Variable Viscosity Coefficient Research Articles

Generalised Couette flow of nanoliquid among two concentric channels with particles injection

In the presence of nanoparticle injection, buoyancy power, constant pressure gradient, variable viscosity coefficient, magnetic field, mass diffusivity of thermophoresis, and Brownian motion, the hydrodynamic nanoliquid conducted with electric current flows through the gap between two concentric cylindrical channels of infinite length. The focus of this article was on generalised Couette flow that is flow in which the outer channel plate moves at a uniform velocity while still being subjected to a pressure gradient. Here we use the RKF45 numerical method and the shooting technique to solve dimensionless momentum, energy, and concentration equations. How the obtained parameters controlled on flow rate, temperature and concentration of the fluid have been investigated and appearances through respective graphs. The high magnitude of nanoliquid flow rate with outer channel wall motion and pressure gradient parameters has been observed. The nanoliquid temperature declines with an annular gap parameter while amplified thermophoresis and magnetic parameter values enrich the fluid temperature. In addition, loftier values of variable viscosity and Brownian motion parameters boost the nanoliquid concentration.

Global well-posedness for the inhomogeneous incompressible MHD equations with variable viscosity coefficient and electrical conductivity

In this paper, we study the Cauchy problem for the inhomogeneous incompressible MHD system with variable viscosity coefficient and electrical conductivity. It is shown that the 3-D inhomogeneous incompressible MHD system has unique global solutions with small initial data conditions. Furthermore, we establish the global well-posedness of the two-dimensional MHD equations in critical spaces, given certain conditions on the density.

Knee Joint Assist in Seated Motion Focusing on Variable Viscosity Property in Exoskeleton Assistive Device -Comparison of Variable and Constant Viscosity Coefficients-

Knee Joint Assist in Seated Motion Focusing on Variable Viscosity Property in Exoskeleton Assistive Device -Comparison of Variable and Constant Viscosity Coefficients-

The effect of heat conduction on the shock wave structure in a non-ideal gas with constant and variable viscosity coefficients

Via using continuum model and dimensionless transformation method, the effect of heat conduction is studied in shock wave structure of non-ideal gas. It turns out that due to the presence of heat conduction, gas velocity in upstream of shock front decreases and it in downstream increases, respectively, the gas temperature or entropy change significantly increases, the maximum of gas viscous stress decreases, and the limiting Mach number of the continuum model and the shock thickness increase. Then, with the increase in the gas non-ideality, the difference in gas viscous stress caused by heat conduction decreases, and the growth rate of gas entropy change increases. The effect of heat conduction in shock compression mechanism is revealed.

Rotated block diagonal preconditioners for Navier-Stokes control problems

Fluid flow control problems play a crucial role in various industrial applications. The optimal control of the Navier-Stokes equations poses a significant challenge. By employing Oseen's approximation to linearize the problem, we encounter a series of large sparse structured linear systems. These coefficient matrices exhibit a two-by-two block structure with square blocks. Leveraging this block structure, we exploit matrix splitting preconditioners. Theoretical analysis indicates that the real parts of all eigenvalues of preconditioned matrix are equal to 1/2. A large number of eigenvalues are clustered in (1±i)/2. The imaginary part of the eigenvalues is bounded explicitly. The eigenvalue distribution predicts the fast convergence of Krylov subspace methods. To avoid solving the saddle point subsystems in the preconditioning procedure, we propose a practical variant of the preconditioner. The theoretical analysis demonstrates that if the approximation is sufficiently close to Schur complement, the eigenvalues of the modified preconditioned matrix will lie within a circle centered at the original eigenvalues with a radius less than 1. This implies that the modified preconditioner exhibits excellent performance in terms of preconditioning. The numerical experiments demonstrate that the generalized minimal residual method, when combined with the proposed preconditioners, proves to be an efficient and effective solution for Oseen's control optimization with a variable viscosity coefficient. The number of iterations required by the preconditioned methods remains unaffected by the mesh size used in finite element discretization and only marginally depends on the regularization parameter.

Solvability of the two-dimensional stationary incompressible inhomogeneous Navier–Stokes equations with variable viscosity coefficient

We show the existence and the regularity properties of (a class of) weak solutions to the two-dimensional stationary incompressible inhomogeneous Navier–Stokes equations with density-dependent viscosity coefficients, by analyzing a fourth-order nonlinear elliptic equation for the stream function. For some stationary symmetric flows, we reformulate the Navier–Stokes equations as ordinary differential equations and give explicit examples of weak solutions. We present some further (ir-)regularity results in the case of piecewise-constant viscosity coefficients.

