Free Convective Couette Flow Research Articles

Magnetohydrodynamics free convection couette flow and heat transfer through a vertical porous plate with heat generation and absorption effect

This research examines the impact of suction/injection and permeability of porous materials on a steady natural convection Couette flow of a viscous incompressible fluid passing through a vertical porous plate. The dimensionless governing momentum and energy equations were solved exactly. Graphs were plotted to check the impact of the governing flow parameters and a table was plotted for comparison of the results. It was found from the investigation that, the fluid injection (λ>0) increases the fluid velocity and temperature distributions while the magnetic field (M) retards the fluid velocity. It is also noteworthy to mention that the suction (λ>0) reduces the fluid velocity and temperature distributions in the channel. The velocity profile is observed to increase with increase in the permeability (K) of the materials.

MHD Free-Convective Couette flow in a Vertical Porous Microchannel Using Non-Linear Boussinesq Approximation

An analytical solution for free convection flow of an electrically conducting fluid in a vertical micro-porous-channel, in the existence of transversely applied magnetic-field and nonlinear Boussinesq approximation is carried out in this article. The governing equations representing stated objective are obtained and solved analytically using method of undetermiend coefficients and direct integration. Pictorial and tabularlar representions of solutions obtained are carried out, so as to ascertain the role of various governing parameters entering flow formation. During the course of numerical simulation of results, it is found that the volumetric flow rate increases with increase in Couette flow parameter, asymmetric heating parameter and suction/injection parameter but decreases with increase in nonlinear Boussinesq approximation parameter.

Free convective couette flow analysis of viscoelastic dusty fluid along with Newtonian heating in a rotating frame

Applications in daily life heavily rely on the viscoelastic fluid's response to Newtonian heating. The importance of viscoelastic fluid rotation in engineering and the production of goods is also varied. Nuclear reactors, gas cooling systems, system temperature control, centrifugal separators, and other systems can all benefit from viscoelastic dusty fluids and Newtonian heating. In light of this inspiration, the current study describes the Newtonian heating effect on a viscoelastic fluid that contains dust particles. In addition, a uniformly applied magnetic field and a free convective heat transfer are taken into account for Couette flow in a rotating frame. Because the dust particles have complex velocities due to rotation, the primary and secondary velocities are combined. Poincare-Light Hill technique has been used for the solution of the system of partial differential equations. The velocity and temperature profile for dust particles and fluid are discussed in this article. The influence of different parameters on the Nusselt number is also discussed thoroughly.

Couette flow of viscoelastic dusty fluid in a rotating frame along with the heat transfer

Viscoelastic fluid is an advanced fluid which exhibits both elastic and viscous properties. Whereas rotation of viscoelastic fluid is a very complex phenomenon and has an immense amount of applications in engineering and product making industries. Due to various applications in real life researchers are working to understand the rheology of viscoelastic fluids. Viscoelastic dusty fluids are used in gas cooling systems. In nuclear reactors, dusty fluids are used to lower the temperature of the system. Such fluids are also used in centrifugal separators, which separate solid particles from the liquid state, etc. Therefore, in the present study, viscoelastic dusty fluid is analyzed. More precisely free convective Couette flow under the influence of the transversely applied uniform magnetic field in a rotating frame is considered. The subject fluid is driven by the sine oscillations of the upper plate along with the effect of free convection. Due to rotation, the fluid and dust particles have complex velocities which is the sum of primary velocity and secondary velocity. The flow regime is modeled in terms of partial differential equations. To non-dimensionalize the system of governing equations, dimensionless variables have been derived through Buckingham-Pi theorem. The system of partial differential equations is solved through assumed periodic solutions (Poincare-Light Hill Technique). The expressions for skin friction (shear stresses at y = 0) and Nusselt number (the rate of heat transfer) are also calculated. Moreover, parametric influence on Nusselt number, and velocity profile of the fluid and the dust particles, is discussed. It is observed that increase in rotation parameter η causes retardation in the velocity of dust particles and the fluid. This is due to the fact that the increase in η enhances the Coriolis forces that are in fact inertial forces, causing a retardation in the velocity of the fluid phase and the dust phase.

