The effect of radial temperature gradient and axial magnetic field on the stability of couette flow: The narrow gap problem

A numerical solution to the MHD stability problem for dissipative Couette flow in a narrow gap is presented under the following conditions: (i) the inner cylinder rotating with the outer cylinder stationary, (ii) corotating cylinders, (iii) counter-rotating cylinders, (iv) an axially applied magnetic field, (v) conducting and nonconducting walls, and (vi) the presence of a radial temperature gradient. Results for the critical wave number a_c, and the critical Taylor number T_c, are presented. The variation of T_c is shown on graphs for both the conducting and nonconducting walls and for different values of ±μ (= Ω₂/Ω₁, where Ω₂ is the angular velocity of the outer cylinder, and Ω₁ is the angular velocity of the inner cylinder), the magnetic field parameter Q, which is the square of the Hartmann number and ± N (= Ra/Ta, where Ra is the Rayleigh number). The effects of ±μ, N and Q on the stability of flow are discussed. It is seen that the effect of the magnetic field is to inhibit the onset of instability, this being more so in the presence of conducting walls and a negative temperature gradient.     

An electrical network for the numerical solution of transient mhd couette flow of a dusty fluid: Effects of variable properties and hall current

The Network Simulation Method (NSM) has been used to study the variations with velocity of suction, hall effect, Reynolds and Hartmann number, particle concentration and Eckert number on the unsteady MHD Couette Flow and heat transfer of a dusty and electrically conducting fluid between parallel plates in the presence of an external uniform magnetic field and uniform suction and injection. The solutions are obtained with the network model proposed and the electric circuit simulation program PSpice. The fluid is acted upon by a constant pressure gradient and an external uniform magnetic field is applied perpendicular to the plates. Due to the presence of uniform suction and injection, the Hall Effect is not dismissed. The NSM is applied to solve the steady-state and transient problems of flow and heat transfer for both the fluid and dust particles. This method requires only discretization of the spatial co-ordinates, while time remains a real continuous variable. Velocity and temperature are studied for different values of the viscosity and magnetic field parameters and for different particle concentrations and upper wall velocities.     

Hydromagnetic slip flow of a radiating fluid with hall currents part 1: Fully developed flow

The problem of slip flow, as provoked primarily by high temperature rather than low pressure, is considered for a thermally radiating gas in the presence of Hall currents and mass transfer in a porous medium. The general differential approximation for radiation is invoked, and the problem, which is fully developed, is tackled numerically and analytically.     

Entropy analysis of unsteady flow on flat plate

The flow generated due to the motion of flat plate is an important problem in fluid mechanics, since it gives insight into the unsteady boundary layer generation. The entropy analysis of such flow problems can provide enlightening information on the viscous dissipation in the fluid flow. In the present study, an impulsively started Couette flow is studied, where a flow between two parallel plates is moved impulsively by moving the lower plate from rest to a finite velocity in the half‐space y > 0. Development of velocity and entropy profiles, at different time scales, has been numerically obtained; the development of total entropy with time, in the space between the plates, has been determined. It is found that entropy generation in the space between the plates is more considerable at initial times of motion than at later times. Copyright © 2001 John Wiley & Sons, Ltd.     

Computational analysis of coupled radiation-convection dissipative non-gray gas flow in a non-Darcy porous medium using the Keller-box implicit difference scheme

The effects of thermal radiation parameter (F), transpiration (γ), Eckert number (Ec), Prandtl number (Pr), buoyancy (Grashof number Gr), a Darcy parameter (Re/Gr Da) and a Forcheimmer inertial parameter (Fs Re/Gr Da) on two-dimensional free convective flow of an optically thin, near-equilibrium, non-gray gas past a vertical surface in a non-Darcy porous medium, are studied using the robust Keller finite-difference technique incorporating Newtonian quasilinearization and block-tridiagonal elimination. The Darcy–Brinkman–Forcheimmer inertial-viscous flow model is used for the momentum equation and the Cogley–Vincenti–Giles formulation is adopted to simulate the radiation component of heat transfer. The one-dimensional thermal radiation model works successfully for gases in the optically thin limit. Pseudo-similarity transformations are employed to simplify the highly non-linear partial differential equations for momentum and heat transfer into numerically manageable pseudosimilar ordinary differential equations which are solved with Keller's box method. Effectively, the radiation contribution is seen to take the form of a linear temperature term Fθ coupled with the streamwise pseudo-similar variable ξ. Local wall shear stress and local heat transfer rates are systematically computed for a wide selection of radiation parameter F values. The results are presented graphically for different gases. © 1998 John Wiley & Sons, Ltd.     

