Steady Couette Flow Research Articles

Impact of entropy generation and temperature gradient heat source on Couette flow in a permeable magnetic field

AbstractThis research paper focused on investigating the influence of various factors on steady Couette flow beneath a permeable bed. Factors studied included aligned magnetic field, thermal radiation, temperature gradient heat source, viscous dissipation, and Joules dissipation. The momentum and energy equations governing flow and heat transmission were analytically solved to predict the generation of entropy. The findings were visually presented through graphical representations, which effectively demonstrated the effect of these factors on the fluid's velocity, temperature, entropy production, and Bejan number. In addition, the shear stress and rate of heat transfer coefficient at the channel walls were computed and their behavior was documented in tables to provide further insights.

Grad's 13 moments-based gas kinetic flux solver with triangle unstructured meshes for simulating continuum and rarefied fluid flows

A numerical framework based on the gas kinetic flux solver (GKFS) with unstructured meshes of triangle cells has been proposed and assessed in this work. Like conventional GKFS, the present scheme only updates the cell-average macroscopic conservative variables in time, thereby saving computational costs. At each cell interface, the numerical normal flux is computed with the GKFS scheme proposed by Liu et al. [J. Comput. Phys. 415, 109548 (2020)], in which the distribution functions at the surrounding points are reconstructed with the Grad's 13 moments (G13). Additionally, a solid wall boundary condition treatment has been proposed in the present G13-GKFS framework, which allows one to model from purely specular to perfectly thermalized solid walls. The present framework has been validated with the steady cylindrical Couette flow, the lid-driven cavity flow, the unsteady Rayleigh flow, and the rarefied flow around the NACA0012 airfoil test-cases, where good agreements are found with references for a quite wide range of flow regimes, from continuum to transitional flow regimes.

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.

Planar Couette flow of power law nanofluid with chemical reaction, nanoparticle injection and variable thermal conductivity

This article presents the transport of thermal energy and mass in the mixed convection steady planar Couette flow of power-law nanofluid with variable thermal conductivity through a permeable microchannel. The entropy production deliberation here is to investigate the irreversibility aspects. The momentum equation has been made by the permeability of the porous medium, Hall current effect, thermal, and solutal bouncy force. The mathematical model for the thermal energy has been formulated by Ohmic dissipation, Brownian motion, temperature-dependent thermal conductivity, and thermophoresis. The microchannel boundaries retain the no-slip boundary conditions. The concentration formulation has been made by nanoparticle injection rate and chemical reaction. The momentum, energy, and solutal formulations have been numerically cracked by means of Runge–Kutta–Fehlberg fourth fifth-order numerical procedure. The applied Hall current effect generates the fluid flow in the transverse direction. The flow along both axial and transverse direction enhances with thermal and solutal Grashof number and diminutions with permeability of the porous medium. Optimum magnitude of thermophoresis and Brownian motion amplifies the thermal energy of the shear thinning fluid. Concentration field exhibits the opposite nature with the nanoparticle injection rate parameter and chemical reaction parameter. Hall current parameter enhances the irreversibility of the Newtonian nanofluid.

Conserved method for specified heat flux boundary in UGKS simulation of microscale gas flow

The unified gas kinetic scheme (UGKS) is a powerful method to simulate microscale gas flows. However, due to the lack of corresponding specified heat flux boundary (SHFB) treatment, there is great difficulty for UGKS to simulate problem with SHFB. In this paper, a SHFB treatment for UGKS is proposed based on gas kinetic theory. In the proposed boundary treatment, the heat flux term is directly added into the gas kinetic conservation equation of heat flux on boundary. In this conservation equation, the heat flux transferring from gas to the boundary is calculated using an extrapolated distribution function of inside gas, and the heat flux transferring form boundary to the gas is calculated using an equilibrium rebounding distribution function. Using the conservation equation of mass on boundary to close conservation equations, the gas density and temperature terms for rebounding gas distribution function can be calculated simultaneously. Distribution function on SHFB is reconstructed using rebounding gas distribution function and extrapolated distribution function of inside gas. Fluxes of gas distribution function and macro variables on SHFB is calculated with the reconstructed distribution function. Typical benchmark cases including steady and unsteady Fourier flow, steady Couette flow, pressure-driven flow, cavity flow and supersonic flow around square cylinder are tested to validate the proposed boundary treatment. The validations prove the accuracy, reliability and universality of the proposed method.