A DOMIAN DECOMPOSITION METHOD FOR STEADY FREE CONVECTIVE COUETTE FLOW IN A VERTICAL CHANNEL WITH NON-LINEAR THERMAL RADIATION, DYNAMIC VISCOSITY AND DYNAMIC THERMAL CONDUCTIVITY EFFECTS

In this paper, we investigate steady free convective Couette flow in a vertical channel with nonlinear thermal radiation, dynamic viscosity and dynamic thermal conductivity effects. The investigation is motivated by the studies of some researchers which assumed linear thermal radiation and constant fluid properties. However, this is uncalled for; as these assumptions do not reflect true behavior of the flow. For instance; increase in temperature affects fluid viscosity, thermal conductivity thereby changing the transport phenomenon. Here; the investigation considers both the fluid viscosity and thermal conductivity to be dependent on temperature with the thermal radiation adopting nonlinear form. Due to this reasons, the associated flow equations are highly nonlinear and exhibit no analytical solution and therefore require the use of Adomian decomposition method (ADM) of solution. The attained ADM solution is then coded into computer algebra package of mathematica where results under the parameters of interest are presented and discussed. Results of the investigation show that raising the thermal radiation leads to corresponding rise in both the velocity and temperature of the fluid in the channel. Furthermore; lessening the viscosity and thermal conduction of the fluid were identified to escalate both velocity and temperature of the fluid.

On a Couette Flow of Conducting Fluid

We discuss the thermal radiation effect on unsteady free-convective Couette flow of conducting fluid in the presence of transverse magnetic field. The mathematical model is highly nonlinear due to the effect of the thermal radiation. Both numerical solution by the finite difference method and the analytical solution of the steady state by the perturbation method are presented. The numerical solution at large time agrees with the analytic solution of the steady state.

Thermal diffusion and diffusion thermo effects on an unsteady heat and mass transfer magnetohydrodynamic natural convection Couette flow using FEM

Abstract The numerical solutions of unsteady hydromagnetic natural convection Couette flow of a viscous, incompressible and electrically conducting fluid between the two vertical parallel plates in the presence of thermal radiation, thermal diffusion and diffusion thermo are obtained here. The fundamental dimensionless governing coupled linear partial differential equations for impulsive movement and uniformly accelerated movement of the plate were solved by an efficient Finite Element Method. Computations were performed for a wide range of the governing flow parameters, viz., Thermal diffusion (Soret) and Diffusion thermo (Dufour) parameters, Magnetic field parameter, Prandtl number, Thermal radiation and Schmidt number. The effects of these flow parameters on the velocity (u), temperature (θ) and Concentration (ϕ) are shown graphically. Also the effects of these pertinent parameters on the skin-friction, the rate of heat and mass transfer are obtained and discussed numerically through tabular forms. These are in good agreement with earlier reported studies. Analysis indicates that the fluid velocity is an increasing function of Grashof numbers for heat and mass transfer, Soret and Dufour numbers whereas the Magnetic parameter, Thermal radiation parameter, Prandtl number and Schmidt number lead to reduction of the velocity profiles. Also, it is noticed that the rate of heat transfer coefficient and temperature profiles increase with decrease in the thermal radiation parameter and Prandtl number, whereas the reverse effect is observed with increase of Dufour number. Further, the concentration profiles increase with increase in the Soret number whereas reverse effect is seen by increasing the values of the Schmidt number. Highlights Studied MHD free convection Couette flow with the effect of Soret & Dufour numbers. Finite Element Method is implemented as the numerical approach. Grid independence of FEM is studied. Enhance the fluid velocity as increasing of temperature and concentration gradient.

Unsteady MHD free convective Couette flow between vertical porous plates with thermal radiation

This study investigates the unsteady MHD free convective Couette flow of viscous incompressible electrically conducting fluid between two infinite vertical porous plates in the presence of transverse magnetic field and thermal radiation. Solutions for time dependent energy and momentum equations are obtained by the implicit finite difference method. To check the accuracy of the numerical solutions, steady state solutions for energy and momentum equations are obtained by using the perturbation method. The effect of various parameters controlling the physical situation is discussed with the aid of line graphs. Significant results from this study are that both velocity and temperature increase with the increase in thermal radiation parameter and time. A series of numerical experiments show that steady state velocity and temperature occur when the dimensionless time approaches the values of Prandtl number of the fluid. During the course of numerical computation, an excellent agreement was found between unsteady and steady state solutions at large value of time.

Effect of chemical reaction and radiation absorption on the unsteady MHD free convection Couette flow in a vertical channel filled with porous materials

This paper deals with effect of chemical reaction and radiation absorption on the unsteady MHD natural convection flow in a vertical channel filled with porous materials. One of the plate moves with a constant velocity in the direction of fluid flow while the other plate is stationary. A uniform magnetic field acts perpendicular to the porous plate, which absorbs the fluid with a suction velocity varying with time. The dimensionless governing equations for this problem are solved analytically using two-term harmonic and non-harmonic perturbation series method. The results of the analytical solutions for velocity, temperature and concentration profiles of both phases are graphically presented and discussed. It is noteworthy to mention that growing permeability and channel width parameter lead to increase in the fluid velocity profile. Results in the present work have been compared with other works in literature and an excellent agreement is found.