GDQ方法在微尺度库埃特流动中的应用

主要讨论微电机系统中常见的微库埃特流动系统.以N-S方程为基础,引入相应的边界条件建立数学模型,用GDQ方法计算新建模型,使得基于连续性假设的理论模型延伸到滑移区和过渡流动区的稀薄气体流动.通过调整边界条件中的重要参数切向动量协调系数σv和热量协调系数σt的值,可以将新建模型的应用范围扩大到克努森数Kn＜1.2的稀薄气体流动中.     

Laminar forced convection with viscous dissipation in a Couette–Poiseuille flow between parallel plates

In this study, analytical solutions are obtained to predict laminar heat-convection in a Couette–Poiseuille flow between two plane parallel plates with a simultaneous pressure gradient and an axial movement of the upper plate. A Newtonian fluid with constant properties is considered with an emphasis on the viscous-dissipation effect. Both hydrodynamically and thermally fully-developed flow cases are investigated. The axial heat-conduction in the fluid is neglected. Two different orientations of the thermal boundary-conditions are considered: the constant heat-flux at the upper plate with an adiabatic lower plate (Case A) and the constant heat-flux at the lower plate with an adiabatic upper plate (Case B). For different values of the relative velocity of the upper plate, the effect of the modified Brinkman number on the temperature distribution and the Nusselt number are discussed. Comparison of the present analytical results for a special case with those available in the literature indicates an excellent agreement.     

Hydromagnetic slip flow of a radiating fluid with hall current Part II: fully developed flow with axial temperature and concentration variations

The problem of slip flow as provoked primarily by high temperature rather than low pressure is considered for a thermally radiating gas in the presence of Hall current and mass transfer in a porous medium. The flow, which is fully developed, is assumed to vary axially with distance and is tackled analytically under an optically thin gas radiative heat transfer differential approximation. The effect of various parameters of interest on the flow model are discussed quantitatively. © 1998 John Wiley & Sons, Ltd.     

Couette flow through a porous medium of a high prandtl number fluid with temperature-dependent viscosity

The velocity and temperature profiles for an impulsively started Couette flow have been derived for a fluid with a high and strongly temperature-dependent viscosity when the flow takes place through a porous medium. The steady as well as the transient state flows are discussed and the influence of the medium permeability is assessed. In the steady state the presence of the porous medium causes higher maximum temperatures only for sufficiently low permeabilities and in all cases significantly lower velocity profiles. The flow development times tend to be higher for the low permeabilities only for high Nahme numbers. For the transient state it is noticeable that, in all cases, the velocity develops much more rapidly than the temperature and that the presence of the porous medium accelerates this tendency. Finally the medium permeability produces skew temperature profiles and higher temperature time gradients at all times.     

Boundary-element method simulation of the impact of bounding walls on the dynamics of a particle group freely moving in a wide-gap Couette flow

In this study, the impact of the bounding walls on the dynamics of a group of neutrally-buoyant identical rigid spheres freely moving at negligible Reynolds numbers in a wide-gap Couette flow, which is important for understanding the particle migrations presented in concentrated suspensions subjected to inhomogeneous shear flows, is simulated by a three-dimensional boundary-element method (BEM) code. The results show that the particle interactions very close to the bounding walls cause the particle group to migrate away from the walls. As the distance of the bounding walls from the group increases, the migration changes direction and the group then move towards the walls. As this distance continues to increase, the migration of the group decreases and beyond a specific distance from the bounding walls the migration of the group is negligible. In addition, the BEM simulations show that the extent and rate of the migration of the group increase as the inter-particle distance decreases.     

