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.     

Fully Coupled Thermo-Hydrodynamic Simulation Model for Journal Bearings

The isothermal form of Reynolds fluid film equation is used to predict the pressure generation in hydrodynamic journal bearings if temperature effects are neglected. Often, however, temperature effects may be important and cannot be neglected, because oil viscosity significantly varies with temperature. Also, thermal expansion of journal shaft and bearing housing must be taken into account since the bearing clearance changes with increasing temperature. Hence, the Reynolds pressure field equation, the energy equation for the fluid film and the heat transfer equations for journal and bearing housing have to be solved simultaneously. The coupled thermo-hydrodynamic fluid flow problem is mathematically defined by a system of nonlinear integro-differential equations. The governing equations are discretized and solved by a finite element approach. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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.     

Convective Heat Transfer past Small Cylindrical Bodies

Convective heat transfer from an array of small, cylindrical bodies of arbitrary shape in an unbounded, two-dimensional domain is a singular perturbation problem involving an infinite logarithmic expansion in the small parameter ε, representing the order of magnitude of the size of the bodies. Using the method of matched asymptotic expansions, we formulate a hybrid asymptotic-numerical method to solve for the dimensionless, steady-state temperature. We assume that the velocity field of the fluid surrounding the bodies is arbitrary but known. From our asymptotic solution for an arbitrary velocity field, we present the results for two special cases: a uniform flow field and a simple shear flow field. We demonstrate the asymptotic results of the hybrid method through a number of examples and, in a particular case, we compare these results to an exact analytical solution.     

Application of the similarity theory including variable property effects to a complex benchmark problem

An asymptotic method to account for variable property effects, recently described in this journal, is now applied to a complex benchmark geometry. It is a room which is ventilated by forced convection through inlet and outlet slit nozzles at the top and bottom of the side walls. Four heating elements standing on the ground floor add heat with constant heat flux density of varying strength. CFD solutions with the full coverage of all property temperature dependencies of air and SF₆ are compared with asymptotic results (ACFD), applied for these fluids. ACFD results are given as systematic expansions with respect to a heat transfer parameter e{\varepsilon} which serves as perturbation parameter. First and second order asymptotic results of the Nu?elt number at the surface of the heating elements are shown as well as temperature distributions along the adiabatic walls of the room. Special attention is given to the reference Nu?elt numbers of zero order (e = 0){(\varepsilon=0)} which are those for constant properties only for pure forced convection.     

Peristaltic transport of a Newtonian fluid in a vertical asymmetric channel with heat transfer and porous medium

The problem of peristaltic flow of a Newtonian fluid with heat transfer in a vertical asymmetric channel through porous medium is studied under long-wavelength and low-Reynolds number assumptions. The flow is examined in a wave frame of reference moving with the velocity of the wave. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The analytical solution has been obtained in the form of temperature from which an axial velocity, stream function and pressure gradient have been derived. The effects of permeability parameter, Grashof number, heat source/sink parameter, phase difference, varying channel width and wave amplitudes on the pressure gradient, velocity, pressure drop, the phenomenon of trapping and shear stress are discussed numerically and explained graphically.     

Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity,non-uniform heat source and radiation

An analysis has been carried out to study the magnetohydrodynamic boundary layer flow and heat transfer characteristics of a non-Newtonian viscoelastic fluid over a flat sheet with a linear velocity in the presence of thermal radiation and non-uniform heat source. The thermal conductivity is assumed to vary as a linear function of temperature. The basic equations governing the flow and heat transfer are in the form of partial differential equations, the same have been reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformation. The transformed equations are solved analytically by regular perturbation method. Numerical solution of the problem is also obtained by the efficient shooting method, which agrees well with the analytical solution. The effects of various physical parameters such as viscoelastic parameter, Chandrasekhar number, Prandtl number, variable thermal conductivity parameter, Eckert number, thermal radiation parameter and non-uniform heat source/sink parameters which determine the temperature profiles are shown in several plots and the heat transfer coefficient is tabulated for a range of values of said parameters. Some important findings reported in this work reveals that combined effect of variable thermal conductivity, radiation and non-uniform heat source have significant impact in controlling the rate of heat transfer in the boundary layer region.     

