The effect of variable properties on the unsteady Couette flow with heat transfer considering the Hall effect

The influence of temperature dependent viscosity and thermal conductivity on the transient Couette flow with heat transfer is studied. An external uniform magnetic field is applied perpendicular to the parallel plates and the Hall effect is taken into consideration. The fluid is acted upon by a constant pressure gradient. The two plates are kept at two constant but different temperatures and the viscous and Joule dissipations are considered in the energy equation. A numerical solution for the governing non-linear equations of motion and the energy equation is obtained. The effect of the Hall term and the temperature dependent viscosity and thermal conductivity on both the velocity and temperature distributions is examined.     

Non-Darcy free convection flow over a horizontal cylinder in a saturated porous medium with variable viscosity,thermal conductivity and mass diffusivity

In this paper, the effects of variable viscosity and thermal conductivity on coupled heat and mass transfer by free convection about a permeable horizontal cylinder embedded in porous media using Ergun mode are studied. The fluid viscosity and thermal conductivity and are assumed to vary as a linear function of temperature while the mass diffusion is assumed to vary as linear function of concentration. The surface of the horizontal cylinder is maintained at a uniform wall temperature and a uniform wall concentration. The transformed governing equations are obtained and solved by using the implicit finite difference method. Numerical results for dimensionless temperature and concentration profiles as well as Nusselt and Sherwood numbers are presented for various values of parameters namely, Ergun number, transpiration parameter, Rayleigh and Lewis numbers and buoyancy ratio parameter.     

NSM solution for unsteady MHD Couette flow of a dusty conducting fluid with variable viscosity and electric conductivity

The effects of dependence on temperature of the viscosity and electric conductivity, Reynolds number and particle concentration on the unsteady MHD flow and heat transfer of a dusty, electrically conducting fluid between parallel plates in the presence of an external uniform magnetic field have been investigated using the network simulation method (NSM) and the electric circuit simulation program Pspice. The fluid is acted upon by a constant pressure gradient and an external uniform magnetic field perpendicular is applied to the plates. We solved the steady-state and transient problems of flow and heat transfer for both the fluid and dust particles. With this method, only discretization of the spatial co-ordinates is necessary, while time remains as a real continuous variable. Velocity and temperature are studied for different values of the viscosity and magnetic field parameters and for different particle concentration and upper wall velocity.     

Numerical study of forced and free convective boundary layer flow of a magnetic fluid over a flat plate under the action of a localized magnetic field

The two-dimensional, steady, laminar, forced and free convective boundary layer flow of a magnetic fluid over a semi-infinite vertical plate, under the action of a localized magnetic field, is numerically studied. The magnetic fluid is considered to be water-based with temperature dependent viscosity and thermal conductivity. The study of the boundary layer is separated into two cases. In case I the boundary layer is studied near the leading edge, where it is dominated by the large viscous forces, whereas in case II the boundary layer is studied far from the leading edge of the plate where the effects of buoyancy forces increase. The numerical solution, for these two different cases, is obtained by an efficient numerical technique based on the common finite difference method. Numerical calculations are carried out for the value of Prandl number Pr =  49.832 (water-based magnetic fluid) and for different values of the dimensionless parameters entering into the problem and especially for the magnetic parameter Mn, the viscosity/temperature parameter Θ _r and the thermal/conductivity parameter S*. The analysis of the obtained results show that the flow field is influenced by the application of the magnetic field as well as by the variation of the viscosity and the thermal conductivity of the fluid with temperature. It is hoped that they could be interesting for engineering applications.     

Numerical study of forced and free convective boundary layer flow of a magnetic fluid over a flat plate under the action of a localized magnetic field

The two-dimensional, steady, laminar, forced and free convective boundary layer flow of a magnetic fluid over a semi-infinite vertical plate, under the action of a localized magnetic field, is numerically studied. The magnetic fluid is considered to be water-based with temperature dependent viscosity and thermal conductivity. The study of the boundary layer is separated into two cases. In case I the boundary layer is studied near the leading edge, where it is dominated by the large viscous forces, whereas in case II the boundary layer is studied far from the leading edge of the plate where the effects of buoyancy forces increase. The numerical solution, for these two different cases, is obtained by an efficient numerical technique based on the common finite difference method. Numerical calculations are carried out for the value of Prandl number Pr =  49.832 (water-based magnetic fluid) and for different values of the dimensionless parameters entering into the problem and especially for the magnetic parameter Mn, the viscosity/temperature parameter Θ _r and the thermal/conductivity parameter S*. The analysis of the obtained results show that the flow field is influenced by the application of the magnetic field as well as by the variation of the viscosity and the thermal conductivity of the fluid with temperature. It is hoped that they could be interesting for engineering applications.     