Temperature‐dependent electrical conductivity impact on radiative and dissipative peristaltic transport of boron nitride‐ethylene glycol nanofluid through asymmetric channels

AbstractMathematical simulation of biological fluids is of upmost significance due to its numerous medical uses. Interpreting various biological flows necessitates a thorough knowledge of the peristaltic mechanism. This paper presents a computational study for the peristaltic pumping within vertical asymmetric channels filled with BN‐EG nanofluid under the influence of temperature‐dependent electrical conductivity and thermal radiation. Experimental study showed that the nanofluid created by suspending Boron Nitride particles in a combination of Ethylene Glycol exhibited non‐Newtonian characteristics. Further, the Carreau's fluid model provides accurate predictions about the rheological properties of BN‐EG nanofluid. Various configurations of the outer boundaries are considered, namely, square wave, multi‐sinusoidal wave, trapezoidal wave, and triangular wave. A uniform magnetic field together with nanoparticles and mass concentrations, joule heating, first‐order chemical reaction as well as viscous dissipation are considered. Influences of the Dufour and Soret numbers are examined, and the cases of biological scientific assumptions which is known as low Reynolds number and long wavelength are applied. All the computations are obtained numerically using Mathematica symbolical software (ND‐Solve), and the obtained results are presented in terms of the axial velocity u, heat transfer rate Z, concentration profile Ω, temperature profile θ, extra stress tensor , pressure gradient , pressure rise and stream function ψ. The major outcomes revealed that the maximizing in electrical conductivity coefficient, variable viscosity coefficient and magnetic field parameter is better to obtain a higher rate of the heat transfer while the increase in thermo‐diffusion effects as well as linear thermal radiation coefficient causes a reduction in the rate of heat transfer.

Simulation and interpretation of MHD peristaltic transport of dissipated third grade nanofluid flow across asymmetric channel under the influences of rheological characteristics and inclined magnetic field as well as heat and mass convection

ABSTRACT Mathematical simulation of biological fluids is of upmost significance due to its numerous medical uses. Interpreting various biological flows necessitates a thorough knowledge of the peristaltic mechanism. This paper presents a computational study for the peristaltic motion within vertical asymmetric channels filled with magnetic third grade nanofluid model under the influences of rheological characteristics. Various configurations of the outer boundaries are considered, namely, square wave, multi-sinusoidal wave, trapezoidal wave, and triangular wave. An inclined magnetic field together with nanoparticles and mass concentrations as well as viscous dissipation are considered. Influences of the Dufour and Soret numbers are examined, and the cases of biological scientific assumptions which is known as low Reynolds number and long wavelength are applied. All the computations are obtained numerically using Mathematica symbolical software (ND-Solve). The major outcomes revealed that the square wave shape gives higher pressure gradients near the inlet and outlet parts while the multi-sinusoidal wave gives periodic behaviors of dp/dx. Also, it is better to maximize the variable viscosity coefficient to enhance the rate of heat transfer while, the rate of heat transfer is diminished by the growth in the thermo-diffusion effects as well as variable thermal conductivity coefficient.

A study based on boundary layer and entropy generation in MHD flow of micropolar fluid with variable viscosity and thermal conductivity: A non-Darcy model approach

This paper aims to analyze the problem with the study of thermal and momentum transport with entropy generation in view of the second law of thermodynamics in Magneto hydrodynamics (MHD) micropolar fluid through porous medium under the consideration of the non-Darcy model, temperature-dependent viscosity and thermal conductivity. In practical situations at higher temperatures and high speed fluid flow, it becomes reasonable to consider variable fluid flow parameters. The governing boundary layer flow equations are first converted into a coupled system of the ordinary differential equations (ODE) under the assumption of differing plate temperatures by applying appropriate similarity transformations. A shooting method has been applied to solve ordinary differential equations numerically. The last effect of microrotation, magnetic field, variable viscosity coefficient, variable thermal conductivity, etc. on momentum and thermal transport has been depicted through various graphs. The table for skin friction coefficient and Nusselt number for ideal cases has been shown to validate the model by previous findings. It is seen that K and m enhance the velocity profile on their increment opposite to this M, [Formula: see text], F and Da have been found to reduce the velocity profile. Table 3 is constructed for numerical values of skin friction coefficient and Nusselt number for different values of parameters where it can be concluded that magnetic parameter M has a tendency to enhance the skin friction and heat transfer, while variable viscosity parameters have a tendency to decline the skin friction and heat transfer.

