Constant Viscosity Case Research Articles

Unstable buoyant viscoelastic fluid flow in a vertical porous layer with temperature-dependent viscosity

The stability of thermally driven buoyant flow of a viscoelastic fluid saturating a vertical porous layer with viscosity depending linearly on temperature is investigated numerically. The rheological behavior of the fluid is described through the Oldroyd-B model, leading to a modified Darcy's law of momentum transfer in the porous medium. The study explores the linear stability of the base flow by analyzing the behavior of normal modes of perturbation. Neutral stability curves and the critical Darcy–Rayleigh number are determined for a wide range of viscoelastic and viscosity parameters. Transition curves from stability to instability in the viscoelastic parameters space are also provided for both constant and variable viscosity cases. Additionally, the results for Newtonian, Boger, and Maxwell fluids are delineated as particular cases from this study.

Incompressible boundary layer flow past a hump with temperature-dependent viscosity

The problem of boundary layer flow past a hump placed on a flat surface, where viscosity is coupled with temperature, is investigated using triple-deck theory. The incompressible Navier–Stokes equations supplemented by the heat and viscosity equations are considered in the limit that the Reynolds number is large. The triple-deck scalings are adopted, and asymptotic expansions are used to obtain some novel triple-deck equations coupled with the thermal boundary layer. We have used the same viscosity–temperature dependence as in Jasmine and Gajjar [Int. J. Heat Mass Transfer 48, 1022–1037 (2005)], in which viscosity varies inversely proportional to the temperature. The linear analysis is performed, and the nonlinear equations are solved numerically. Our results show that increasing the characteristic constant of the viscosity leads to enhanced peaks and troughs in the pressure and in the skin friction over the hump, as compared to the constant viscosity case. This suggests that temperature-dependent viscosity is more likely to provoke separation.

Comparison of using air, CO2 and helium for the cooling of square-shaped electronic parts: CFD study with entropy generation analysis

Numerical simulation has been used in the current work to investigate improving the cool-down of electronic parts of cubical form involving dummy parts within a rectangular duct. Three working fluids (air, CO2, and helium) were used to cool 12 electrical chip arrays in the duct. The simulation investigates the effects of cooling fluid type and shifting hot element placements on whole cooling functioning at various Reynolds numbers. Also, the impact of the distance among electronic parts is researched. This is accomplished by moving the heat sources while leaving other components in their original positions as dummies to preserve the flow characteristics. The Reynolds number falls between (500-19000). The dimensionless entropy generation number reduces with the rise of the Reynolds number, while the pumping power ratio increases. It is determined that the dimensionless entropy generation computed for the case of constant viscosity of air yields slightly greater values than those obtained for the case of temperature-dependent viscosity. A high level of agreement in the experimental work is used to verify the standard k-model.

Blottner finite difference analysis for non-Darcy flow of variable viscosity power-law nanofluids over a truncated cone with Arrhenius activation energy

Examining the behaviors of power-law nanofluid flow and the rate of heat transfer over different surfaces has received great attention due to its numerous industrial applications, such as polymer solutions, molten plastics, pulps, and foods. Also, the investigators focused on the case of constant viscosity, while in several practical situations, the dynamic viscosity of the power-law suspension is variable. So this study aims to examine non-similar solutions for the coupled flow of power-law non-Newtonian nanofluids over a truncated cone. The dynamic viscosity is varied according to the Reynolds viscosity model, and an exponential decaying form is considered for the internal heat generation. The non-Darcy model, where the quadratic drag is significant, is applied to formulate this situation, and the medium's permeability is varied according to the modified Ostwald-de-Waele power law model. Both the Arrhenius activation energy and non-linear thermal radiation impacts are considered. The solution methodology is based on the effective finite differences method with the Blottner scheme. The significant outcomes revealed that the rise in the power-law index n accelerates the flow and boosts the heat transfer rate. The values of the local Nusselt number in the case of the Darcy flow are higher than those of the non-Darcy case. Additionally, considering the case of variable dynamic viscosity, it is recommended to enhance the heat transfer rate. Furthermore, the rate of the heat transfer is enhanced by 29.1% viscosity parameter δ is varied from 0 to 0.5.

