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We consider a non–homogeneous incompressible and heat conducting fluid confined to a 3D domain perforated by tiny holes. The ratio of the diameter of the holes and their mutual distance is critical, the former being equal to ε 3 , the latter proportional to ε, where ε is a small parameter. We identify the asymptotic limit for ε → 0, in which the momentum equation contains a friction term of Brinkman type determined uniquely by the viscosity and geometric properties of the perforation. Besides the inhomogeneity of the fluid, we allow the viscosity and the heat conductivity coefficient to depend on the temperature, where the latter is determined via the Fourier law with homogenized (oscillatory) heat conductivity coefficient that is different for the fluid and the solid holes. To the best of our knowledge, this is the first result in the critical case for the inhomogenous heat–conducting fluid.

We consider equations for the three-dimensional unsteady motion of mixtures of viscous compressible heat-conducting fluids in the multi-velocity approach. We prove the existence, globally in time and the input data, of a generalized (dissipative) solution of the initial-boundary value problem corresponding to flows in a bounded domain.

We investigate an initial boundary value problem of two-dimensional nonhomogeneous heat conducting magnetohydrodynamic equations. We prove that there exists a unique global strong solution. Moreover, we also obtain the large time decay rates of the solution. Note that the initial data can be arbitrarily large and the initial density allows vacuum states. Our method relies upon the delicate energy estimates and Desjardins’ interpolation inequality (B. Desjardins, Regularity results for two-dimensional flows of multiphase viscous fluids, Arch. Rational Mech. Anal. 137(2) (1997) 135–158).

On the basis of experimental data on the local values of the combustion rate of condensed systems along the heat-conducting filaments placed therein, regression models were constructed to relate the value of the local combustion rate with such characteristics of heat-conducting filaments as the thermal diffusivity and melting point. The obtained regression model was used to assess a possible expansion of the variation range of the local combustion rate when using various crystalline forms of CVD diamonds as heat-conducting filaments. It was shown that a local increase in the combustion rate could exceed the baseline value by 200 times. The possibility of controlling the transformation of the combustion surface by using heat-conducting filaments with variable characteristics was confirmed.

Purpose This paper aims to study numerically the simulation of convective–radiative heat transfer under an effect of variable thermally generating source in a rotating square chamber. The performed analysis deals with a development of passive cooling system for the electronic devices. Design/methodology/approach The domain of interest of size H rotating at a fixed angular velocity has heat-conducting solid walls with a constant cooling temperature for the outer boundaries of the vertical walls and with thermal insulation for the outer borders of the horizontal walls. The chamber has a heater on the bottom wall with a time-dependent volumetric heat generation. The internal surfaces of the walls and the energy element are both grey diffusive emitters and reflectors. The fluid is transparent to radiation. Computational model has been written using non-dimensional parameters and worked out by the finite difference technique. The effect of the angular velocity, volumetric heat generation frequency and surface emissivity has been studied and described in detail. Findings The results show that growth of the surface emissivity leads to a diminution of the mean heater temperature, while a weak rotation can improve the energy transport for low volumetric thermal generation frequency. Originality/value An efficient computational approach has been used to work out this problem. The originality of this work is to analyze complex (conductive–convective–radiative) energy transport in a rotating system with a local element of time-dependent volumetric heat generation. To the best of the authors’ knowledge, an interaction of major heat transfer mechanisms in a rotating system with a heat-generating element is scrutinized for the first time. The results would benefit scientists and engineers to become familiar with the analysis of complex heat transfer in rotating enclosures with internal heat-generating units, and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors and electronics.

We establish the existence of global large smooth solutions to one-dimensional, compressible Navier--Stokes system for a viscous and heat-conducting ionized gas when the viscosity depends on the de...

© 2020 Taylor & Francis Group, LLC. Conjugate natural convection heat transfer inside a differentially heated square cavity having a heat conducting and sinusoidal corrugated solid partition has been investigated numerically in the present study. The fluid flow and the heat transfer within the cavity are governed by two-dimensional Navier–Stokes and energy equations, and those are solved using the finite element method. Numerical simulation is carried out for a wide range of Rayleigh number (103 ≤ Ra ≤ 109) with a fixed Prandtl number (Pr = 0.71) since the working fluid in the cavity is considered as air. The variations of both corrugation amplitude and corrugation frequency of the sinusoidal partition wall on the average Nusselt number of the heated wall are observed in order to assess the influence of the roughness of the solid partition on the heat transfer characteristics of the cavity. Moreover, different types of partition material are selected to scrutinize the effect of thermal conductivity of the solid partition on the heat transfer performance. Finally, a correlation is proposed to predict the average Nusselt number of the heated wall of the cavity from the governing parameters (such as Rayleigh number, corrugation frequency and thermal conductivity ratio) within the selected range of the present investigation.