Study of the influence of temperature dependent viscosity on fluid flow in annular channels

For all liquids, a change in viscosity depending on temperature is characteristic. In most cases, this dependency is commonly overlooked; however, when studying the flow of liquids under conditions of intense heat exchange, the temperature-dependent viscosity can have a significant impact on mass and heat transfer processes. It should be noted that for some liquids, such as polymer solutions or biological fluids, the temperature dependence of viscosity can be extremely complex and nonlinear. In such cases, ignoring this dependence can lead to inaccurate results and errors. Annular channels find wide applications in various technical systems, including heat exchangers and hydraulic devices. Understanding the factors influencing the fluid flow and discharge in such channels is a key aspect of optimizing their design and operation. One of the main factors influencing the flow process and fluid discharge in annular channels is the temperature-dependent viscosity of the fluid. This work investigates the influence of the thermo-viscous parameter with monotonic and non-monotonic temperature-dependent viscosity, as well as the geometric parameter of the annular channel on the fluid flow process and discharge. The mathematical model includes the continuity equation, Navier-Stokes equations, and the temperature equation. The method of control volume and the SIMPLE algorithm, modified to account for the variable viscosity coefficient, were applied for the numerical solution of these equations. It is shown that in the case of liquid flow in an annular channel with a monotonic dependence of viscosity on temperature, the steady-state discharge closely approaches the discharge at maximum viscosity. However, in the case of a liquid with non-monotonic viscosity dependence on temperature, the discharge significantly depends on the thermo-viscous parameter.

Dark energy density and Israel–Stewart (IS) bulk viscosity model

In this paper, we investigate the thermodynamics of a dark energy bulk viscosity model as a cosmic fluid. In this regard, the two theories of Eckart and Israel–Stewart (IS) are the bases of our work. Therefore, we first investigate the thermodynamics of cosmic fluids in the dark energy bulk viscosity model and the general relationships. Then, we express the thermodynamic relationships of Eckart’s theory. Due to the basic equations of Eckart’s theory and Friedmann’s equations, we consider two states, one is [Formula: see text] (standard) and the other is [Formula: see text] (non-standard). In the standard state, we define the pressure [Formula: see text], energy density [Formula: see text] and bulk viscosity coefficient [Formula: see text] of the cosmic fluid in terms of cosmic time and we obtain its relations. We also mention that in this standard state, because of [Formula: see text], the value of [Formula: see text] is zero, so [Formula: see text] is not defined in this state. But in the non-standard case [Formula: see text], the bulk viscosity coefficient [Formula: see text] is zero and only the scale factor, pressure and energy density of the cosmic fluid are defined. We also consider two states of constant and variable bulk viscosity coefficients and obtain three Hubble constant parameters and scale factor in terms of cosmic time, and energy density in terms of scale factor. In the state of variable bulk viscosity coefficient, we consider the viscosity coefficient as the power law from energy density [Formula: see text], which is [Formula: see text] and a constant. Following this, we discuss about the dissipative effects of cosmic fluids and examine the effects of energy density for dark energy in the IS theory. The results are comprehensively presented in Tables 1 and 2. Also, according to observational constraints, the results of the likelihood analysis for the IS viscous model are summarized in Table 3.

Numerical investigation of MHD flow of Williamson nanofluid with variable viscosity pasting a wedge within porous media: A non‐Darcy model approach

AbstractThe present analysis is done for the investigation of the effect of various physical parameters on magnetohydrodynamic Williamson nanofluid boundary layer flow past a wedge through porous media taking a non‐Darcy–Falkner–Skan model with consideration of varying wall temperature, variable viscosity, the effect of Brownian motion, and thermophoresis in the presence of heat source. The corresponding governing equations under the appropriate boundary conditions are first converted into ordinary differential equations (ODEs) in view of similarity transformations. Application of shooting method has been made to deal with these ODEs, and the effects of various parameters on nondimensional velocity, temperature, and concentration are investigated through graphs. Also, the effects of various parameters on surface skin friction, heat, and mass transfer rates are analyzed and are shown in Table 3. It has been noticed that heat and mass transfer rates are enhanced with variable viscosity coefficient and reduced with Brownian motion and thermophoresis parameters. As a significant outcome, the skin friction is found to be increased with increasing values of the Williamson parameter while it is found to be decreased with increasing value of variable viscosity coefficient. At last, validation of the current findings is attended to after comparing with similar results obtained earlier.