Dark Matter Cosmology with Varying Viscosity: A Possible Resolution to the S 8 Tension

We study varying forms of viscous dark matter (DM) and try to address the intriguing tensions of the standard model of cosmology with recent cosmological data, including the Hubble and S 8 tensions. We note that by assuming the DM viscosity depends on the Hubble parameter, DM density, or both, one can improve the statistics. Although the models tend to aggravate the Hubble tension a bit, they tend to reduce the S 8 tension, even in comparison with the constant viscosity case. Since similar-to-viscosity massive neutrinos suppress the power spectrum of matter on small length scales, considering them along with the viscous DM, we find that the neutrino mass range is tightened.

On variable viscosity and enhanced dissipation

In this article we consider the two-dimensional Navier–Stokes equations with variable viscosity depending on the vertical position. As our main result we establish linear enhanced dissipation near the non-affine stationary states replacing Couette flow. For instance, these shear flows may grow exponentially. Moreover it turns out that, in contrast to the constant viscosity case, decreasing viscosity leads to stronger enhanced dissipation and increasing viscosity leads to weaker dissipation.

Performance analysis of annular disks with non-Newtonian Rabinowitsch fluid model: Influence of squeeze film pressure, surface roughness, porosity and viscosity variation

In various systems of energy, such as turbo-machinery and viscous-lock system, squeeze film plays a crucial role for improving transport systems. The importance of the aforementioned applications led us to explore the physical behavior of Rabinowitsch fluid flow for several values of viscosity, [Formula: see text], load capacity [Formula: see text], nonlinear factor, [Formula: see text], dimensionless film thickness [Formula: see text], dimensionless radius of the capillary tube [Formula: see text], dimensionless thickness of porous pad [Formula: see text]), inner and outer radius ratio [Formula: see text], roughness parameter [Formula: see text] through a squeeze film with two rough porous annular discs. Five-point Gauss quadrature integral formula has been used to examine the characteristics of annular discs, and small perturbation method has been used to discretize the governing Rabinowitsch fluid flow (RFF) equations. The modified Reynolds equation for rough, porous and viscosity change with film thickness is developed using Christensen’s stochastic theory, modified Darcy’s theory and the association between viscosity and film thickness agreement. The impacts of [Formula: see text] on the behavior of porosity and viscosity variability of RFF have been visually depicted in terms of film pressure, load capacity and squeeze reaction time of annular discs. It has been determined that for RFF with variable viscosity and roughness parameter on a porous media, the performance of the annular disks enhances for [Formula: see text] (dilatant lubricant), and diminishes for [Formula: see text] (pseudo-plastic lubricant). It has been found that the film pressure in case of dilatant lubricant is increased by the influence of Rabinowitsch fluids on porous walls, but the behavior of pseudo-plastic lubricants has an opposite tendency relative to Newtonian lubricants. It has also been found that the impact of variability in porosity, roughness and viscosity diminishes the load-carrying capacity (LCC) with increased film thickness than the case of nonporous, smooth surface and constant viscosity of Rabinowitsch fluid.

Approximate Analytical Study of Natural Convection Flow of Non-newtonian Fluid Through Parallel-Pates With Heat Generation

In this present paper, approximate analytical study of natural convection flow of non-Newtonian fluid through Parallel-plates with heat generation is considered. The coupled non-linear momentum and energy equations was solved using perturbation technique. The cases of constant viscosity and temperaturedependent viscosity are treated with the case of temperature-dependent viscosity considered in two models: Reynold's model and Vogel's model. Within the constant viscosity case, results show that increase in the non-Newtonian parametersß, M, decreases the velocity of the fluid flow and increase in these parameters enhances the temperature of the plates. The effects of non-Newtonian and viscosity indices of both Reynold's and Vogel's models on velocity and temperature profiles are presented.

