Heat-conducting Fluid Research Articles

Approximate analytical and numerical investigation of Oseen-type forced convection around a sphere in a low Reynolds number slip flow

Convective heat transfer around a spherical particle submerged in a viscous heat-conducting fluid at very low Reynolds numbers is analytically investigated using Oseen’s theory. The size of the sphere is assumed to be small enough so that the temperature jump condition of dilute gas dynamics is valid on the sphere surface. Approximate analytical formulations are presented for the mean Nusselt number, the local Nusselt number and the temperature field. The presented formulations outperform the existing analytical solutions for the Oseen-type heat transfer around the sphere for both no-slip and slip flows. The new formulations do not diverge by increasing the Reynolds number and are capable of predicting acceptable results even up to Reynolds numbers beyond the validity of the Oseen’s theory. While the existing asymptotic solutions only give the mean Nusselt number, the proposed solutions additionally yield the local Nusselt number and the temperature field. A numerical solution of Oseen’s equation is also conducted for comparison. Based on the results presented, recommendations are made on the use of various formulations to achieve accurate results.

Homogenization of a Thermoelastic Bristly Structure Immersed in a Thermofluid

The article considers the mathematical model describing the joint motion of a viscous compressible heat-conducting fluid and a thermoelastic plate with a fine two-level thermoelastic bristly microstructure attached to it. The bristly microstructure consists of a great amount of taller and shorter bristles, which are periodically located on the surface of the plate, and the model under consideration incorporates a small parameter, which is the ratio of the characteristic lengths of the microstructure and the entire plate. Using classical methods in the theory of partial differential equations, we prove that the initial-boundary value problem for the considered model is well-posed. After this, we fulfill the homogenization procedure, i.e., we pass to the limit as the small parameter tends to zero, and, as a result, we derive the effective macroscopic model in which the dynamics of the interaction of the ‘liquid–bristly structure’ is described by equations of two homogeneous thermoviscoelastic layers with memory effects. The homogenization procedure is rigorously justified by means of the Allaire–Briane three-scale convergence method. The developed effective macroscopic model can potentially find application in further mathematical modeling in biotechnology and bionics taking account of heat transfer.

Stokes-type conjugate heat transfer and thermoelasticity analysis of a hollow spherical particle in a slip flow

Conjugate heat transfer around a spherical particle submerged in a viscous heat-conducting fluid at very low Reynolds numbers is analytically investigated. The cases of spherically symmetric and axisymmetric temperature fields are solved. The temperature jump condition of dilute gas dynamics is assumed. The induced thermal stresses in the sphere in the case of spherical symmetry are analytically solved as well. The effect of temperature jump, heat conductivity ratio between the solid and fluid media, the heat generation and the inner radius of the sphere on the temperature, displacement, radial stress and circumferential stresses are studied. Furthermore, an exact correlation is proposed between the Reynolds, Knudsen and Nusselt numbers as well as the drag coefficient of the sphere, which is valid for slip flow at the Stokes limit. Whether it is accurate at higher Reynolds numbers would need further research.

Global Dynamics of 3D Compressible Viscous and Heat-Conducting Micropolar Fluids with Vacuum at Infinity

Global Dynamics of 3D Compressible Viscous and Heat-Conducting Micropolar Fluids with Vacuum at Infinity

Low Mach number limit on perforated domains for the evolutionary Navier–Stokes–Fourier system

We consider the Navier–Stokes–Fourier system describing the motion of a compressible, viscous and heat-conducting fluid on a domain perforated by tiny holes. First, we identify a class of dissipative solutions to the Oberbeck–Boussinesq approximation as a low Mach number limit of the primitive system. Secondly, by proving the weak–strong uniqueness principle, we obtain strong convergence to the target system on the lifespan of the strong solution.

Numerical study of the use of shear-thinning nanofluids in a microchannel heat sink with different pin densities and including vortex generator

This article numerically investigates the thermal and hydraulic performance of shear-thinning nanofluids when used as heat-conducting fluids in a microchannel heat sink device. Five geometries are evaluated: four with different pin densities and one with vortex generators. Six Reynolds numbers are studied, ranging between 200 and 1200. Numerical experiments show a comparison of using a water/ethylene-glycol mixture with and without alumina nanoparticles and multiwalled carbon nanotubes. Two different concentrations of nanoparticles were evaluated, both given shear-thinning nanofluid behavior. The viscous properties of the fluids are fitted from previously reported experimental data. The other thermophysical properties are modeled using single-phase expressions adjusted to consider hybrid nanofluids. Numerical results show that the heat transfer rates and pressure drop increase when the pin density increases, resulting in thermal blocking in the case of higher pin density. These key findings are a result of the increase in the heat transfer of shear-thinning nanofluids and the reduction of the pressure drop when compared with Newtonian fluids. Apparent viscosity contours are used to understand the thermal and hydraulic performance. Between the two nanofluids studied, the one with the lowest power-law index was the best in terms of heat extraction and pressure drop, indicating that fluids with thinning rheology may be recommended for heat transport in microchannel heat sink devices.

