Heat-conducting Fluid Research Articles

Exponential stability and regularity of compressible viscous micropolar fluid with cylinder symmetry

<p style='text-indent:20px;'>This paper is concerned with three-dimensional compressible viscous and heat-conducting micropolar fluid in the domain to the subset of <inline-formula><tex-math id="M1">$ R^3 $</tex-math></inline-formula> bounded with two coaxial cylinders that present the solid thermoinsulated walls, being in a thermodynamical sense perfect and polytropic. We prove that the regularity and the exponential stability in <inline-formula><tex-math id="M2">$ H^2 $</tex-math></inline-formula>.</p>

Stochastic Navier-Stokes-Fourier equations

We study the full Navier--Stokes--Fourier system governing the motion of a general viscous, heat-conducting, and compressible fluid subject to stochastic perturbation. Stochastic effects are implemented through (i) random initial data, (ii) a forcing term in the momentum equation represented by a multiplicative white noise, (iii) random heat source in the internal energy balance. We establish existence of a weak martingale solution under physically grounded structural assumptions. As a byproduct of our theory we can show that stationary martingale solutions only exist in certain trivial cases.

On the Asymptotic Behavior of the Conjugate Problem Describing a Creeping Axisymmetric Thermocapillary Motion

In this paper the conditions for the law of temperature behavior on a solid cylinder wall describes, under which the solution of a linear conjugate inverse initial-boundary value problem describing a two-layer axisymmetric creeping motion of viscous heat-conducting fluids tends to zero exponentially with increases of time

Characterization of heat transfer in consolidated, highly porous media using a hybrid-scale CFD approach

A pore-scale CFD approach has been adopted to improve the phenomenological understanding of transport phenomena governing heat transfer in consolidated, highly porous media with single-phase fluid flow. The CFD model has already been developed and validated in a previous work [1]. In this contribution, the model has been used to characterize different types of irregular sponge (=open-cell foam) structures and regular porous structures with similar structural parameters, such as e.g. porosity. The results of the convective heat transfer coefficient have been obtained from a local analysis of the simulated temperature and heat flux fields. A dimensionless result analysis in terms of the Nusselt number (Nu) for all sponges investigated yielded one common and consistent functional dependency on the Reynolds number (Re). This Nu-Re-characteristic allows the identification of two main heat transfer regimes present for the laminar flow conditions considered in this work: stagnant fluid heat conduction (Nu ~ Re0 at Re → 0) and boundary-layer dominated heat convection (Nu ~ Re0.5). These findings are in accordance with the classical approaches known from the boundary layer theory and have been used to develop a new physically-based Nu-Re-correlation which is needed for targeted heat exchanger designs. Furthermore, the applicability of the so-called Generalized Lévêque Equation (GLE), i.e. the analogy of heat and momentum transfer processes, has been discussed and is supported by using the results from the CFD analysis. Finally, the CFD model and the physical insights gained for sponges have been used to quantify and analyze the heat transport behavior of consolidated, highly porous media with regular structure – like Kelvin or cubic unit cell structures – while maintaining structural parameters like porosity and specific surface area. Unifying characteristics have been detected and discussed as well as limits of the approach's applicability.

Global regularity to the 2D heat-conducting MHD fluids

In this paper, we study an initial value problem of incompressible MHD system for nonhomogeneous viscous heat-conducting fluids in $${\mathbb {R}}^2$$. The global existence of strong solutions with arbitrarily large data is established. The initial density may contain interior vacuum. Some decay estimates of the global solutions are also obtained.

On global-in-time weak solutions to the magnetohydrodynamic system of compressible inviscid fluids

We consider the motion of an inviscid compressible fluid under the mutual interactions with magnetic field. We show that the initial value problem is ill-posed in the class of weak solutions for a large class of physically admissible data. We also consider the same problem for inviscid heat-conductive fluid and show the same result under certain restrictions imposed on the magnetic field. The main tool is the method of convex integration adapted from the Euler system with ‘variable coefficients’.

