fields with heat and mass transfer are simulated for opposing and aiding thermo‐solutal buoyancy forces by assuming suitable boundary conditions for energy and concentration equations. The effect of Richardson number (0.1?Ri?10) and buoyancy ratio (?10?N?10) on the recirculation bubble and Nusselt and Sherwood numbers are studied in detail. For Richardson number greater than unity, distinct variations in the gradients of Nusselt number and Sherwood number with buoyancy ratio are observed for flow regimes with opposing and aiding buoyancy forces. Copyright © 2009 John Wiley & Sons, Ltd.     

Scaling Transformation for the Effect of Temperature-Dependent Fluid Viscosity with Thermophoresis Particle Deposition on MHD-Free Convective Heat and Mass Transfer Over a Porous Stretching Surface

This article concerns with a steady two-dimensional flow of an electrically conducting incompressible fluid over a vertical stretching sheet. The flow is permeated by a uniform transverse magnetic field. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equations. The system remains invariant due to some relations among the parameters of the transformations. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation, and two second-order ordinary differential equations corresponding to energy and diffusion equations are derived. The equations along with the boundary conditions are solved numerically. It is found that the decrease in the temperature-dependent fluid viscosity makes the velocity to decrease with the increasing distance of the stretching sheet. At a particular point of the sheet, the fluid velocity decreases with the decreasing viscosity but the temperature increases in this case. Impact of thermophoresis particle deposition in the presence of temperature-dependent fluid viscosity plays an important role on the concentration boundary layer. The results, thus, obtained are presented graphically and discussed.     

Homotopy simulation of nanofluid dynamics from a non-linearly stretching isothermal permeable sheet with transpiration

In this article we derive semi-analytical/numerical solutions for transport phenomena (momentum, heat and mass transfer) in a nanofluid regime adjacent to a nonlinearly porous stretching sheet by means of the Homotopy analysis method (HAM). The governing equations are reduced to a nonlinear, coupled, non-similar, ordinary differential equation system via appropriate similarity transformations. This system is solved under physically realistic boundary conditions to compute stream function, velocity, temperature and concentration function distributions. The results of the present study are compared with numerical quadrature solutions employing a shooting technique with excellent correlation. Furthermore the current HAM solutions demonstrate very good correlation with the non-transpiring finite element solutions of Rana and Bhargava (Commun. Nonlinear Sci. Numer. Simul. 17:212–226, 2012). The influence of stretching parameter, transpiration (wall suction/injection) Prandtl number, Brownian motion parameter, thermophoresis parameter and Lewis number on velocity, temperature and concentration functions is illustrated graphically. Transpiration is shown to exert a substantial influence on flow characteristics. Applications of the study include industrial nanotechnological fabrication processes.     

Mixed convection effects on heat and mass transfer in a non Newtonian fluid with chemical reaction over a vertical plate

This paper studies mixed convection, double dispersion and chemical reaction effects on heat and mass transfer in a non-Darcy non-Newtonian fluid over a vertical surface in a porous medium under the constant temperature and concentration. The governing boundary layer equations, namely, momentum, energy and concentration, are converted to ordinary differential equations by introducing similarity variables and then are solved numerically by means of fourth-order Runge-Kutta method coupled with double-shooting technique. The velocity, temperature concentration, heat and mass transfer profiles are presented graphically for various values of the parameters, and the influence of viscosity index n, thermal and solute dispersion, chemical reaction parameter χ are observed.     

Pulsatile magneto-biofluid flow and mass transfer in a non-Darcian porous medium channel

A numerical study of pulsatile flow and mass transfer of an electrically conducting Newtonian biofluid via a channel containing porous medium is considered. The conservation equations are transformed and solved under boundary conditions prescribed at both walls of the channel, using a finite element method with two-noded line elements. The influence of magnetic field on the flow is studied using the dimensionless hydromagnetic number, Nm, which defines the ratio of magnetic (Lorentz) retarding force to the viscous hydrodynamic force. A Darcian linear impedance for low Reynolds numbers is incorporated in the transformed momentum equation and a second order drag force term for inertial (Forchheimer) effects. Velocity and concentration profiles across the channel width are plotted for various values of the Reynolds number (Re), Darcy parameter (λ), Forchheimer parameter (Nf), hydro-magnetic number (Nm), Schmidt number (Sc) and also with dimensionless time (T). Profiles of velocity varying in space and time are also provided. The conduit considered is rigid with a pulsatile pressure applied via an appropriate pressure gradient term. Increasing the hydromagnetic number (Nm) from 1 to 15 considerably depresses biofluid velocity (U) indicating that a magnetic field can be used as a flow control mechanism in, for example, medical applications. A rise in Nf from 1 to 20 strongly retards the flow development and decreases the velocity, U, across the width of the channel. The effects of other parameters on the flowfield are also discussed at length. The flow model also has applications in the analysis of electrically conducting haemotological fluids flowing through filtration media, diffusion of drug species in pharmaceutical hydromechanics, and also in general fluid dynamics of pulsatile systems.     