Weak solutions to the heat conducting compressible self-gravitating flows in time-dependent domains

In this paper, we consider the heat-conducting compressible self-gravitating fluids in time-dependent domains, which typically describe the motion of viscous gaseous stars. The flow is governed by the 3D Navier–Stokes–Fourier–Poisson equations where the velocity is supposed to fulfill the full-slip boundary condition and the temperature on the boundary is given by a non-homogeneous Dirichlet condition. We establish the global-in-time weak solution to the system. Our approach is based on the penalization of the boundary behavior, viscosity, and the pressure in the weak formulation. Moreover, to accommodate the non-homogeneous boundary heat flux, the concept of ballistic energy is utilized in this work.

Relativistic Heat Conduction in the Large-Flux Regime.

We propose a general procedure for evaluating, directly from microphysics, the constitutive relations of heat-conducting fluids in regimes of large fluxes of heat. Our choice of hydrodynamic formalism is Carter's two-fluid theory, which happens to coincide with Öttinger's GENERIC theory for relativistic heat conduction. This is a natural framework, as it should correctly describe the relativistic "inertia of heat" as well as the subtle interplay between reversible and irreversible couplings. We provide two concrete applications of our procedure, where the constitutive relations are evaluated, respectively, from maximum entropy hydrodynamics and Chapman-Enskog theory.

The global stability of 3-D axisymmetric solutions to compressible viscous and heat-conductive fluids

The global stability of 3-D axisymmetric solutions to compressible viscous and heat-conductive fluids

On spherically symmetric solutions for the equations of heat-conducting and compressible fluids

On spherically symmetric solutions for the equations of heat-conducting and compressible fluids

A wellbore fluid performance parameters–temperature–pressure coupling prediction model during the managed pressure cementing injection stage

AbstractManaged pressure cementing (MPC) is a new technology based on managed pressure drilling, which has a greater advantage in facing narrow density window formations. However, the existing pressure prediction models during MPC injection stage consider fewer factors and have lower accuracy. To this end, combined with the characteristics of the injection stage, a predictive model of the distribution of annular fluid type was first proposed. Then, based on the experimental results, fluid density and rheology as a function of temperature and pressure were fitted. The governing equation of temperature‐pressure field was established. Eventually the fluid performance parameters–temperature–pressure coupling prediction model was developed in this paper. By comparing the predicted pump pressure with the measured pump pressure, the maximum relative error is not more than 10%. Using this model, the fluid type distribution, temperature field distribution, and pressure field distribution were investigated. The results indicated that the distribution of fluid types in the wellbore presented a complex variation, with up to 10 fluids in the casing and up to five fluids in the annulus. The trend of temperature field is complex, with three turning points. The larger the formation temperature gradient, the higher the fluid temperature in the annulus. The influence law of fluid heat conduction coefficient is reversed at 6750 m. Decreasing drilling fluid density will trigger gas channeling, while increasing drilling fluid density will increase the risk of fracturing formation, and safe operation can be realized by MPC. The variation of the static pressure in the casing is more complicated than in the annulus and the annular circulation pressure in the eccentric casing is smaller than that of the concentric casing, which is due to the smaller annular friction pressure. This study can provide a theoretical basis for the prediction of hydrodynamic parameters during the MPC injection stage.

Global existence and decay of small solutions for quasi-linear second-order uniformly dissipative hyperbolic-hyperbolic systems

This paper is concerned with quasilinear systems of partial differential equations consisting of two hyperbolic operators interacting dissipatively. Its main theorem establishes global-in-time existence and asymptotic stability of strong solutions to the Cauchy problem close to homogeneous reference states in d≥3 space dimensions. Notably, the operators are not required to be symmetric hyperbolic, instead merely the existence of symbolic symmetrizers is assumed. The dissipation is characterized by algebraic conditions implying the uniform decay of all Fourier modes at the reference state. On a technical level, the theory developed herein uses para-differential operators as its main tool. Apparently being the first to apply such operators in the context of global-in-time existence of small solutions for quasi-linear hyperbolic systems, the present work contains a new version of the strong Gårding inequality. In the context of theoretical physics, the theorem applies to recent formulations for the relativistic dynamics of viscous, heat-conductive fluids such as notably that of Bemfica, Disconzi and Noronha (2018) [2].

Research of the problems of heat conduction in fluids

In the fluid of the pipeline, the phenomena of heat convection, heat conduction, and radiation heat transfer occur between the pipeline and the outside world as well as between the pipeline and the inside. In the calculation of the relevant temperature and heat, we need to know the heat transfer coefficient, pipeline characteristic length, flow velocity, and other data to get the results. Based on previous research results, this paper will use Ansys software to explore the change law of heat transfer effect with various parameters. We can find that in the simulation, as the flow rate increases, the heating effect will become worse and worse.