Couette flow with frictional heating in a fluid with temperature and pressure dependent viscosity

This study investigates the effects of variable viscosity and frictional heating on the laminar flow in a horizontal channel having a wall at rest and a moving wall subjected to a prescribed shear stress. The wall at rest is thermally insulated, while the moving wall is kept at a uniform temperature. This investigation concerns fluids whose viscosity depends exponentially on the pressure and temperature. An appropriate approximation is introduced to analyze the interplay between the dependence of viscosity on the pressure and temperature and the viscous dissipation. It is shown that the nonlinear term in the equation for the balance of energy representing the frictional heating may lead to the existence of dual solutions of the boundary value problem for fixed values of the material parameters that characterize the fluid. The results obtained are compared with those predicted by the generalization of the Oberbeck-Boussinesq approximation for a fluid with pressure and temperature dependent viscosity. It is found that the results for the approximation carried out in this paper and those that stem from the Oberbeck-Boussinesq approximation are markedly different.     

Investigation of basic molecular gas structural effects on hydrodynamics and thermal behaviors of rarefied shear driven micro/nano flow using DSMC

In the present work, rarefied gas flow between two parallel moving plates maintained at the same uniform temperature is simulated using the direct simulation Monte Carlo (DSMC) method. Heat transfer and shear stress behavior in the micro/nano-Couette flow is studied and the effects of the important molecular structural parameters such as molecular diameter, mass, degrees of freedom and viscosity–temperature index on the macroscopic behavior of gases are investigated. Velocity, temperature, heat flux and shear stress in the domain are studied in details. Finally, a discussion on the role of the molecular structural parameters in the decrease or increase of amounts of hydrodynamics and thermal properties of the gas is presented.     

On the transition for a generalized Couette flow of a reactive third-grade fluid with viscous dissipation

We study the thermal transition of a reactive flow of a third-grade fluid with viscous heating and chemical reaction between two horizontal flat plates, where the top is moving with a uniform speed and the bottom plate is fixed in the presence of imposed pressure gradient. This study is a natural continuation of earlier work on rectilinear shear flows. The governing equations are non-dimensionalized and the resulting system of equations are not coupled. An approximate explicit solution is found for the flow velocity using homotopy-perturbation technique and the range of validity is determined. After the velocity is known, the heat transport may be analyzed. It is found that the temperature solution depends on the non-Newtonian material parameter of the fluid, Λ, viscous heating parameter, Γ, and an exponent, m. Attention is focused upon the disappearance of criticality of the solution set {β, δ, θ_max} for various values of Λ, Γ and m, and the numerical computations are presented graphically to show salient features of the solution set.     

Boundary-element simulation of hydrodynamic interaction of two smooth spheres suspended in an unbounded Couette flow

The hydrodynamic interaction between two particles, suspended in shear flows, is fundamental to the macroscopic characterization of suspension flows. Although the understanding of the hydrodynamic interaction between two particles suspended in a quiescent or linear shear flow is mature, studies of the interaction in a non-linear shear field are rare. The current study calculates such interactions between two neutrally-buoyant smooth spheres moving at negligible Reynolds numbers in an unbounded wide-gap Couette flow by three-dimensional boundary-element method (BEM) simulations. Both the identical sphere-pair and the disparate sphere-pair are considered. The numerical results show that there is a preferential cross-streamline migration of the center-of-gravity of the sphere-pair in the plane of shear in the unbounded wide-gap Couette flow that does not arise in simple shear-flow. This migration is always directed towards low-shear regions when the sphere having the larger translational velocity approaches the other sphere, and reverses towards high-shear regions when the faster sphere leads the other sphere in the plane of shear. There is also a cross-streamline migration of the center-of-gravity of the sphere-pair in the plane of vorticity, but this migration does not have a preferential direction. These migrations are symmetric about the point where the spheres are at the minimum separation, and are only significant when the hydrodynamic interaction of the spheres is sufficiently strong. These results show that the migration of the center-of-gravity of the sphere-pair can be attributed to the non-linearity of the shear field. The hydrodynamic interaction between the two spheres has been quantified under various conditions by the BEM simulations for both identical and disparate spheres.     