FINITE ELEMENT ANALYSIS OF UNSTEADY RADIATIVE MHD NATURAL CONVECTION COUETTE FLOW BETWEEN PERMEABLE PLATES WITH VISCOUS ND JOULE DISSIPATION

This paper discusses the unsteady magnetohydrodynamic free convection Couette flow of an incompressible viscous fluid between two infinite vertical permeable plates in the presence of thermal radiation with an exponentially decaying pressure gradient. A uniform magnetic field that is perpendicular to the plates, and uniform suction and injection through the plates are applied. The magnetic field lines are assumed to be fixed relative to the moving plate. The momentum equation takes buoyancy forces into consideration, while the energy equation considers thermal radiation effects and viscous and Joule dissipations. The fluid is considered to be a gray absorbing-emitting but nonscattering medium in the optically thick limit. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The coupled pair of non-linear partial differential equations is discretized using the Galerkin finite element method. This yields a system of non-linear algebraic equations which is solved using an iterative method to obtain the velocity and temperature distributions. The effects of suction parameter S, radiation parameter Rd, Received: May 15, 2014 c © 2015 Academic Publications, Ltd. url: www.acadpubl.eu Correspondence author 124 V.M. Job, S.R. Gunakala Grashof number Gr, magnetic parameter H, Prandtl number Pr and Eckert number Ec on the velocity and temperature distributions are investigated. AMS Subject Classification: 76R10, 76W05

Unsteady/Steady Free Convective Couette Flow of Reactive Viscous Fluid in a Vertical Channel Formed by Two Vertical Porous Plates

This paper presents unsteady as well as steady-state free convection Couette flow of reactive viscous fluid in a vertical channel formed by two infinite vertical parallel porous plates. The motion of the fluid is induced due to free convection caused by the reactive nature of viscous fluid as well as the impulsive motion of one of the porous plates. The Boussinesq assumption is applied, and the nonlinear governing equations of motion and energy are developed. The time-dependent problem is solved using implicit finite difference method, and steady-state problem is solved by applying regular perturbation technique. During the course of computation, an excellent agreement was found between the well-known steady-state solutions and transient solutions at large value of time.

Radiation Effects on Unsteady MHD Free Convective Couette Flow of Heat Generation/Absorbing Fluid

effects on free convection MHD Couette flow of a viscous incompressible heat generating fluid confined between vertical plates have been studied. The governing equations are solved analytically using the Laplace transform technique. The variations of velocity and fluid temperature are presented graphically. It is observed that the velocity decreases with an increase in either magnetic parameter or radiation parameter or generation parameter or Prandtl number. It is also observed that the velocity increases with an increase in either Grashof number or time. An increase in either radiation parameter or Prandtl number leads to fall in the fluid temperature. It is seen that the fluid temperature increases with an increase in either heat generation parameter or time. Further, it is seen that the absolute value of shear stress at the moving plate increases with an increase in either magnetic parameter or radiation parameter while it decreases with an increase in either heat generation parameter or Prandtl number. The rate of heat transfer increases with an increase in either Prandtl number or heat generation parameter or time.

Magnetohydrodynamic Free Convective Couette Flow With Suction and Injection

This paper considers the unsteady MHD free convective Couette flow of a viscous incompressible electrically conducting fluid between two parallel vertical porous plates. Both cases of the applied magnetic field being fixed either to the fluid or to the moving porous plate are considered. The solution of the governing equations has been obtained by using a Laplace transform technique. However, the Riemann-sum approximation method is used to invert the Laplace domain to the time domain. The unified solution obtained for the velocity have been used to compute the skin friction, while the temperature has been used to compute the Nusselt number. The effect of various flow parameters entering into the problem such as Prandtl number, Grashof number, and the suction/injection parameter are discussed with the aid of line graphs. The skin friction have been seen to decrease with both suction and injection on the surface of the moving plate when the channel is being cooled, while on the stationary plate, the magnitude of the skin friction increases with injection.

Three dimensional free convection couette flow with transpiration cooling

Free convection flow between two vertical parallel plates with transverse sinusoidal injection of the fluid at the stationary plate and its corresponding removal by constant suction through the plate in uniform motion has been analyzed. Due to this type of injection velocity, the flow becomes three-dimensional. Analytical expressions for the velocity, temperature, skin friction and rate of heat transfer were obtained. The important characteristics of the problem, namely the skin friction and the rate of heat transfer are discussed in detail with the help of graphs.