Application of Exponential Temperature Dependent Viscosity Model for Fluid Flow over a Moving or Stationary Slender Surface

The problem of laminar flow around a moving thin needle or slender surface with free stream velocity is analyzed when viscosity is supposed to have an exponential temperature dependency. Additionally, the temperature dependence in thermal conductivity is retained. Consideration of variable viscosity and thermal conductivity makes the governing equations coupled and non-linear. A self-similar solution of the problem is achieved, which depends on a parameter θw, which is the quotient of wall and ambient temperatures. A comparison of present findings is made with those of inversely linear temperature-dependent viscosity and constant viscosity cases. The size of the needle plays an important part in enhancing thermal boundary layer thickness. The expressions of skin friction coefficient and local Nusselt number in case of exponential temperature dependent viscosity are just derived in this study. An important observation is that computational results are qualitatively like those noticed for the case of inversely linear temperature dependency.

Two-layer channel flow involving a fluid with time-dependent viscosity

A pressure-driven two-layer channel flow of a Newtonian fluid with constant viscosity (top layer) and a fluid with a time-dependent viscosity (bottom layer) is numerically investigated. The bottom layer goes through an ageing process in which its viscosity increases due to the formation of internal structure, which is represented by a Coussot-type relationship. The resultant flow dynamics is the consequence of the competition between structuration and de-structuration, as characterised by the dimensionless timescale for structuration \((\tau )\) and the dimensionless material property \((\beta )\) of the bottom fluid. The development of Kelvin-Helmholtz type instabilities (roll-up structures) observed in the Newtonian constant viscosity case was found to be suppressed as the viscosity of the bottom layer increased over time. It is found that, for the set of parameters considered in the present study, the bottom layer almost behaves like a Newtonian fluid with constant viscosity for \(\tau >10\) and \(\beta >1\). It is also shown that decreasing the value of the Froude number stabilises the interfacial instabilities. The wavelength of the interfacial wave increases as the capillary number increases.

Unsteady hybrid nanoparticle-mediated magneto-hemodynamics and heat transfer through an overlapped stenotic artery: Biomedical drug delivery simulation.

Two-dimensional laminar hemodynamics through a diseased artery featuring an overlapped stenosis was simulated theoretically and computationally. This study presented a mathematical model for the unsteady blood flow with hybrid biocompatible nanoparticles (Silver and Gold) inspired by drug delivery applications. A modified Tiwari-Das volume fraction model was adopted for nanoscale effects. Motivated by the magneto-hemodynamics effects, a uniform magnetic field was applied in the radial direction to the blood flow. For realistic blood behavior, Reynolds' viscosity model was applied in the formulation to represent the temperature dependency of blood. Fourier's heat conduction law was assumed and heat generation effects were included. Therefore, the governing equations were an extension of the Navier-Stokes equations with magneto-hydrodynamic body force included. The two-dimensional governing equations were transformed and normalized with appropriate variables, and the mild stenotic approximation was implemented. The strongly nonlinear nature of the resulting dimensionless boundary value problem required a robust numerical method, and therefore the FTCS algorithm was deployed. Validation of solutions for the particular case of constant viscosity and non-magnetic blood flow was included. Using clinically realistic hemodynamic data, comprehensive solutions were presented for silver, and silver-gold hybrid mediated blood flow. A comparison between silver and hybrid nanofluid was also included, emphasizing the use of hybrid nanoparticles for minimizing the hemodynamics. Enhancement in magnetic parameter decelerated the axial blood flow in stenotic region. Colored streamline plots for blood, silver nano-doped blood, and hybrid nano-doped blood were also presented. The simulations were relevant to the diffusion of nano-drugs in magnetic targeted treatment of stenosed arterial diseases.