Numerical Computation of Heat and Mass Transfer in Fluidized Beds with Liquid Injection

The goal of this work is the simulation of concentration and temperature distributions insides fluidized bed with a uniform liquid distribution. Further, a physically based 2D model is developed for the heat and mass transfer processes in fluidized beds with a spray nozzle. The model is a coupled and semi-linear system of convection-reaction-diffusion equations. We considered the numerical solution of these semi-linear partial differential equations with discrete boundary conditions using linear finite elements on an adaptive triangular grid in space and implicit methods in time. We present calculations using, semi implicit and implicit methods in time, and different solvers for solving the linear systems. The complex correlations of mass and liquid flow rates, mass transfer, heat transfer, drying, and transient two dimensional air humidity, air temperature, degree of wetness, liquid film temperature and particle temperature were simulated. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of thermal radiation and space porosity on MHD mixed convection flow in a vertical channel using homotopy analysis method

A study of MHD mixed convection flow through porous space in the presence of a temperature dependent heat source in a vertical channel with radiation has been analyzed. The Rosseland approximation is considered in the modeling of the conduction radiation heat transfer and temperatures of the walls are assumed constants. The governing equations are expressed in non-dimensional form and the series solutions of coupled system of equations are constructed for velocity and temperature using homotopy analysis method (HAM). The effects of various involved parameters on the velocity and temperature field are shown and discussed. The coefficient of skin friction, and the rate of heat transfer coefficient are obtained and illustrated graphically.     

Effects of the magnetic field on direct contact melting transport processes during rotation

Contact melting heat transfer occurs via relative motion between the heating source and a phase change material (PCM) during melting in various applications. In this study, we investigated the physics of the close contact melting process generated by rotation and when subjected to an applied magnetic field. We transformed the physical model comprising the three-dimensional mass, momentum, and energy equations of the liquid melt layer in the cylindrical coordinate system, including the effects of the Lorentz forces and coupled with an interfacial energy jump condition, into a set of nonlinear similarity equations. Various characteristic dimensionless variables were identified, including an external force parameter σ, which defines the relationship between the external load on the PCM and the centrifugal force due to rotation, and a magnetic field parameter M. Numerical results were obtained and we systematically studied and interpreted the effects of various dimensionless variables on the contact melting and heat transfer processes during rotation, including the structures of the flow and thermal fields, melt layer thickness, and the melting and heat transfer rates. In particular, our results demonstrate that the melting and heat transfer rates increase while the liquid melt film becomes thinner as the external force parameter σ increases. By contrast, an increase in the magnetic field parameter M decreases the melting and heat transfer rates, while yielding relatively thicker melt layers.     

Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with thermal radiation and non-uniform heat source/sink

An analysis has been carried out to study the flow and heat transfer characteristics for MHD viscoelastic boundary layer flow over an impermeable stretching sheet with space and temperature dependent internal heat generation/absorption (non-uniform heat source/sink), viscous dissipation, thermal radiation and magnetic field due to frictional heating. The flow is generated due to linear stretching of the sheet and influenced by uniform magnetic field, which is applied vertically in the flow region. The governing partial differential equations for the flow and heat transfer are transformed into ordinary differential equations by a suitable similarity transformation. The governing equations with the appropriate conditions are solved exactly. The effects of viscoelastic parameter and magnetic parameter on skin friction and the effects of viscous dissipation, non-uniform heat source/sink and the thermal radiation on heat transfer characteristics for two general cases namely, the prescribed surface temperature (PST) case and the prescribed wall heat flux (PHF) case are presented graphically and discussed. The numerical results for the wall temperature gradient (the Nusselt number) are presented in tables and are discussed.     

