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.     

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.     

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.     

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.     

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.     

Natural convection boundary layer flow of fluid with temperature-dependent viscosity from a horizontal elliptical cylinder with constant surface heat flux

This study deals with the temperature-dependent viscosity effects on the natural convection boundary layer on a horizontal elliptical cylinder with constant surface heat flux. The mathematical problem is reduced to a pair of coupled partial differential equations for the temperature and the stream function, and the resulting nonlinear equations are solved numerically by cubic spline collocation method. Results for the heat transfer characteristics are presented as functions of eccentric angle for various values of viscosity variation parameters, Prandtl numbers and aspect ratios. Results show that an increase in the viscosity variation parameter tends to accelerate the fluid flow near the surface and increase the maximum velocity, thus decreasing the velocity boundary layer thickness. As the viscosity variation parameter is increased, the surface temperature tends to decrease, thus increasing the local Nusselt number. Moreover, the local Nusselt number of the elliptical cylinder increases as the Prandtl number of the fluid is increased.     

Heat transfer and Couette flow of a chemically reacting non‐linear fluid

In this paper we study the flow and heat transfer in a chemically reacting non‐linear fluid between two long horizontal parallel flat plates that are at different temperatures. The top plate is sheared, whereas the bottom plate is fixed. The fluid is modeled as a generalized power‐law fluid whose viscosity is also assumed to be a function of the concentration. The effects of radiation are neglected. The equations are made dimensionless and the boundary value problem is solved numerically; the velocity and temperature profiles are obtained for various dimensionless numbers. Published in 2009 by John Wiley & Sons, Ltd.     

Lie group analysis for thermal-diffusion and diffusion-thermo effects on free convective flow over a porous stretching surface with variable stream conditions in the presence of thermophoresis particle deposition

A study has been carried out to obtain the solutions for heat and mass transfer from natural convection flow along a vertical surface with temperature-dependent fluid viscosity embedded in a porous medium due to thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects. This paper concerns with a steady two-dimensional flow of incompressible fluid over a vertical stretching sheet. 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 impact of thermophoresis particle deposition with chemical reaction in the presence of thermal-diffusion and diffusion-thermo effects plays an important role on the temperature and concentration boundary layer. The results thus obtained are presented graphically and discussed.     

MHD power-law fluid flow and heat transfer over a non-isothermal stretching sheet

This article presents a numerical solution for the magnetohydrodynamic (MHD) non-Newtonian power-law fluid flow over a semi-infinite non-isothermal stretching sheet with internal heat generation/absorption. The flow is caused by linear stretching of a sheet from an impermeable wall. Thermal conductivity is assumed to vary linearly with temperature. The governing partial differential equations of momentum and energy are converted into ordinary differential equations by using a classical similarity transformation along with appropriate boundary conditions. The intricate coupled non-linear boundary value problem has been solved by Keller box method. It is important to note that the momentum and thermal boundary layer thickness decrease with increase in the power-law index in presence/absence of variable thermal conductivity.     

Effects of temperature-dependent viscosity and variable thermal conductivity on MHD non-Darcy mixed convective diffusion of species over a stretching sheet

A numerical model is presented to study the effects of temperature-dependent viscosity and variable thermal conductivity on mixed convection problem. Two important types of wall heating conditions namely, prescribed surface temperature and prescribed wall heat flux which arise in polymer industries are considered. The problem is solved numerically by using the fifth-order Runge–Kutta Fehlberg method with shooting technique. It is found that the Prandtl number is to decrease the skin friction coefficient, local Nusselt number and local Sherwood number. The effects of non-uniform heat source/sink and porous parameter are analyzed on velocity, temperature, skin friction co-efficient, Nusselt and Sherwood numbers.     

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.     

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 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.     

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.     

Radiation instability of a circular cylinder in a uniform flow of a two-layer fluid

A solution of the plane linear problem of the oscillations of a horizontal circular cylinder in a uniform flow of a two-layer unbounded fluid is obtained using the method of multipole expansions. The direction of the flow is perpendicular to the cylinder axis. The whole cylinder Ges in the upper or lower layer. The fluid is assumed to be ideal and incompressible, the flow in each layer being a potential one. All the components of the radiation load (the apparent masses and damping coefficients) are determined and the regions of existence of radiation instability are found, depending on the flow velocity for a cylinder suspended by horizontal and vertical elastic links. By solving the integro-differential equation numerically the relative oscillations of the body under specified initial conditions are found.     

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.     

Similarity solution for a cylindrical shock wave in a rotational axisymmetric dusty gas with heat conduction and radiation heat flux

The propagation of shock waves in a rotational axisymmetric dusty gas with heat conduction and radiation heat flux, which has a variable azimuthally fluid velocity together with a variable axial fluid velocity, is investigated. The dusty gas is assumed to be a mixture of non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-condition is maintained and variable energy input is continuously supplied by the piston (or inner expanding surface). The fluid velocities in the ambient medium are assume to be vary and obey power laws. The density of the ambient medium is assumed to be constant, the heat conduction is express in terms of Fourier’s law and the radiation is considered to be of the diffusion type for an optically thick grey gas model. The thermal conductivity K and the absorption coefficient α_R are assumed to vary with temperature and density. In order to obtain the similarity solutions the angular velocity of the ambient medium is assume to be decreasing as the distance from the axis increases. The effects of the variation of the heat transfer parameter and non-idealness of the gas in the mixture are investigated. The effects of an increase in (i) the mass concentration of solid particles in the mixture and (ii) the ratio of the density of solid particles to the initial density of the gas on the flow variables are also investigated.     

Effect of double stratification on MHD free convection in a micropolar fluid

This paper analyzes the flow and heat and mass transfer characteristics of the free convection on a vertical plate with variable wall temperature and concentration in a doubly stratified micropolar fluid. A uniform magnetic field is applied normal to the plate. The governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Keller-box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The non-dimensional velocity, microrotation, temperature and concentration are presented graphically for various values of magnetic parameter, coupling number, thermal and solutal stratification parameters. In addition, the Nusselt number, the Sherwood number, the skin-friction coefficient, and the wall couple stress are shown in a tabular form.     

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 on viscoelastic fluid flow past a rigid body

Viscoelastic non-Newtonian fluids can be achieved by adding a small amount of polymer additives to a Newtonian fluid. In this paper, numerical simulations are used to investigate the influence of such polymer additives on the behavior of flow past a circular cylinder. A numerical method is proposed that discretizes the non-linear viscoelastic system on a uniform Cartesian grid, with a penalization method to model the presence of the cylinder. The drag of the cylinder and the flow behavior under the effect of different Reynolds numbers ($\mathrm{Re}$), Weissenberg numbers (Wi) and polymer viscosity ratios (ε) are studied. Numerical results show that different flow characteristics are exhibited in different parameter zones. The polymer viscosity ratio plays an important role at low Weissenberg and Reynolds numbers, but as the Reynolds and Weissenberg numbers increase, the influence of ε weakens. The drag force of the cylinder is mostly affected by the Reynolds and Weissenberg numbers. At low Reynolds numbers, the drag of the cylinder and the flow fields are only affected by a large value of Wi when the elastic forces are strong. Non-trivial drag reduction occurs only when there is vortex shedding in the wake flow, whereas drag enhancement happens when the vortex shedding is inhibited.