Introduction. For controlled thermal management of power electronics devices, an important task is to increase the efficiency of heat removal from active components. Aim. To introduce a new approach to placing a linear contact-type heat source on the surface of thin samples in order to study the features of propagation of heat fluxes in oxide substrates from materials with different thermal conductivities. Methods and materials. The paper presents the results of studies of the propagation of heat fluxes in oxide substrates with different thermal conductivity (glassceramic and aluminum oxide ceramic - polycor). To generate the heat flux, a linear heat source was used, for which an electrically conductive carbon fiber was applied. Results. Thermograms and temperature distribution profiles were obtained at different periods of heating time on the surface of the substrate with a heating element and on its reverse side. It was shown that the placement of the linear heat source, implemented using an electrically conductive carbon filament, on the surface of the studied samples and time monitoring of thermograms from two opposite surfaces of the samples allowed to obtain data for evaluating the thermal properties of oxide substrates. The distribution of the heat flux in a homogeneous material near the generation point had the form of a cone of a heat pipe with a base on the surface with a heat source. The thermal cone for an aluminum oxide ceramic substrate had a larger angle of inclination than that in the case of glassceramic. Conclusion. The results obtained allowed to propose a method for reduction of thermal resistance of a heatconducting substrate by creating conditions for increasing the area of heat-conducting section.

In this paper, we consider a compressible dissipative Baer–Nunziato-type system for a mixture of two compressible heat conducting gases. We prove that the set of weak solutions is stable, meaning that any sequence of weak solutions contains a (weakly) convergent subsequence whose limit is again a weak solution to the original system. Such type of results is usually considered as the most essential step to the proof of the existence of weak solutions. This is the first result of this type in the mathematical literature. Nevertheless, the construction of weak solutions to this system however remains still an (difficult) open problem.

Formation of one-dimensional flows arising as a result of interaction of a viscous heat-conducting gas and a heat-conducting wall in the process of reflection of a normally incident weak shock wave is considered. Formation of the flow field with small perturbations of parameters is studied on the basis of the Navier -Stokes equations linearized around the values of the parameters in the initial state, and the wall temperature distribution is modeled by linear heat equation. Analytical solutions of the linearized system of equations are obtained that allow one to analyze the influence of viscosity, thermal conductivity, and other factors on the formation of a continuous flow field structure with the formation of dissipative and ideal inviscid and non-heat-conducting zones.

A characteristic analysis of the equations of a single-velocity heat-conducting vapor–gas–drop mixture with interfractional heat transfer is carried out. The equations are shown to be hyperbolic. Calculation formulas for a Godunov-type method with a linearized Riemann solver are presented. These formulas are used to calculate some mixture flows.

A mathematical model is proposed for determining the quality of applying a heat-conducting compound, and simulation results are presented. The model is based on the theory of heat transfer in a solid. The model has been verified using experimental data obtained by measuring the temperature at the points of contact of two bodies using thermocouples. It is shown that the data obtained using thermocouples coincide with the data obtained using thermopower.

In quantum-dots-converted white-light-emitting diodes (QDs-WLEDs), red-emitting quantum dots are usually mixed with yellow-emitting phosphors in luminescent polymer layer to achieve a high color re...

Для энергосбережения при сушке зерна в контактно-конвективной сушилке предлагается использовать тепло охлаждающей жидкости двигателя внутреннего сгорания. Жидкость поступает в трубки контактно-конвективной сушилки. Трубки теплоносителя расположены наклонно под углом 40° параллельно друг другу по всей ширине сушилки. Над ними, в шахматном порядке – паросборники. Над паросборниками установлен плавающий разравнивающий транспортёр, который изменяет своё положение в зависимости от объёма зерна в контактно-конвективной сушилке. Рассмотрена отдельная зерновка, движущаяся по поверхности трубки теплоносителя. В результате нагрева зерновки происходит её отпотевание – появление влаги на поверхности зерновки. Произведён теплотехнический расчёт поверхности теплообмена теплоносителя и зернового вороха, определено количество тепла, передающегося зерновому вороху в результате контактного теплообмена. Установлено, что использование тепла охлаждающей жидкости двигателя внутреннего сгорания в контактно-конвективной сушилке приводит к энергосбережению при сушке зерна. For energy saving at grain drying in contact-convection drier it is proposed to use heat of cooling liquid of internal combustion engine. The liquid enters the tubes of the contact-convection drier. Heat carrier tubes are set at an angle of 40 ° parallel to each other along the full width of the drier. There are steam headers staggering above them. An amphibious leveling carrier is installed above the steam headers which changes its position depending on the volume of grain in the contact-convection drier. Separate caryopsis moving along surface of heat-conducting medium tube is considered. As a result of the heating of the caryopsis its sweating occurs – the appearance of moisture on the surface of the caryopsis. Thermotechnical calculation of heat-exchange surface of heat-conducting medium and grain trashed heap is performed, amount of heat transferred to grain trashed heap as a result of contact heat exchange is determined. It has been found that using the cooling liquid heat of the internal combustion engine in the contact-convection drier leads to energy saving when drying grain.