Unsteady flow and heat transfer in a thin film of Ostwald–de Waele liquid over a stretching surface

In this paper, the effects of viscous dissipation and the temperature-dependent thermal conductivity on an unsteady flow and heat transfer in a thin liquid film of a non-Newtonian Ostwald–de Waele fluid over a horizontal porous stretching surface is studied. Using a similarity transformation, the time-dependent boundary-layer equations are reduced to a set of non-linear ordinary differential equations. The resulting five parameter problem is solved by the Keller–Box method. The effects of the unsteady parameter on the film thickness are explored numerically for different values of the power-law index parameter and the injection parameter. Numerical results for the velocity, the temperature, the skin friction and the wall-temperature gradient are presented through graphs and tables for different values of the pertinent parameter. One of the important findings of the study is that the film thickness increases with an increase in the power-law index parameter (as well as the injection parameter). Quite the opposite is true with the unsteady parameter. Furthermore, the wall-temperature gradient decreases with an increase in the Eckert number or the variable thermal conductivity parameter. Furthermore, the surface temperature of a shear thinning fluid is larger compared to the Newtonian and shear thickening fluids. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena.     

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.     

Effects of Hall current and heat transfer on rotating flow of a second grade fluid through a porous medium

The effects of Hall current and heat transfer on the rotating flow of a second grade fluid past a porous plate with variable suction are examined. The medium considered is porous and suction and external flow velocities vary periodically. The plate is assumed to be at a higher temperature than the fluid. The influences of the Hall parameter and porosity of the medium have been seen and discussed on the velocity and temperature profiles. Moreover, these influences have also been seen on the drag and lateral stress. Finally, the obtained solutions are also compared with the previous studies in the literature and found quite agreement.     

Coupled flow and heat transfer in viscoelastic fluid with Cattaneo–Christov heat flux model

This letter presents a research for coupled flow and heat transfer of an upper-convected Maxwell fluid above a stretching plate with velocity slip boundary. Unlike most classical works, the new heat flux model, which is recently proposed by Christov, is employed. Analytical solutions are obtained by using the homotopy analysis method (HAM). The effects of elasticity number, slip coefficient, the relaxation time of the heat flux and the Prandtl number on velocity and temperature fields are analyzed. A comparison of Fourier’s Law and the Cattaneo–Christov heat flux model is also presented.     

Heat transfer in channel flow of a micropolar fluid

The study of heat transfer in channel flow has been done by previous authors for Newtonian and elastico-viscous fluids. It is the aim of the present paper to study the temperature profile for flow of a micropolar fluid in a channel induced by a constant axial pressure gradient, when the walls are maintained at constant temperatures. We have examined the effects of microrotation on the temperature profile and on the kinetic energy of the fluid. Three cases have been chosen by us for detailed study: (i) both the walls are maintained at different constant temperatures, (ii) both the walls are maintained at the same constant temperature, (iii) one wall is kept at a constant temperature and there is no heat flux at the other wall.     

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 the heat transfer in porous media with small thermal conductivity

An approximate analytical solution for the one-dimensional problem of heat transfer between an inert gas and a porous semi-infinite medium is presented. Perturbation methods based on Laplace transforms have been applied using the solid thermal conductivity as small parameter. The leading order approximation is the solution of Nusselt (or Schumann) problem. Such solution is corrected by means of an outer approximation. The boundary condition at the origin has been taking into account using an inner approximation for a boundary layer. The gas temperature presents a discontinuous front (due to the incompatibility between initial and boundary conditions) which propagates at constant velocity. The solid temperature at the front has been smoothed out using an internal layer asymptotic approximation. The good accuracy of the resulting asymptotic expansion shows its usefulness in several engineering problems such as heat transfer in porous media, in exhausted chemical reactions, mass transfer in packed beds, or in the analysis of capillary electrochromatography techniques.     

壁面马赫数分布规律可控的新型内收缩基准流场设计方法

根据有旋特征线理论,设计出了沿程马赫数下降规律可控的轴对称基准流场,分析了基准流场的几何参数(前缘压缩角及中心体半径)的影响规律,发现选取较小的前缘压缩角和中心体半径有利于得到性能优良的基准流场;然后在设计状态Ma=6时研究了三种典型的马赫数下降规律对这种轴对称流场性能的影响。最后考虑了粘性的影响,并进行了粘性修正探索,结果表明,采用附面层位移厚度修正方法后,基准流场的壁面压力分布和无粘情况吻合良好。 