Viscous dissipation effect on steady natural convection Couette flow with convective boundary condition

Abstract The present article explores the effect of viscous dissipation on steady natural convection Couette flow subject to convective boundary condition. Due to the nonlinearity and coupling of the governing equations in the present situation, the homotopy perturbation method was employed to obtain the solutions of the energy and momentum equations. The impacts of the controlling parameters were investigated and discussed graphically. In the course of investigation, it was found that fluid temperature increases with an increase in viscous dissipation while the reverse trend was observed in fluid velocity. However, it was also discovered that heat generation leads to a decrease in the rate of heat transfer on the heated plate and it increases on the cold plate. Finally, it was concluded that the velocity boundary layer thickness increases with an increase in Biot number.

Solving Fredholm second-kind integral equations with singular right-hand sides on non-smooth boundaries

A numerical scheme is presented for the solution of Fredholm second-kind boundary integral equations with right-hand sides that are singular at a finite set of boundary points. The boundaries themselves may be non-smooth. The scheme, which builds on recursively compressed inverse preconditioning (RCIP), is universal as it is independent of the nature of the singularities. Strong right-hand-side singularities, such as 1/|r|α with α close to 1, can be treated in full machine precision. Adaptive refinement is used only in the recursive construction of the preconditioner, leading to an optimal number of discretization points and superior stability in the solve phase. The performance of the scheme is illustrated via several numerical examples, including an application to an integral equation derived from the linearized BGKW kinetic equation for the steady Couette flow.

Effect of wall conduction on steady natural convection couette flow in a vertical channel

Effect of wall conduction on steady natural convection couette flow in a vertical channel

An analytical study on effects of viscous dissipation and suction/injection on a steady mhd natural convection couette flow of heat generating/absorbing fluid

This work concerns a theoretical investigation on the effects of suction/injection, magnetic field, permeability of porous materials and viscous dissipation on an electrically conducting incompressible fluid passes through a vertical porous channel filled with porous materials. One of the plates moves in the flow direction while the other is stationary. The governing coupled flow equations have been solved analytically using Homotopy Perturbation Method (HPM). The influences of the flow parameters on velocity and temperature were plotted on graphs while numerical values for rate of heat transfer and shear stress on the heated and cold plates were presented in tables. Excellent agreements were found when compared with the previous works. It is noteworthy to mention that the hydrodynamic and thermodynamic distributions of the fluid increase with increase in viscous dissipation [Formula: see text]. It is also found that the shear stress decreases with increase in the magnetic field [Formula: see text] while a reverse case was observed for growing the permeability of the porous materials [Formula: see text]. It is further found that the velocity and temperature distributions decrease with increase in suction [Formula: see text].

Effects of viscous dissipation and boundary wall thickness on steady natural convection Couette flow with variable viscosity and thermal conductivity

Abstract This study theoretically examines the effects of boundary plate thickness and viscous dissipation on a steady natural convection flow of an incompressible viscous fluid of variable properties. This is due to the fact that several investigations in literature have neglected the thickness and material composition of the boundary plates and as such, their results are either over-determined or under-determined. The viscosity and thermal conductivity of the heat generating/absorbing fluid were assumed to be functions of temperature. Due to the nonlinearity and coupling nature of the governing flow equations, homotopy perturbation method (HPM) has been used to solve the problem. The effects of the thermophysical and flow parameters were captured in graphs and tables. It has been discovered from the study that the velocity profile increases with increase in thermal conductivity. Increase in boundary plate thickness ( d ) was found to boost the fluid flow across the medium while the temperature decreases near the heated plate. It’s further observed that the skin friction decreases on both plates with increase in fluid viscosity and boundary plate thickness ( d ) while the rate of heat transfer decreases on both the plates with an increase in boundary plate thickness ( d ). The volume flow rate is discovered to increase with increase in Brinkman number ( B r ) while a decrease was observed with increase in boundary plate thickness ( d ).

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.