We are concerned with the Cauchy problem of the multidimensional inhomogeneous incompressible heat conducting Navier–Stokes flows with fractional dissipation. We show that the problem admits a unique global strong solution. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states.

The problem of the emergence of turbulence is one of the unsolved problems of physics and technology of the 20th century. It is noted that in order to understand the emergence of turbulence in a viscous heat-conducting gas, it is necessary to take into account the compressibility of the medium. A definition of turbulence in a viscous heat-conducting gas is given, which is a cyclically repeating process of the emergence and decay of coherent vortex structures described by a vector wave equation. The decay of vortex structures is accompanied by an explosive, asymptotic increase in pressure pulsations, which triggers a new cycle of turbulence generation. The emergence and decay of coherent vortex structures in the boundary layer on a plate and in a round jet is considered.

The large time behavior is considered for the solutions of the Navier-Stokes equations for one-dimensional viscous polytropic ideal gas in unbounded domains. Using the local anti-derivatives functions technique, we obtain the power type decay estimates for the generalized solutions as time goes to infinity

In this paper, we study the limit process as the bulk viscosity goes to zero for global weak solutions to the Navier–Stokes equations of compressible heat-conducting flows with density-dependent vi...

This paper investigates decay rates for the spatial behaviour of solutions for functionally graded heat-conducting materials. From a mathematical point of view, we obtain a new inequality of Poincarétype. This new result allows us to give new decay rates for functionally graded materials when the inhomogeneity depends on the radial variable and the axial variable of the cylinder. The case when the cross-section is increasing is also considered. Besides, we propose to obtain estimates for the case of mixtures. Some pictures illustrate our estimates.

We study positive radial solutions of quasilinear elliptic systems with a gradient term in the form $$ \left\{ \begin{aligned} \Delta_{p} u&=v^{m}|\nabla u|^{\alpha}&&\quad\mbox{ in }\Omega,\\ \Delta_{p} v&=v^{\beta}|\nabla u|^{q} &&\quad\mbox{ in }\Omega, \end{aligned} \right. $$ where $\Omega\subset\R^N$ $(N\geq 2)$ is either a ball or the whole space, $10$, $\alpha\geq 0$, $0\leq \beta\leq m$ and $(p-1-\alpha)(p-1-\beta)-qm\neq 0$. We first classify all the positive radial solutions in case $\Omega$ is a ball, according to their behavior at the boundary. Then we obtain that the system has non-constant global solutions if and only if $0\leq \alpha, Comment: 21 pages, 2 figures

Paper presents the problem of heating the damaged insulation of an orbiter. Changes of the insulation?s thermal properties, made by adding conductive material of high value of specific heat in a form of a dope to the protective layer, were examined. An iterative algorithm determining a variable of dope concentration in the material was developed. Insulating material LI900 was used for calculations. Determination of distribution of conductive material concentration was made for materials which, after verification, demonstrated the most beneficial effect on protective properties of the modified insulation layer. Change of properties was to enable time extension of the LI900 insulation tile heating up to the maximal temperature and, additionally, to lowering this temperature.

This paper presents a numerical study of ultra-lean hydrogen-methane flames stabilized behind a rectangular, highly conducting metallic bluff body acting as a flame holder. Using high fidelity numerical simulations, we show that lean inverted steady flames exist below normal flammability limits. They have distinct stabilization mechanism from pure methane flames. These flames are blown-off for sufficiently small velocities, a phenomenon called anomalous blow-off. At even leaner conditions oscillating ultra–lean hydrogen-methane flames can be established. These oscillating flames exist within a rather small range of equivalence ratios and inflow velocities, and move to mean locations closer to the flame holder as the reactant flow is increased. We show that the oscillations are associated with the shedding of flame balls from the downstream end of a “residual flame” that remains attached. Unlike their steady counterparts, the oscillating flames exhibit blow-off at both low velocities (anomalous blow-off) and at sufficiently high inflow velocities (normal blow-off). We show that normal blow-off is linked to heat losses to the flame holder.

In this paper we consider the non-stationary 1-D flow of a compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. Since the strong nonlinearity and degeneracies of the equations due to the temperature equation and vanishing of density, there are a few results about global existence of classical solution to this model. In the paper, we obtain a global classical solution to the equations with large initial data and vacuum. Moreover, we get the uniqueness of the solution to this system without vacuum. The analysis is based on the assumption \begin{document}$ \kappa(\theta) = O(1+\theta^q) $\end{document} where \begin{document}$ q\geq0 $\end{document} and delicate energy estimates.