Couple stress fluid flow with variable properties: A second law analysis

The present work examines the combined influence of variable thermal conductivity and viscosity on the irreversibility rate in couple stress fluid flow in between asymmetrically heated parallel plates. The dimensionless fluid equations are solved by using homotopy analysis method (HAM) and validated with Runge‐Kutta shooting method (RKSM). The convergent series solution is then used for the irreversibility analysis in the flow domain. The effects of thermal conductivity and viscosity variation parameters, couple stress parameter, Reynolds number, Grashof number, Hartmann number on the velocity profile, temperature distribution, entropy production, and heat irreversibility ratio are presented through graphs, and salient features of the solutions are discussed. The computations show that the entropy production rate decreases with increased magnetic field and thermal conductivity parameters, whereas it rises with increasing values of couple stress parameter, Brinkman number, viscosity variation parameter, and Grashof number. The study is relevant to lubrication theory.     

Melting heat and mass transfer in stagnation point micropolar fluid flow of temperature dependent fluid viscosity and thermal conductivity at constant vortex viscosity

Steady mixed convection micropolar fluid flow towards stagnation point formed on horizontal linearly stretchable melting surface is studied. The vortex viscosity of micropolar fluid along a melting surface is proposed as a constant function of temperature while dynamic viscosity and thermal conductivity are temperature dependent due to the influence of internal heat source on the fluid. Similarity transformations were used to convert the governing equation into non-linear ODE and solved numerically. A parametric study is conducted. An analysis of the results obtained shows that the flow-field is influenced appreciably by heat source, melting, velocity ratio, variable viscosity and thermal conductivity.     

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.     

非牛顿流体内流传热研究

在本文中,研究了注入轴对称模腔非牛顿流体非定常流动.本文的第二部份研究了上随体Maxwell流体管内热流动.对于注入模腔流动.其本构方程采用幂律流体模型方程.为了避免在表现粘度中温度关系引起的非线性.引进了一特征粘度的概念.描述本力学过程的基本方程是,本构方程、定常状态的运动方程、非定常能量方程及连续方程.该方程组在空间是二维问题,在数学上是三维问题.采用分裂差分格式求得本方程组的数值解答.分裂法曾成功应用于求解牛顿流体问题.在本文中,首次将分裂法成功地应用解决非牛顿流体流动问题.对于圆管内热流,给出了差分格式,使基本方程组化为一个三对角方程组.其结果,给出了不同时刻的模腔内二维温度分布.     

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.     

Radiative magnetogasdynamic Couette flow with variable parameters

Couette flow of an electrically conducting compressible fluid with uniform magnetic field applied transversely between flat walls of arbitrary electrical conductivity, radiative emissivity and temperature is analysed. The equations of steady flow are formulated with the introduction of temperature dependent coefficients of viscosity and thermal and electrical conductivity, together with absorption coefficient in addition dependent upon the density. Profiles of velocity, induced magnetic field, radiative flux and temperature are derived numerically under a one-dimensional modelling. The parameter dependence, expressed as a power law, is found to have a marked effect upon the velocity and magnetic field but to be of little import for the thermal profiles. Similar influence is found for the effect of wall electrical conductivity and emissivity. On the other hand, changes in the strength of the fluid thermal conductivity significantly affect the temperature profile in the presence of electromagnetic interaction.

---

Résumé Pour un fluide conducteur, rayonnant et compressible sous l'influence d'un champ magnétique constant et transverse l'écoulement de Couette entre deux surfaces planes conductrices et rayonnantes avec des températures arbitraires est analysé. On formule les équations d'un écoulement permanent quand la viscosité, la conductibilité thermique et la conductibilité électrique dépendent de la température et le coffficient d'absorption de la densité. On calcule la vitesse, le champ magnétique induit, le rayonnement et la température pour des écoulements qui ne sont fonction que de la cordonnée transverse.La vitesse et le champ magnétique dépendent de façon significative de ce paramètre, mais pas la température ni le rayonnement. On obtient des résultats similaires pour la conductibilité électrique et l'emissivité de rayonnement des surfaces planes. D'autre part quand la conductiblité électrique du fluide n'est pas nulle, une variation de la conductibilité thermique modifie la température d'une manière significative.

     

Lie group analysis for the effect of temperature-dependent fluid viscosity with thermophoresis and chemical reaction on MHD free convective heat and mass transfer over a porous stretching surface in the presence of heat source/sink

This paper 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 equation 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. It is found that with the increase of magnetic field intensity the fluid velocity decreases but the temperature increases at a particular point of the heated stretching surface. Impact of thermophoresis particle deposition with chemical reaction in the presence of heat source/sink plays an important role on the concentration boundary layer. The results thus obtained are presented graphically and discussed.     