Steady natural convection Couette flow with wall conduction and thermal boundary condition of third kind

AbstractThis study theoretically investigates the effects of viscous dissipation and boundary plate thickness on an incompressible heat generating/absorbing fluid with non‐uniform internal temperature unlike lumped heat capacitance assumption. The flow, which is laminar is induced by free convection caused by asymmetric heating of the channel boundaries and internally generated energy caused by viscous dissipation. In addition, convection through the boundary plates is also considered in the flow formation. One of the plates channel moves along the flow direction while the other is stationary. Due to the non‐linear and coupling nature of the governing flow equations, homotopy perturbation method (HPM) has been adopted to analytically find the approximate solution to the problem. The effects of thermodynamic and hydrodynamic parameters are depicted in graphs and tables. It is discovered from the investigation that, both the velocity and temperature profiles increase with increase in viscous dissipation. Velocity distribution decreases with increase in Biot number while the temperature distribution near the heated plate increases with increase in Biot number. The increase in boundary plate thickness d causes a boost in the fluid flow across the medium and reduces the temperature of the fluid near the heated plate. It is further discovered that the rate of heat transfer on both plates increase with increase in Biot number while they drastically dropped when the boundary plate thickness d is increased. The shear stresses on the surface of both plates increase with increase in heat generation while reverse cases were observed with increase in heat absorption . It is further observed that the volume flow rate within the channel increases with increase in viscous dissipation .

Steady Plane Poiseuille Flow of Viscous Incompressible Fluid between Two Porous Parallel Plates in Magnetic Field

In this paper we have investigated the steady plane Couette flow of viscous incompressible fluid between two porous parallel plates in magnetic field. We have studied the velocity, average velocity, shearing stress, skin frictions, the volumetric flow, drag coefficients and stream lines. Keywords: Steady Couette flow, viscous parallel plates, incompressible fluid and magnetic field. NOMENCLATURE u = velocity component along x - axis v = velocity component along y - axis t = the time = the density of fluid P = the fluid pressure K= the thermal conductivity of the fluid

Steady planar Couette flow of rarefied binary gaseous mixture based on kinetic modeling

The planar Couette flow of binary gaseous mixtures is studied on the basis of the kinetic model introduced by Kosuge (2009). The calculations were carried out for a wide range of the gas rarefaction, various values of the mole fraction and for two values of the wall speed corresponding to linear and non-linear Couette flow configurations. The kinetic model shear stress, number density, temperature and the mole fraction have been found to be in very good agreement with corresponding ones obtained by the DSMC method. However, the difference in the velocity profiles obtained by the Kosuge model and the DSMC method can be large, especially near the free molecular regime. Also, very good agreement between the Kosuge model results and the Chapman–Enskog solutions is observed. Moreover, the influence of the intermolecular potential is investigated by comparing the results of the Hard-Sphere model with those for a Realistic potential. It was shown that the shear stress significantly depends on the intermolecular potential when the wall speed is large. Finally, applying the equivalent single gas approach it is deduced that this concept can be applied in binary gas mixture Couette flows at any pressure when the molecular mass ratio approaches unity, but only at high pressure when the ratio is large. • The Couette flow problem is solved on the basis of the Kosuge model. • Very good agreement between Kosuge model and the DSMC method has been provided for the shear stress, number density, temperature and the mole fraction. • The differences in the velocity distributions of the individual species can be large. • The influence of the intermolecular potential is investigated. • The validity of the equivalent single gas approach is analyzed.

Viscous Dissipation Effect on a Steady Generalised Couette Flow of Heat-Generating/Absorbing Fluid in a Vertical Channel

Abstract This article investigates the viscous dissipation effect on steady generalised Couette flow of heat-generating/absorbing fluid in a vertical channel. Equations of energy and momentum are obtained and solved using the homotopy perturbation method. The influences of the dimensionless flow parameter have been plotted graphically and discussed for varying values of the controlling parameters. During the course of computation, it is found that fluid temperature and velocity increase with an increase in viscous dissipation and also seen that growing mixed convection parameter Gre leads to a corresponding rise in temperature and velocity. It is further discovered that heat absorption leads to increase in the heat transfer on the heated wall. Finally, it is concluded that heat generation contributes to increase the mixed convection, hence, it requires decrease in mixed convection parameter to bring about a reverse flow near the stationary plate.

Couette Flow of a Viscoelastic Maxwell-Type Medium with Two Relaxation Times

A Couette flow of a viscoelastic medium is considered that is described by the Johnson–Segalman–Oldroyd model with two relaxation times. The development of singularities related to the appearance of internal discontinuities is studied both analytically and numerically within one-dimensional nonstationary hyperbolic models of viscoelastic Maxwell-type media. A numerical model for calculating nonstationary one-dimensional discontinuous solutions is constructed, discontinuous solutions are studied, and the hysteresis phenomenon, i.e., the dependence of the structure of a steady Couette flow on the prehistory of its formation, is analyzed.

High-order weighted essentially nonoscillatory finite-difference formulation of the lattice Boltzmann method in generalized curvilinear coordinates.