A modified, generalized-equilibrium model of a one-velocity heterogeneous medium is presented, which accounts for the viscosity and thermal conductivity of the mixture, as well as for interfractional heat transfer. A characteristic analysis of the model′s equations has been carried out, and their hyperbolicity is shown. A description is given of Godunov′s method with a linearized Riemann solver intended for calculating mixture flows on curvilinear grids, with the use of which a number of problems for a vapor–air mixture has been investigated.

At the backdrop of energy conservation efforts in building sector, this research paper presents a passive approach by producing less heat conducting concrete with the inclusion of coal combustion r...

The plane stationary flow of viscous gas is considered, which is induced by the jet impacting the unbounded space and the domain between two diverging flat walls. Existence criteria of the Landau self-similar solutions are established for the source of gas flowing from the apex of a wedge with the thermally insulated walls and of wedge with the prescribed walls temperature. The analytical solutions are constructed in the case when the gas temperature is constant along the lines of flow and when the transfer coefficients are power functions of temperature.

We study the Cauchy problem for the equations describing a heat-conducting compressible fluid in three dimensional space with non-negative density. The global existence of unique strong solution is established, in case when the initial energy is assumed to be small. In addition, the decay rates for the solutions and their derivatives are derived.

The article presents the results of experiments to determine the dependence of thermopower on the quality of applying a heat-conducting compound. The data of deposition quality of the heat-conducting compound, which is obtained by thermocouples, coincides with the data, which is obtained using thermopower, but with a slight deviation due to the intrinsic inertia of thermocouples and fluctuations in the ambient temperature. The analysis of the data revealed that the value of the emerging thermopower increases linearly with the deterioration of the quality of the thermal interface application.

Successful joining of heat conducting materials, to high-temperature components is of significant importance for heat management in nuclear power plants and liquid propellant launch vehicles. Solid-state processes are considered for joining such dissimilar materials. Diffusion bonding of a copper alloy (C18150) to a Ni-based superalloy (GH4169) was investigated in this work. The bonding trials at 900°C for 60 min under a constant 10 MPa pressure led to formation of sound joints free from intermetallic, pores, voids and discontinuities. Conventional tensile testing led to the failure within the copper alloy and away from the joint. Due to the softening of the copper alloy during the bonding process, the maximum tensile strength of the as-bonded copper alloy was only 48% of its as-received strength. Post-bonding solution treatment at 960°C for 60 min followed by ageing at 450°C for 3.5 h, restored the tensile strength of the copper alloy up to 77%.

We prove the existence of large-data global-in-time weak solutions to an evolutionary PDE system describing flows of incompressible \emph{heat-conducting} viscoelastic rate-type fluids with stress-diffusion, subject to a stick-slip boundary condition for the velocity and a homogeneous Neumann boundary condition for the extra stress tensor. In the introductory section we develop the thermodynamic foundations of the proposed model, and we document the role of thermodynamics in obtaining critical structural relations between the quantities of interest. These structural relations are then exploited in the mathematical analysis of the governing equations. In particular, the definition of weak solution is motivated by the thermodynamic basis of the model. The extra stress tensor describing the elastic response of the fluid is in our case purely spherical, which is a simplification from the physical point of view. The model nevertheless exhibits features that require novel mathematical ideas in order to deal with the technically complex structure of the associated internal energy and the more complicated forms of the corresponding entropy and energy fluxes. The paper provides the first rigorous proof of the existence of large-data global-in-time weak solutions to the governing equations for \emph{coupled thermo-mechanical processes} in viscoelastic rate-type fluids.

We consider nonstationary 1-D flow of a compressible viscous and heat-conducting micropolar fluid which is in the thermodynamical sense perfect and polytropic. In the first part of the work we present corresponding initial-boundary value problems whereby we allow non-homogeneous boundary conditions for velocity, microrotation or temperature. In the second part of the work we present existence results for described problems under the additional assumption that the initial density and initial temperature are strictly positive.

The research reported in this paper was funded by King Abdullah University of Science and Technology. We are thankful for the computing resources of the Supercomputing Laboratory and the Extreme Computing Research Center at King Abdullah University of Science and Technology.

We compute the effective thermal contact resistance of a pair of materials formed by AISI 304 stainless steel and 200 nickel alloy in the presence of a periodic array of gaps filled with a heat-conducting medium (argon, water, helium, oxygen, or air) on the interface of these materials. In the nondeformed state, the surface of AISI 304 stainless steel has a microtextured topography formed by regularly located grooves of identical shapes, while the surface of 200 nickel alloy is perfectly flat. We estimate the level of thermal rectification for structures of this kind for different values of the applied mechanical and thermal loads and the maximal height of the surface grooves.