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.     

Squeezed flow and heat transfer over a porous surface for viscous fluid

Flow and heat transfer over a permeable sensor surface placed in a squeezing channel is analyzed. A constant transpiration through the sensor surface is assumed. Locally non-similar momentum and energy equations are solved by three different methods, against the transpiration parameter τ, for different values of the squeezing parameter b, and Prandtl number Pr. From the investigation, it is found that when the channel being squeezed, the skin-friction reduces but the heat transfer coefficient increases. Increase in the value of the squeezing parameter onsets reverse flow at the sensor surface when fluid is being injected and the affect is enhanced with the increase of injection through the surface. It is further observed that increase of suction of fluid through the sensor thins the thermal and the momentum boundary layer regions, whereas injection of fluid leads to thickening of both the thermal and the momentum boundary layer regions. Heat transfer from the surface of the sensor increases with the increase of the value of Pr for the entire range of surface mass-flux parameter τ. M. A. Hossain is on leave of absence from University of Dhaka.     

Thermal radiation effects on MHD flow past a semi-infinite inclined plate in the presence of mass diffusion

MHD mixed free-forced heat and mass convective steady incompressible laminar boundary layer flow of a gray optically thick electrically conducting viscous fluid past a semi-infinite inclined plate for high temperature and concentration differences is studied. A uniform magnetic field is applied perpendicular to the plate. The density of the fluid is assumed to reduce exponentially with temperature and concentration. The usual Boussinesq approximation is neglected due to the high temperature and concentration differences between the plate and the ambient fluid. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The boundary layer equations governing the flow are reduced to ordinary differential equations, which are numerically solved by applying an efficient technique. The effects of the density/temperature parameter n, the density/concentration parameter m, the local magnetic parameter M_x and the radiation parameter R are examined on the velocity, temperature and concentration distributions as well as the coefficients of skin-friction, heat flux and mass flux.     

Free convection through conducting non-Newtonian fluids over a thin axisymmetric body

An analysis of free convection heat transfer in electrically conducting power law non-Newtonian fluid over a thin axisymmetric body of constant temperature is carried out. The uniform external magnetic field acts normally to the surface through the induced boundary layer. In view of the fact that most of the non-Newtonian fluids have large Prandtl number, the momentum equation is simplified. The equations of conservation of mass, momentum and energy which govern and describe the flow and heat transfer are solved numerically. The effect of the magnetic field on the velocity, temperature, the coefficient of friction and the Nusselt number are investigated. Numerical results are tabulated, presented graphically and discussed.     

Simultaneous heat and mass transfer by natural convection from a plate embedded in a porous medium with thermal dispersion effects

The problem of steady, laminar, simultaneous heat and mass transfer by natural convection flow over a vertical permeable plate embedded in a uniform porous medium in the presence of inertia and thermal dispersion effects is investigated for the case of linear variations of both the wall temperature and concentration with the distance along the plate. Appropriate transformations are employed to transform the governing differential equations to a non-similar form. The transformed equations are solved numerically by an efficient implicit, iterative, finite-difference scheme. The obtained results are checked against previously published work on special cases of the problem and are found to be in good agreement. A parametric study illustrating the influence of the porous medium effects, heat generation or absorption, wall suction or injection, concentration to thermal buoyancy ratio, thermal dispersion parameter, and the Schmidt number on the fluid velocity, temperature and concentration as well as the skin-friction coefficient and the Nusselt and Sherwood numbers is conducted. The results of this parametric study are shown graphically and the physical aspects of the problem are highlighted and discussed.     