The Ekman spiral for piecewise-constant eddy viscosity

ABSTRACT We investigate the classical problem of wind-stress-induced non-equatorial steady ocean currents, considering a three-valued piecewise-constant eddy viscosity. This extends and generalizes recent results on piecewise-uniform eddy viscosity with only two layers. The aim is to determine how variations in the relative values of the eddy viscosity at different depths may account for the deviations from the surface current deflection of 45, predicted in the classical constant eddy viscosity case. Such variations are observed in field data, and we investigate analytically the effect the presence of a third region makes compared to the two-layer case.

New effective pressure and existence of global strong solution for compressible Navier–Stokes equations with general viscosity coefficient in one dimension

In this paper we prove the existence of a unique global strong solution for the Cauchy problem associated to the one dimensional Navier–Stokes equations with general degenerate viscosity coefficients. The cornerstone of the proof is the introduction of a new effective pressure which allows to obtain an Oleinik-type estimate for the so called effective velocity. In our proof we make use of additional regularizing effects on the velocity which requires to extend the techniques developed by Hoff for the constant viscosity case.

Numerical and perturbation solutions of third-grade fluid in a porous channel: Boundary and thermal slip effects

The steady flow of a third-grade fluid due to pressure gradient is considered between parallel plane walls which are kept at different temperatures. The space between the plane walls is assumed to be a porous medium of constant permeability. The viscosity of the fluid is taken as constant as well as a function of temperature. It is further assumed that the fluid may slip at the wall surfaces. The consequence of this assumption results in non-linear boundary conditions at the plane walls. The temperature field is also supposed to satisfy thermal slip condition at the walls. The governing equations are modelled under these assumptions and the approximate solution is obtained using the perturbation theory. The skin friction coefficient is a decreasing function of slip parameters in the case of temperature-dependent viscosity models while no variation is noted for the case of constant viscosity via boundary slip parameter. The heat transfer rate increases with the boundary slip parameter and decreases with the thermal slip parameter. The validity of the approximated solution is checked by calculating the numerical solution as well. The absolute error is calculated and listed in tabular form in the case of constant and temperature-dependent viscosity via boundary and thermal slip parameters. The influence of various emerging parameters on flow velocity and temperature profile is discussed through graphs.

Global strong solutions to compressible Navier–Stokes system with degenerate heat conductivity and density-depending viscosity

We consider the compressible Navier-Stokes system where the viscosity depends on density and the heat conductivity is proportional to a positive power of the temperature under stress-free and thermally insulated boundary conditions. Under the same conditions on the initial data as those of the constant viscosity and heat conductivity case ([Kazhikhov-Shelukhin. J. Appl. Math. Mech. 41 (1977)], we obtain the existence and uniqueness of global strong solutions. Our result can be regarded as a natural generalization of the Kazhikhov's theory for the constant heat conductivity case to the degenerate and nonlinear one under stress-free and thermally insulated boundary conditions.

Numerical solution for flow of a Eyring–Powell fluid in a pipe with prescribed surface temperature

In the current study, the flow and heat transfer of MHD Eyring–Powell fluid in a circular infinite pipe is discussed. The rheology of fluid is described by constitutive equation of Eyring–Powell fluid. The solution is constructed for both constant and variable viscosity cases. For variable viscosity case, the viscosity function is defined by Reynolds and Vogel’s models. The solution of each case is calculated numerically with the help of eminent iterative numerical technique. The effects of thermo-fluidic parameters on flow and heat transfer phenomenon are highlighted through graphs. The velocity and temperature profiles diminish against magnetic parameter $$(M_{e} )$$ and material parameter (M) in all cases, whereas both velocity and temperature profiles rise via magnitude of the pressure gradient and material parameter Y. The validity of our numerical results due to shooting method is presented by comparing them with the numerical results produced by pseudo-spectral collocation method. Relative absolute errors are plotted, and achieved accuracies are of the order four and five in w and $$\theta$$, respectively. The outcomes of current investigation may be useful in thin film, catalytic reactors, polymer solutions and paper production, etc.

Global strong solutions to magnetohydrodynamics with density-dependent viscosity and degenerate heat-conductivity**Partially supported by NNSFC 11671027 and 11471321.