Computation of entropy generation in dissipative transient natural convective viscoelastic flow

Entropy generation is an important aspect of modern thermal polymer processing optimization. Many polymers exhibit strongly non‐Newtonian effects and dissipation effects in thermal processing. Motivated by these aspects in this study, a numerical analysis of the entropy generation with viscous dissipation effect in an unsteady flow of viscoelastic fluid from a vertical cylinder is presented. The Reiner‐Rivlin physical model of grade 2 (second‐grade fluid) is used, which can envisage normal stress variations in polymeric flow‐fields. Viscosity variation is included. The obtained governing equations are resolved using implicit finite difference method of Crank‐Nicolson type with well imposed initial and boundary conditions. Key control parameters are the second‐grade viscoelastic fluid parameter (), viscosity variation parameter (), and viscous dissipation parameter (). Also, group parameter (), Grashof number (Gr), and Prandtl number (Pr) are examined. Numerical solutions are presented for steady‐state flow variables, temperature, time histories of friction, wall heat transfer rate, entropy, and Bejan curves for distinct values of control parameters. The results specify that entropy generation decreases with augmenting values of , , and Gr. The converse trend is noticed with increasing Pr and . Furthermore, the computations reveal that entropy and Bejan lines only occur close to the hot cylinder wall.     

Hydromagnetic free convection of a radiating fluid

Natural convection of an electrically conducting and radiating fluid in the presence of an external magnetic field is investigated numerically. The two opposing side walls are differentially heated with a temperature difference specified, while the top and bottom walls are insulated. The coupled momentum and energy equations associating with the electromagnetic retarding force as well as the buoyancy force terms are solved by an iterative procedure using the SIMPLER algorithm based on control volume approach. Steady-state conditions are assumed. The finite-volume method is utilised to solve the radiation transport adopting the same computational grid as used in solving the flow field, with which the radiating fluids in an enclosure are assumed to be radiatively opaque, transparent and participating, respectively. After validating the numerical procedures, the changes in the buoyant flow patterns and temperature distribution affected by combined radiation and a magnetic field are focused mainly. Comparative results for the velocity profiles and the heat transfer rates are presented too. Based on the results of this study, it was found that the radiation played a significant role in developing the hydromagnetic free convective flow in a differentially heated enclosure.     

Biodiesel production in a serpentine minireactor—Effect of flow distribution

The present work aims to find out the influence of flow pattern on pressure drop and fatty acid methyl ester (FAME) yield in a reactive system. Experiments are carried out with Jatropha oil and methanol by using potassium hydroxide (KOH) as catalyst for biodiesel production in two serpentine minireactors made of glass capillary of 2‐mm internal diameter. One is having a circular cross section, and the other is annulus. Slug flow, slug with droplet flow, and dispersed flow are observed in both the reactors. Effects of flow distribution on pressure drop and FAME yield have been studied. FAME yield of 98.5% is observed in both reactors for a molar ratio 20 (methanol to Jatropha oil), and the time for this yield in the first reactor is 16.6 minutes and that for the second reactor is 7.7 minutes. Higher yield also resulted in lower pressure drop due to lower viscosity of biodiesel in comparison with oil.     