Navier-Stokes-Fourier fluids interacting with elastic shells

We study the motion of a compressible heat-conducting fluid in three dimensions interacting with a non-linear flexible shell. The fluid is described by the full Navier--Stokes--Fourier system. The shell constitutes an unknown part of the boundary of the physical domain of the fluid and is changing in time. The solid is described as an elastic non-linear shell of Koiter type; in particular it possesses a non-convex elastic energy. % Its deformation is modelled by a (non-linear) elastic Koiter shell. We show the existence of a weak solution to the corresponding system of PDEs which exists until the moving boundary approaches a self-intersection or the non-linear elastic energy of the shell degenerates. It is achieved by compactness results (in highest order spaces) for the solid-deformation and fluid-density. Our solutions comply with the first and second law of thermodynamics: the total energy is preserved and the entropy balance is understood as a variational inequality.

Compressible Flows with Oscillating Boundaries

The flow of a viscous compressible heat-conducting fluid in a plane channel with rigid oscillating walls is considered. It is shown that even a vanishingly small compressibility can be the reason for the onset of a resonance, i.e., sharp increase in the amplitude of oscillations of the flow parameters at a properly selected wall oscillation frequency. An exact analytical expression for the leading resonant frequency is given. Numerical calculations have demonstrated the possibility of a cumulative effect, namely, sharp increase in the mass flow rate even at constant pressure gradient.

Global strong solutions to the Cauchy problem of the 3D heat-conducting fluids

In this paper, we study the global strong solutions to the three-dimensional (3D) heat-conducting incompressible Navier–Stokes equations with density-temperature-dependent viscosity and heat-conducting coefficients in . By using the t-weighted a priori estimates, we prove the global existence and exponential decay-in-time rates of strong solutions to the Cauchy problem when the -norm of the initial density is suitably small. It should be noted that the velocity and absolute temperature can be large initially, and the initial density contains vacuum case.

The Study of Three-Dimensional Fluid Flow Regimes on the Basis of the Exact Solution to the Convection Equations

We consider the evaporation/condensation process of diffusion type in two-layer fluid flows under the assumption that both viscous heat-conducting incompressible fluids, a liquid and a gas-vapor mixture, have a common interface and occupy an infinite threedimensional rectangular channel. Based on the exact solution to the convection equations, we study the fluid flows arising in the case of a linearly distributed thermal load on the substrate and thermal insulation of the upper and lateral walls of the channel. It is observed that some complex vortex structures are formed under the action of the longitudinal temperature gradient and transversely directed gravity field. For the ethanol–nitrogen system we present the characteristics of hydrodynamic, thermal, and concentration fields, in particular, the profiles of the evaporative mass flow rates and interface tangential stresses, the topology of flows, and the temperature and vapor concentration distributions.

Stability with respect to domain of the low Mach number limit of compressible heat-conducting viscous fluid

We investigate the asymptotic limit of solutions to the Navier-Stokes-Fourier system with the Mach number proportional to a small parameter $\rightarrow 0$, the Froude number proportional to $\sqrt{}$ and when the fluid occupies large domain with spatial obstacle of rough surface varying when $\rightarrow 0$. The limit velocity field is solenoidal and satisfies the incompressible Oberbeck–Boussinesq approximation. Our studies are based on weak solutions approach and in order to pass to the limit in a convective term we apply the spectral analysis of the associated wave propagator (Neumann Laplacian) governing the motion of acoustic waves.

BICOMPACT SCHEMES FOR COMPRESSIBLE NAVIER–STOKES EQUATIONS

For the first time, bicompact schemes are generalized to non-stationary Navier–Stokes equations for a compressible heat-conducting fluid. The proposed schemes have an approximation of the fourth order in space and the second order in time, are absolutely stable (in the frozen-coefficients sense), conservative, and efficient. One of the new schemes is tested on several two-dimensional problems. It is shown that when the mesh is refined, the scheme converges with an increased third order. A comparison is made with the WENO5-MR scheme. The superiority of the chosen bicompact scheme in resolving vortices and shock waves, as well as their interaction, is demonstrated.

An unconditionally energy stable method for binary incompressible heat conductive fluids based on the phase–field model

This paper proposes an unconditionally energy stable method for incompressible heat conductive fluids under the phase–field framework. We combine the complicated system by the Navier–Stokes equation, Cahn–Hilliard equation, and heat transfer equation. A Crank–Nicolson type scheme is employed to discretize the governing equation with the second-order temporal accuracy. The unconditional energy stability of the proposed scheme is proved, which means that a significantly larger time step can be used. The Crank–Nicolson type discrete framework is applied to obtain the second-order temporal accuracy. We perform the biconjugate gradient method and Fourier transform method to solve the discrete system. Several computational tests are performed to show the efficiency and robustness of the proposed method.