We deal with the equations of a planar magnetohydrodynamic compressible flow with the viscosity depending on the specific volume of the gas and the heat conductivity proportional to a positive power of the temperature. Under the same conditions on the initial data as those of the constant viscosity and heat conductivity case (Kazhikhov 1987 Boundary Value Problems for Equations of Mathematical Physics (Krasnoyarsk)), we obtain the global existence and uniqueness of strong solutions which means no shock wave, vacuum, or mass or heat concentration will be developed in finite time, although the motion of the flow has large oscillations and the interaction between the hydrodynamic and magnetodynamic effects is complex. Our result can be regarded as a natural generalization of the Kazhikhov’s theory for the constant viscosity and heat conductivity case to that of nonlinear viscosity and degenerate heat-conductivity.

Fully Compressible Low-Mach Number Simulations of Carbon-dioxide at Supercritical Pressures and Trans-critical Temperatures

This work investigates fully developed turbulent flows of carbon-dioxide close to its vapour-liquid critical point in a channel with a hot and a cold wall. Two direct numerical simulations are performed at low Mach numbers, with the trans-critical transition near the channel centre and the cold wall, respectively. An additional simulation with constant transport properties is used to selectively investigate the effect of the non-linear equation of state on turbulence. Compared to the case where the pseudo-critical transition occurs in the channel center, the case with the pseudo-critical transition close to the cold wall reveals that compressibility effects can exist in the near-wall region even at low Mach numbers. An analysis of the velocity streaks near the hot and the cold walls also indicates a greater degree of streak coherence near the cold wall. A comparison between the constant and variable viscosity cases at the same Reynolds number, Mach number and having the same isothermal wall boundary conditions reveals that variable viscosity increases turbulence near the cold wall and also causes higher velocity gradients near the hot wall. We also show that the extended van Driest transformation results in a better agreement of the velocity profile with the log-law of the wall compared to the standard van Driest transformation. The semi-locally scaled turbulent velocity fluctuations and the turbulent kinetic energy budgets on the hot and the cold sides of the channel collapse on top of each other, thereby establishing the validity of Morkovin’s hypothesis.

Linear stability of supersonic Couette flow of a molecular gas under the conditions of viscous stratification and excitation of the vibrational mode

The linear stability of viscous two-dimensional perturbations in the supersonic plane Couette flow of perfect and vibrationally excited gases is investigated. In both cases an alternative is considered so that the transport coefficients were taken either constant or dependent on the static flow temperature. The Sutherland model is used to take the temperature dependence of the shear viscosity into account. It is shown that “viscous” stratification increases considerably the flow stability as compared with the case of constant viscosity. At the same time, the simple constant viscosity model conserves all characteristic features of the development of viscous perturbations in the Sutherland model. The dissipation effect of excitation of the vibrational mode is conserved in taking the temperature dependence of the transport coefficients into account. For both models the corresponding increase in the critical Reynolds number is of approximately 12%.

A terrain-following model of wave boundary layers

Over a variable seabed, conventional boundary layer approximations are rendered to be inadequate because of the large variations in bed elevation in the direction of wave propagation. Applying the method of conformal transformation to map the flow domain with a corrugated boundary onto a uniform strip, we put forward a terrain-following modeling approach for Stokes boundary layer flows, accompanying the recent development of the exact Floquet theory of water waves over a generally periodic seabed. For a non-steep seabed profile, but not necessarily small undulation height compared with the water depth, we solve the vorticity equation to obtain the analytical solutions for the boundary layer velocities, bed shear stress and rate of viscous dissipation, explicitly showing the variations both across the boundary layer and along the bed. For a relatively steep bed profile, a remedy is proposed that allows the velocity profiles to be locally determined across the boundary layer avoiding solving the 2-D differential equation for the vorticity. The modeling methodology is presented here for a constant viscosity, including the case of constant eddy viscosity, but can be extended to the case of variable eddy viscosity to improve turbulence modeling.