Aspects of Arrhenius kinetics and Hall currents on gyratory Couette flow of magnetized ethylene glycol containing bi-hybridized nanomaterials

Incomparable thermal features of hybrid nanofluids (NFs) have been well recognized. Hybrid nanomaterials are prolifically used in chemistry processes, enzyme nanotechnology, pharmaceutical manufacturing, and so on. Motivated by numerous novel applications, in the present article, a theoretical study is conducted to demonstrate a time-dependent hydro-magnetic Couette flow and heat transport features inside a gyrating channel filled with a reactive second-grade hybrid NF (copper–alumina–ethylene glycol) and Darcian porous medium under multiparty impacts of Hall currents, temperature-dependent thermal conductivity, and Arrhenius chemical reaction. The modeled momentum equations are rendered nondimensional and solved analytically by means of the sophisticated Laplace transform technique. ND Solver in Mathematica is deployed to estimate the numerical solution of the energy equation. The computational outcomes are plotted and interpreted via physical constraints using line graphs and tables. The graphical outcomes assert that Hall currents significantly modify the gyratory flow dynamics and thermal features. The thermal profile and heat transfer rate manifest a diminishing pattern over widening Hall and rotation parameters. The change in thermal conductivity has a substantial impact on heat transmission. The novelty of the research study is a new insight into the hydro-thermal manners of magnetized rotational non-Newtonian hybrid NF.     

Solidification of electrically conducting liquid flow driven by shear and pressure gradients subject to viscous and Joule heating

Solidification of a liquid in motion driven by shear and pressure gradients occurs in many natural settings and technological applications. When the liquid is electrically conducting, its solidification rates can potentially be modulated by an imposed magnetic field. The shearing motion results in viscous dissipation and the Lorentz force induced by the magnetic field causes Joule heating of the fluid, which can influence the structure of the flow, thermal fields, and thereby the solidification process. In this study, a mathematical model is developed to study the combined effects of shear and pressure gradients in the presence of a magnetic field on the solidification of a liquid between two parallel plates, with one of them being insulated and under constant motion, and the other being cooled convectively and at rest. Under the quasi-steady assumption, closed-form semianalytical solutions are obtained for the instantaneous location of the solid–liquid interface, Nusselt number, and dimensionless power density as a function of various characteristic parameters such as the Hartmann number, pressure gradient parameter, Brinkman number, and Biot number. Furthermore, an interesting remelt or steady-state condition for the interfacial location is derived as arising from the competing effects of the solid side heat flux and viscous dissipation and Joule heating on the liquid side. The newly derived analytical results are shown to reduce to the various classical results in the limiting cases. A detailed systematic study is performed by the numerical solution of the semianalytical formulation, and the effects of different characteristic parameters on the solidification process are discussed.     

BEM simulation of hydrodynamic interaction between two identical neutrally buoyant smooth spheres freely moving in a wide gap Couette flow

In this paper, the hydrodynamic interaction between two identical neutrally buoyant smooth spheres freely moving at negligible Reynolds numbers in an unbounded wide gap Couette flow is investigated by three dimensional boundary element method (BEM) simulations. Such information is fundamental to the macroscopic characterization of suspension flows. The numerical results show that the hydrodynamic interaction of the sphere-pair causes both spheres to experience repulsive cross-streamline displacements, which are in opposite directions, when the trailing sphere is approaching the leading one. These cross-streamline displacements reach their maxima when the sphere-pair is at their closest center-to-center distance due to the strongest hydrodynamic interaction at this instant. After that, the initially trailing sphere becomes the leading one, and the sphere-pair begins to separate, causing the hydrodynamic interaction to decrease gradually and the spheres to return to their individual initial streamlines. The center of gravity of the sphere-pair in this non-linear shear field experiences a preferential cross-streamline migration in the plane of shear when they meet, firstly moving from regions of higher shear rates towards those of lower ones before the meeting and then experiencing a “reverse migration”, that is, moving from regions of low shear rates to those of higher ones, after the meeting, which is not presented in a linear shear field such as in a simple shear flow. There is also a cross-streamline migration of the center of gravity of the sphere-pair in the plane of vorticity, but this migration does not have a preferential direction. All these results suggest that the non-linearity of the shear field is responsible for the preferential cross-streamline displacement and the particle migration in concentrated suspensions undergoing inhomogeneous shearing. In addition, the hydrodynamic interaction between the sphere-pair has also been quantified under various conditions by the BEM simulations.