A non-steady system with friction boundary conditions for flow of heat-conducting incompressible viscous fluids

In this paper we are concerned with a non-steady system for motion of incompressible viscous Newtonian heat-conducting fluids under mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak and one-sided leak conditions based on total stress, velocity, total pressure, rotation, total stress together and the conditions for temperature may include Dirichlet, Neumann and Robin conditions together. Relying on the relations among strain, rotation, normal derivative of velocity and shape of boundary surface, we get variational formulation. The formulation consists of a variational inequality for velocity due to the boundary conditions of friction type and a variational equation for temperature. We first study existence, estimation and relative compactness of solutions to an approximate equation. By passing to limits as the parameter for approximation goes to zero, we get existence of a solution with “defect measure” for temperature.

Sound Scattering by a Thermoelastic Ball with a Continuously Inhomogeneous Coating in a Heat-Conducting Fluid

Direct and inverse problems on the diffraction of a plane harmonic sound wave on a thermoelastic ball with a coating in the form of a radially inhomogeneous thermoelastic spherical layer bounded by inviscid heat-conducting fluid are solved. Oscillations of the coated ball are considered in terms of a linear model of coupled thermoelasticity. The wave fields are determined in the spherical body and outside it. The calculation results are presented for the frequency and angular dependences of the amplitude of a scattered acoustic field in the far zone. The significant difference between the sound scattering characteristics for thermoelastic and elastic bodies is shown. The coating is simulated to provide the least sound scattering in the given frequency range and angular observation sector. Functionals expressing the intensity of the sound reflection are constructed and an algorithm for their minimization based on a combination of random search and coordinate descent methods is presented. The heterogeneity patterns of a thermoelastic coating with the optimal sound reflecting properties are found.

Asymptotic stability in a second-order symmetric hyperbolic system modeling the relativistic dynamics of viscous heat-conductive fluids with diffusion

This paper establishes nonlinear asymptotic stability of homogeneous reference states in dissipative relativistic fluid dynamics. The result is a counterpart for general non-barotropic fluids of one obtained by the author in a previous paper on barotropic fluids. Differently from that of this earlier finding, the proof here crucially relies on analyzing the corresponding linearized problem in Fourier space, with different scalings for small and large wave numbers.

Two-dimensional stationary flow of two immiscible fluids in a cylinder taking into account the internal energy of the interface

In this paper, the problem of a two-dimensional stationary flow of two immiscible viscous heat-conducting fluids in a cylinder is solved. The fluids have a common movable non-deformable interface. The cylinder has a solid outer wall. At the same time the mass forces are absent. The total energy condition at the interface is taken into account. The temperature in liquids is distributed in a quadratic law, which is consistent with the velocity field of the Himenz type. From a mathematical point of view, this initial-boundary value problem is nonlinear and inverse with respect to pressure gradients along the cylinder axis. The modified Galerkin method is used to solve the problem. The effect of the Marangoni number on the fluids flow is investigated.

The effect of interfacial heat transfer energy on a two-layer creeping flow in a flat channel

The study of convective currents in the channel received substantial attention for potential use in numerous engineering and manufacturing processes. The paper considers the two-dimensional motion of an immiscible incompressible binary mixture and a viscous heat-conducting fluid in a flat layer. The fluid system is bounded by solid walls. The solution of the equations of thermal diffusion convection is described in a special form: one of the velocity components linearly depends on the longitudinal coordinate, the temperature and concentration fields have a quadratic dependence on the horizontal coordinate. This velocity field corresponds to the well-known solution of Himenz for a purely viscous fluid. At the interface of liquids, the condition of energy exchange is taken into account. An exact stationary solution of the convective problem is constructed. It allows studying the influence of interfacial heat exchange energy on the dynamics of fluid and mixture flow.

Noncoercive Stationary Navier–Stokes Equations of Heat-Conducting Fluids Modeled by Hemivariational Inequalities: An Equilibrium Problem Approach

In this paper, we study the existence of solutions for noncoercive stationary Navier–Stokes equations of heat-conducting fluids with nonmonotone boundary conditions modeled by hemivariational inequalities. Our method is new and differs from most of the existing techniques developed in the literature. It is based on a recent approach developed on the existence of solutions for mixed equilibrium problems described by the sum of a maximal monotone bifunction and a pseudomonotone bifunction in the sense of Brezis. We introduce a Browder–Tikhonov regularization method for mixed equilibrium problems by means of the duality mapping with gauge function $$\mu (t)$$. By using this regularization procedure and techniques from the recession analysis, we study the existence of solutions for the problem considered in this paper.