In this work, a high-order weighted essentially nonoscillatory (WENO) finite-difference lattice Boltzmann method (WENOLBM) is developed and assessed for an accurate simulation of incompressible flows. To handle curved geometries with nonuniform grids, the incompressible form of the discrete Boltzmann equation with the Bhatnagar-Gross-Krook (BGK) approximation is transformed into the generalized curvilinear coordinates and the spatial derivatives of the resulting lattice Boltzmann equation in the computational plane are solved using the fifth-order WENO scheme. The first-order implicit-explicit Runge-Kutta scheme and also the fourth-order Runge-Kutta explicit time integrating scheme are adopted for the discretization of the temporal term. To examine the accuracy and performance of the present solution procedure based on the WENOLBM developed, different benchmark test cases are simulated as follows: unsteady Taylor-Green vortex, unsteady doubly periodic shear layer flow, steady flow in a two-dimensional (2D) cavity, steady cylindrical Couette flow, steady flow over a 2D circular cylinder, and steady and unsteady flows over a NACA0012 hydrofoil at different flow conditions. Results of the present solution are compared with the existing numerical and experimental results which show good agreement. To show the efficiency and accuracy of the solution methodology, the results are also compared with the developed second-order central-difference finite-volume lattice Boltzmann method and the compact finite-difference lattice Boltzmann method. It is shown that the present numerical scheme is robust, efficient, and accurate for solving steady and unsteady incompressible flows even at high Reynolds number flows.

Study on Non-Newtonian Behaviors of Lennard-Jones Fluids via Molecular Dynamics Simulations

Using nonequilibrium molecular dynamics simulations, we study the non-Newtonian rheological behaviors of a monoatomic fluid governed by the Lennard-Jones potential. Both steady Couette and oscillatory shear flows are investigated. Shear thinning and normal stress effects are observed in the steady Couette flow simulations. The radial distribution function is calculated at different shear rates to exhibit the change of the microscopic structure of molecules due to shear. We observe that for a larger shear rate the repulsion between molecules is more powerful while the attraction is weaker, and the above phenomena can also be confirmed by the analyses of the potential energy. By applying an oscillatory shear to the system, several findings are worth mentioning here: First, the phase difference between the shear stress and shear rate increases with the frequency. Second, the real part of complex viscosity first increases and then decreases while the imaginary part tends to increase monotonically, which results in the increase of the proportion of the imaginary part to the real part with the increasing frequency. Third, the ratio of the elastic modulus to the viscous modulus also increases with the frequency. These phenomena all indicate the appearance of viscoelasticity and the domination of elasticity over viscosity at high oscillation frequency for Lennard-Jones fluids.

Steady laminar flow of fractal fluids

We study laminar flow of a fractal fluid in a cylindrical tube. A flow of the fractal fluid is mapped into a homogeneous flow in a fractional dimensional space with metric induced by the fractal topology. The equations of motion for an incompressible Stokes flow of the Newtonian fractal fluid are derived. It is found that the radial distribution for the velocity in a steady Poiseuille flow of a fractal fluid is governed by the fractal metric of the flow, whereas the pressure distribution along the flow direction depends on the fractal topology of flow, as well as on the fractal metric. The radial distribution of the fractal fluid velocity in a steady Couette flow between two concentric cylinders is also derived.

Centrifugal instability of pulsed Taylor-Couette flow in a Maxwell fluid.

Centrifugal instability of a pulsed flow in a viscoelastic fluid confined in a Taylor-Couette system is investigated. Both cylinders are subject to an out-of-phase modulation of rotation with equal modulation amplitude and modulation frequency. The fluid is assumed to obey a linear Maxwell fluid with a relaxation time and a constant viscosity. Attention is focused on the linear stability analysis and on the effect of Deborah and frequency numbers on the critical values of the Taylor and wave numbers. Using Floquet theory, we show that in the limit of low frequency, the Deborah number has no effect on the stability of the basic state which tends to the classical configuration of steady circular Couette flow. When the frequency number increases, the stability of the basic flow is enhanced and the Deborah number has a destabilizing effect which is strongly pronounced in the high-frequency limit. In this frequency limit, the critical parameters tend to constant values independently of the frequency number. These numerical results are in good agreement with the asymptotic solutions obtained in the limit of low and high frequencies. Moreover, a correlation between the rheological proprieties of the fluid in a rheometric experience, especially the loss and storage modulus, and this hydrodynamical instability behavior is presented.