Heat and mass transfer on a MHD third grade fluid with partial slip flow past an infinite vertical insulated porous plate in a porous medium

The influence of third grade, partial slip and other thermophysical parameters on the steady flow, heat and mass transfer of viscoelastic third grade fluid past an infinite vertical insulated plate subject to suction across the boundary layer has been investigated. The space occupying the fluid is porous. The momentum equation is characterized by a highly nonlinear boundary value problem in which the order of the differential equation exceeds the number of available boundary conditions. An efficient numerical scheme of midpoint technique with Richardson’s extrapolation is employed to solve the governing system of coupled nonlinear equations of momentum, energy and concentration. Numerical calculations were carried out for different values of various interesting non-dimensional quantities in the slip flow regime with heat and mass transfer and were shown with the aid of figures. The values of the wall shear stress, the local rate of heat and mass transfers were obtained and tabulated. The analysis shows that as the fluid becomes more shear thickening, the momentum boundary layer decreases but the thermal boundary layer increases; the magnetic field strength is found to decrease with an increasing temperature distribution when the porous plate is insulated. The consequences of increasing the permeability parameter and Schmidt number decrease both the momentum and concentration boundary layer thicknesses respectively whereas an increase in the thermal Grashof number gives rise to the thermal boundary layer thickness.     

A Survey of Multicomponent Mass Diffusion Flux Closures for Porous Pellets: Mass and Molar Forms

Heterogeneous catalysis is of paramount importance in many areas of gas conversion and processing in chemical engineering industries. In porous pellets, the catalytic reactions may be affected by diffusional limitations such that the global rate can be different from the intrinsic reaction rate. In the literature, a number of multicomponent diffusion flux closures have been applied to characterize the diffusion process within different units in chemical process plants. The main purpose of this paper is to outline the derivation of the different diffusion flux models: the rigorous Maxwell–Stefan and dusty gas models, and the simpler Wilke and Wilke–Bosanquet models. Usually the diffusion fluxes are derived and presented with respect to the molar average velocity definition. In this study, also the diffusion flux closures with respect to the mass average velocity definition is outlined. Thus, if the temperature equation and the momentum equation are used in the pellet model, a consistently closed set of pellet equations is obtained on mass basis holding only the mass average velocity. On the other hand, for the closed set of pellet equations on molar basis, the component balances hold the molar averaged velocity whereas the temperature and momentum equations hold the mass average velocity due to the physical laws applied deriving these fundamental balances. Nevertheless, the Maxwell–Stefan and dusty gas models are manipulated and put on the convenient Fickian form. The second purpose of this article is the evaluation of the diffusion flux closures derived. For this purpose, a transient model is developed to describe the evolution of the species composition, pressure, velocity, temperature, total concentration, and fluxes within a spherical pellet. The catalyst problem has been simulated for the methanol dehydration process producing dimethyl ether (DME), with computed efficiency factor values in the range 0.06–0.6 for pellet pore diameters of 0.1–100 nm. Identical results are expected for the mole and mass based pellet equations. However, deviations are obtained in the component fractions comparing the mass and mole based pellet model formulations where the mass fluxes were described according to the Wilke and Wilke–Bosanquet models. On the other hand, the rigorous Maxwell–Stefan and dusty gas models gave identical results.     

Effects of heat generation on g-Jitter induced natural convection flow in a channel with isothermal or isoflux walls

This paper discusses the behavior of g-jitter induced free convection in microgravity under the influence of a transverse magnetic field and in the presence of heat generation or absorption effects for a simple system consisting of two parallel impermeable infinite plates held at four different thermal boundary conditions. The governing equations for this problem are derived on the basis of the balance laws of mass, linear momentum, and energy modified to include the effects of thermal buoyancy, magnetic field and heat generation or absorption as well as Maxwell's equations. The fluid is assumed to be viscous, Newtonian and have constant properties except the density in the body force of the balance of linear momentum equation. The governing equations are solved analytically for the induced velocity and temperature distributions as well as for the electric field and total current for electrically-conducting and insulating walls. This is done for isothermal–isothermal, isoflux–isothermal, isothermal–isoflux and isoflux–isoflux thermal boundary conditions. Graphical results for the velocity amplitude and distribution are presented and discussed for various parametric physical conditions.     

Transient mixed convection flow arising due to thermal and mass diffusion over porous sensor surface inside squeezing horizontal channel

The double diffusion effect on the mixed convection flow over a horizontal porous sensor surface placed inside a horizontal channel is analyzed.With the appropriate transformations,the unsteady equations governing the flow are reduced to non-similar boundary layer equations which are solved numerically for the time-dependent mixed convection parameter.The asymptotic solutions are obtained for small and large values of the time-dependent mixed convection parameter.The results are discussed in terms of the skin friction,the heat transfer coefficient,the mass transfer coefficient,and the velocity,temperature,and concentration profiles for different values of the Prandtl number,the Schmidt number,the squeezing index,and the mixed convection parameter.