Optimization of the circular microchannel heat sink under viscous heating effect using entropy generation minimization method

The present numerical study carries out the optimization of the channel dimension (DN corresponding to N-number of channels) under the consideration of viscous heating effects in entropy generation (EG) through a uniformly heated microchannel heat sink (MCHS). The numerical computations are performed for a constant total mass flow rate ṁtot and constant total heat flow rateq̇tot. In EG formulation, the partial differential equations (PDEs) are discretized by the first-order forward difference method and the temperature in the denominator is taken as the local one. The EG due to fluid friction (Sgen,FR) and heat conduction (Sgen,HT) individually as well as simultaneously is also reported. The EG due to fluid heat conduction in the radial (Sgen,HT-rad) and axial (Sgen,HT-ax) directions are also examined. The results indicate that the frictional entropy generation (Sgen,FR) is significant towards the micro dimensions of the channel. Additionally, the optimum diameter (D*) corresponding to the optimum number (N*) of the channels is designed at minimum total EG (Sgen,tot).

Solvability of a problem for the equations of dynamics of one-temperature mixtures of heat-conducting viscous compressible fluids

A system of partial differential equations governing the three-dimensional unsteady flow of a homogeneous two-component mixture of heat-conducting viscous compressible fluids (gases) is considered within the multivelocity approach. The model is complete in the sense that it retains all terms in the equations, which are a natural generalization of the Navier-Stokes-Fourier model for the motion of a single-component medium. The existence of weak solutions to the initial-boundary value problem describing the flow in a bounded domain is proved globally in time and the input data.

Solvability of a Problem for the Equations of the Dynamics of One-Temperature Mixtures of Heat-Conducting Viscous Compressible Fluids

Solvability of a Problem for the Equations of the Dynamics of One-Temperature Mixtures of Heat-Conducting Viscous Compressible Fluids

Boundary-layer phenomena for the boundary layer for the heat-conductive incompressible viscous fluids in the half space

This paper is concerned with the initial–boundary value problem of the heat-conductive viscous fluid in R+2. We prove the convergence rate of the solutions as the heat diffusive coefficient k goes to zero using some uniform-in-k estimates. Moreover, the thickness of the boundary layer is obtained and the boundary layer solution is constructed to describe the behavior of boundary layers.

Global attractors for a nonlinear one-dimensional compressible viscous micropolar fluid model

This paper considers the dynamical behavior of solutions of constitutive systems for 1D compressible viscous and heat-conducting micropolar fluids. With proper constraints on initial data, we prove the existence of global attractors in generalized Sobolev spaces $$H_{\delta }^{(1)}$$ and $$H_{\delta }^{(2)}$$ . These attractors are unique in corresponding phase spaces.

Exponential stability for the compressible micropolar fluid with cylinder symmetry in R3

This paper is concerned with three-dimensional compressible viscous and heat-conducting micropolar fluid in the domain to the subset of R3 bounded with two coaxial cylinders that present the solid thermoinsulated walls, being in a perfect and polytropic thermodynamical sense. We prove that cylindrically symmetric solutions decay to a constant exponentially as time goes to infinity based on the assumptions that the initial total energy is sufficiently small and initial data are sufficiently smooth cylindrically symmetric functions.

The Strong Solution for the Viscous Polytropic Fluids with Non-Newtonian Potential

The authors study an initial boundary value problem for the three-dimensional Navier-Stokes equations of viscous heat-conductive fluids with non-Newtonian potential in a bounded smooth domain. They prove the existence of unique local strong solutions for all initial data satisfying some compatibility conditions. The difficult of this type model is mainly that the equations are coupled with elliptic, parabolic and hyperbolic, and the vacuum of density causes also much trouble, that is, the initial density need not be positive and may vanish in an open set.

The Behavior of Boundary Layer for the Compressible Planar MHD Equations at Small Shear Viscosity

The vanishing shear viscosity limit to an initial-boundary value problem of planar MHD equations for compressible viscous heat-conducting fluids is justified and the convergence rates are obtained. More important, to capture the behavior of the solutions at small shear viscosity, both the boundary-layer thickness and the boundary-layer corrector are discussed.