Analysis of Schwarz waveform relaxation for the coupled Ekman boundary layer problem with continuously variable coefficients

In this paper, we present a global-in-time non-overlapping Schwarz method applied to the Ekman boundary layer problem. Such a coupled problem is representative of large-scale atmospheric and oceanic flows in the vicinity of the air-sea interface. Schwarz waveform relaxation (SWR) algorithms provide attractive methods for ensuring a “tight coupling” between the ocean and the atmosphere. However, the convergence study of such algorithms in this context raises a number of challenges. Numerous convergence studies of Schwarz methods have been carried out in idealized settings, but the underlying assumptions to make these studies tractable may prohibit them to be directly extended to the complexity of climate models. We illustrate this aspect on the coupled Ekman problem, which includes several essential features inherent to climate modeling while being simple enough for analytical results to be derived. We investigate its well-posedness and derive an appropriate SWR algorithm. Sufficient conditions for ensuring its convergence for different viscosity profiles are then established. Finally, we illustrate the relevance of our theoretical analysis with numerical results and suggest ways to improve the computational cost of the coupling. Our study emphasizes the fact that the convergence properties can be highly sensitive to some model characteristics such as the geometry of the problem and the use of continuously variable viscosity coefficients.

Boundary-Domain Integral Equations equivalent to an exterior mixed BVP for the variable-viscosity compressible Stokes PDEs

Two direct systems of Boundary-Domain Integral Equations, BDIEs, associated with a mixed boundary value problem for the stationary compressible Stokes system with variable viscosity coefficient in an exterior domain of $ \mathbb{R}^3 $ are derived. This is done by employing the Stokes surface and volume potentials based on an appropriate parametrix (Levi function) in the third Green identities for the velocity and pressure. Mapping properties of the potentials in weighted Sobolev spaces are analysed. Finally, the equivalence between the BDIE systems and the BVP is shown and the isomorphism of operators defined by the BDIE systems is proved.

Entropy production minimization and non-Darcy resistance within wavy motion of Sutterby liquid subject to variable physical characteristics

Non-Darcy resistance in peristaltic transport of Sutterby liquid in curved configuration is modeled. Variable characteristics of material (i.e., thermal conductivity and viscosity) are taken as temperature-dependent. Soret and Dufour features have also been retained. Problem is modeled by using conservation laws. Long wavelength and small Reynolds number have been invoked. Resulting problems have been solved numerically. Entropy optimization analysis is made. Axial velocity, temperature, concentration, entropy, Bejan number and heat transfer rate are examined for influential variables. It is found that velocity increases for variable viscosity coefficient and porous-space parameter. Temperature decreases for increased values of variable thermal conductivity. Opposite behavior of mass and energy is noted for Soret and Dufour parameters. Entropy minimized for thermal conductivity and viscosity coefficients. Entropy enhancement is noticed for Soret and Dufour parameters. Heat transfer rate at upper wall is enhanced for Soret and Dufour variables.

Boundary‐domain integral equation systems to the Dirichlet and Neumann problems for compressible Stokes equations with variable viscosity in 2D

In this paper, the Dirichlet and Neumann boundary value problems for the steady‐state Stokes system of partial differential equations for a compressible viscous fluid with variable viscosity coefficient is considered in two‐dimensional bounded domain. Using an appropriate parametrix, this problem is reduced to a system of direct segregated boundary‐domain integral equations (BDIEs). The BDIEs in the two‐dimensional case have special properties in comparison with the three dimension because of the logarithmic term in the parametrix for the associated partial differential equations. Consequently, we need to set conditions on the function spaces or on the domain to ensure the invertibility of corresponding parametrix‐based hydrodynamic single layer and hypersingular potentials and hence the unique solvability of BDIEs. Equivalence of the BDIE systems to the Dirichlet and Neumann BVPs and the invertibility of the corresponding boundary‐domain integral operators in appropriate Sobolev spaces are shown.