Effects of variable viscosity on non-Darcy MHD free convection along a non-isothermal vertical surface in a thermally stratified porous medium

An analysis is performed for non-Darcy free convection flow of an electrically conducting fluid over an impermeable vertical plate embedded in a thermally stratified, fluid saturated porous medium for the case of power-law surface temperature. The present work examines the effects of non-Darcian flow phenomena, variable viscosity, Hartmann–Darcy number and thermal stratification on free convective transport and demonstrates the variation in heat transfer prediction based on three different flow models. The wall effect on porosity variation is approximated by an exponential function. The effects of thermal dispersion and variable stagnant thermal conductivity are taken into consideration in the energy equation. The resulting non-similar system of equations is solved using a finite difference method. Results are presented for velocity, temperature profiles and local Nusselt number for representative values of different controlling parameters.     

Hydromagnetic stability of convective flow of variable viscosity fluids generated by internal heat sources

The stability of convective motion of a variable viscosity fluid contained in a vertical layer generated by uniformly distributed internal heat sources in the presence of a transverse magnetic field is studied. The viscosity of the fluid is assumed to depend on the temperature. The undisturbed steady state motion is assumed to consist of purely vertical motion with a nonlinear temperature distribution across the layer. The equations were solved by the spectral collocation method. The results show that thermal running waves are the most unstable modes and dominate the shear modes when the viscosity decreases.     

Hydromagnetic stability of convective flow of variable viscosity fluids generated by internal heat sources

The stability of convective motion of a variable viscosity fluid contained in a vertical layer generated by uniformly distributed internal heat sources in the presence of a transverse magnetic field is studied. The viscosity of the fluid is assumed to depend on the temperature. The undisturbed steady state motion is assumed to consist of purely vertical motion with a nonlinear temperature distribution across the layer. The equations were solved by the spectral collocation method. The results show that thermal running waves are the most unstable modes and dominate the shear modes when the viscosity decreases.     

微极流体薄膜层通过以滑移速度移动的可渗透无限平板时流体特性变化和热辐射对流动和热传导的影响

微极流体薄膜层通过按滑移速度移动的可渗透无限竖直平板时,研究热辐射对混合对流薄膜层流动和热传导的影响.假定流体粘度和热传导率变化是温度的一个函数.对一些典型的可变参数值,应用Chebyshev谱方法,数值求解流动的控制方程.将所得结果与已发表文献的结果进行比较,结果是一致的.绘出并讨论了可变参数对速度、微旋转速度、温度分布曲线、表面摩擦因数和Nusselt数的影响.     

热辐射对粘性流体流过多孔非线性收缩平面时的MHD流动和热传导的影响

研究热辐射对多孔非线性收缩平面上磁流体动力学(MHD)流动和热传导的影响.假设收缩平面的速度和横向磁场,按离原点距离的幂函数而变化;又假设粘性按与其有关的温度的反函数变化,热传导率按温度的线性函数变化.通过广义相似变换,将偏微分方程的控制方程,简化为耦合的非线性常微分方程,然后通过有限差分法进行数值求解.在不同的参数取值下,得到速度和温度分布,以及多孔平面上表面摩擦因数和热传导率的数值结果.     

Transport of Mass,Momentum and Energy through Periodic Open Cell Metal Foams Applied in Catalysis

An ODE model to predict the temperature field of periodic open cell metal foams applied in catalysis as carrier structures is presented. The catalytic and highly endothermic reaction takes place in a porous layer which surround the struts of the foam and releases gas from a fluid. The one-dimensional model includes dependencies of the foam structure (strut radius, shape of strut), process conditions (surrounding velocity, surrounding fluid: liquid and/or gas), chemical conditions (reaction enthalpy, activation energy) and material parameters (thermal conductivity, density, viscosity). This makes it possible to estimate optimal parameters, that are able to provide sufficient heat to the reaction. The advantage of this model is the substantial time saving in contrary to three dimensional finite volume simulations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Falling film flow of a viscoelastic fluid along a wall

In this paper, we study the heat transfer in the fully developed flow of a viscoelastic fluid, a slag layer, down a vertical wall. A new constitutive relation for the stress tensor of this fluid is proposed, where the viscosity depends on the volume fraction, temperature, and shear rate. For the heat flux vector, we assume the Fourier's law of conduction with a constant thermal conductivity. The model is also capable of exhibiting normal stress effects. The governing equations are non‐dimensionalized and numerically solved to study the effects of various dimensionless parameters on the velocity, temperature, and volume fraction. The effect of the exponent in the Reynolds viscosity model is also discussed. The different cases of shear‐thinning and shear‐thickening, cooling and heating, are compared and discussed. The results indicate that the viscous dissipation and radiation (at the free surface) cause the temperature to be higher inside the flow domain. Copyright © 2013 John Wiley & Sons, Ltd.     

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

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