Numerical computing for axisymmetric transport phenomenon in Carreau liquid using variable conductance models

Conservation laws and variable conductance (viscosity, thermal conductivity and mass diffusion coefficient) models are used to develop mathematical problems describing transport mechanism in Carreau fluid over a non-uniformly moving surface. Boundary conditions are developed by no-slip theory. Mathematical models are transformed into suitable residual integrals which are approximated by Galerkin approximations. The obtained residuals are used for solving problems numerically using finite element method. Numerical investigation of variable viscosity, thermal conductivity and mass diffusion coefficients is carried out to examine the impact of parameters. The heat dissipated as a result of friction among the particles of the fluid of constant viscosity is greater than the heat dissipated due to friction force in the fluid of temperature-dependent viscosity. It is also found that ohmic phenomenon in the fluid of variable viscosity is prominent than that in the fluid of constant viscosity. Therefore, this fact must be in mind while using the fluids of variable viscosity in engineering applications. The transport of mass in fluid of constant viscosity is greater than that in fluid of variable viscosity. The Lorentz force is observed to oppose the flow. Hence, flow is decelerated by an increase in the intensity of magnetic field. The rate of transportation of mass has shown increasing trend when mass diffusion coefficient increases due to temperature.

Analysis of activation energy and its impact on hybrid nanofluid in the presence of Hall and ion slip currents

Chemical reaction is considered with entropy generation in mixed convection magnetohydrodynamic (MHD) hybrid nanoliquid flow across a porous medium containing Hall and ion slip currents. The main focus of this research is the entropy production, SWCNT-MWCNT/water hybrid nanofluids and Hall effect. The complex coupled system of differential equations is transformed into a non-dimensional form through an acceptable similarity transformation. To measure the rate of heat transfer the volume fraction of MWCNT is taken fixed 3% and for SWCNT changes 1–5%. The influence of different flow field parameters on axial velocity, temperature distribution, concentration field, entropy generation, and Bejan number is expressed graphically. The comparison of nanofluid and hybrid nanofluid is shown graphically. The enhances value of variable viscosity parameter, porous parameter, and coefficient of inertia decreases the velocity distribution. Further the solid volume fraction enhances the velocity and temperature distribution.

Weak dissipative solutions to a free-boundary problem for finitely extensible bead-spring chain molecules: Variable viscosity coefficients

We investigate the global existence of weak solutions to a free boundary problem governing the evolution of finitely extensible bead-spring chains in dilute polymers. The free boundary in the present context is defined with regard to a density threshold of $ \rho = 1, $ below which the fluid is modeled as compressible and above which the fluid is modeled as incompressible. The present article focuses on the physically relevant case in which the viscosity coefficients present in the system depend on the polymer number density, extending the earlier work [8]. We construct the weak solutions of the free boundary problem by performing the asymptotic limit as the adiabatic exponent $ \gamma $ goes to $ \infty $ for the macroscopic model introduced by Feireisl, Lu and Süli in [10] (see also [6]). The weak sequential stability of the family of dissipative (finite energy) weak solutions to the free boundary problem is also established.

Nonlinear creep model and parameter identification of mudstone based on a modified fractional viscous body

To study the evident nonlinear creep characteristics of mudstone, the creep process of rock is regarded as the superposition of linear and nonlinear creep processes. Using an element combination model for reference, we introduce the mechanical element (FC) with a fractional derivative based on fractional calculus theory. Compared with the Newtonian element, the FC can react more effectively to the nonlinear gradual process of rheological problems. The variable viscosity coefficient FC element with fractional calculus is connected to both Kelvin and spring elements in series instead of a Newton body element. In addition, considering the effects of load level and time damage variables, a five-element nonlinear creep damage model is proposed that can simulate the entire process of mudstone creep, particularly the accelerated creep phase of mudstone, and both constitutive and creep equations of the model can be derived. Based on the creep model’s use of multiple parameters under graded loading, this study employs a modified particle swarm optimization algorithm with a genetic crossover factor and least-square method joint inversion algorithm. Using creep experimental data of mudstone, this study identifies the parameters for the proposed five-element fractional creep damage model and derives reasonable parameter values. A parameter sensitivity analysis of the constitutive model is also conducted. The results show that the size of the stress loading level $$ \sigma $$ determines the length of the stable creep phase of the mudstone and the time to enter the accelerated creep phase. The derivative order $$ \gamma $$ becomes a direct influence factor on the rock creep rate.