Constant Heat Conductivity Research Articles

High-precision, programmable soft wireless robotics for cooling tower cleaning based on Internet of Things technology

Soft robotics with high flexibility & adaptability gain attention for precision tasks in unstructured environments. However, non-contact robotics’ reliance on thermal/optical fields limits stability & stimulus uniformity, resulting in low accuracy, poor scalability, & limited adaptability. This paper introduces a new soft robotic system (PM10B2C robotic) incorporated Internet of Things (IoT) technology and leveraged the Joule thermal effect. The robotic platform is constructed by self-prepared boron nitride nanosheets (BNNS) that exhibit a higher planar area-to-thickness ratio. When the actuation voltage is 8 V, the soft wireless robotic can complete κ = 1.19 cm−1 deformation with deformation efficiency and recovery efficiency of 0.11 cm−1·s−1 and 0.17 cm−1·s−1, and exhibits excellent actuation stability under 500 cycles of testing. Based on the Timoshenko bimetallic constant temperature device model and heat conduction theory, a κmax-U analytical model is constructed to achieve effective prediction of the optimal curvature-low voltage D.C. relationship of PM10B2C robotics. The smart-controlled soft robotic operates continuously and stably within the harsh internal environments and complex spatial configurations of thermal power plant in cooling towers. This design offers novel prospects for developing cleaning robotics tailored for extreme environments and complex spaces in such facilities.

On the asymptotic behavior of the one-dimensional motion of the polytropic ideal gas with degenerate heat conductivity

We consider the one dimensional compressible Navier-Stokes system with constant viscosity and the nonlinear heat conductivity being proportional to a positive power of the temperature which may be degenerate. This problem is imposed on the stress-free boundary condition, which reveals the motion of a viscous heat-conducting perfect polytropic gas with adiabatic ends putting into a vacuum. We prove that the solution of one dimensional compressible Navier-Stokes system with the stress-free boundary condition shares the same large-time behavior as the case of constant heat conductivity.

Global solution to the compressible non-isothermal nematic liquid crystal equations with constant heat conductivity and vacuum

This paper considers the initial-boundary value problem of the one-dimensional full compressible nematic liquid crystal flow problem. The initial density is allowed to touch vacuum, and the viscous and heat conductivity coefficients are kept to be positive constants. Global existence of strong solutions is established for any H^{2} initial data in the Lagrangian flow map coordinate, which holds for both vacuum and non-vacuum case. The key difficulty is caused by the lack of the positive lower bound of the density. To overcome such difficulty, it is observed that the ratio of frac{rho _{0(y)}}{rho (t,y)} is proportional to the time integral of the upper bound of temperature and vector director field, along the trajectory. Density weighted Sobolev type inequalities are constructed for both temperature and director field in terms of frac{rho _{0(y)}}{rho (t,y)} and small dependence on their dissipation estimates. Besides this, to deal with cross terms arising due to liquid crystal flow, higher order priori estimates are established by using effective viscous flux.

Global strong solution to a thermodynamic compressible diffuse interface model with temperature‐dependent heat conductivity in 1D

In this paper, we investigate the wellposedness of the nonisentropic compressible Navier–Stokes/Allen–Cahn system with the heat conductivity proportional to a positive power of the temperature. This system describes the flow of a two‐phase immiscible heat‐conducting viscous compressible mixture. The phases are allowed to shrink or grow due to changes of density in the fluid and incorporates their transport with the current. We established the global existence and uniqueness of strong solutions for this system in 1D, which means no phase separation, vacuum, shock wave, mass, or heat or phase concentration will be developed in finite time, although the motion of the two‐phase immiscible flow has large oscillations and the interaction between the hydrodynamic and phase‐field effects is complex. Our result can be regarded as a natural generalization of the Kazhikhov–Shelukhin's result (Kazhikhov and Shelukhin, 1977) for the compressible single‐phase flow with constant heat conductivity to the non‐isentropic compressible immiscible two‐phase flow with degenerate and nonlinear heat conductivity.

Large-time Behavior of Magnetohydrodynamics with Temperature-Dependent Heat-Conductivity

For the strong solutions to the equations of a planar magnetohydrodynamic compressible flow with the heat conductivity proportional to a nonnegative power of the temperature, we first prove that both the specific volume and the temperature are proved to be bounded from below and above independently of time. Then, we also show that the global strong solution is nonlinearly exponentially stable as time tends to infinity. This is the first result obtaining the exponential stability behavior of strong solutions to the equations of a planar magnetohydrodynamic compressible flow without any smallness conditions on the data. Our result can be regarded as a natural generalization of the previous ones for the compressible Navier-Stokes system to MHD system with either constant heat-conductivity or nonlinear and temperature-depending heat-conductivity. As a direct consequence, it is shown that the global strong solution to the constant heat-conductivity MHD system whose existence is obtained by Kazhikhov in 1987 is nonlinearly exponentially stable.

Global existence of strong solutions to MHD with density-depending viscosity and temperature-depending heat-conductivity in unbounded domains

We study the equations of a planar magnetohydrodynamic (MHD) compressible flow with the viscosity depending on the specific volume of the gas and the heat conductivity being proportional to a positive power of the temperature. In particular, we obtain the global existence of the unique strong solutions to the Cauchy problem or the initial-boundary-value one under natural conditions on the initial data in one-dimensional unbounded domains. This result generalizes the classical one of the compressible Navier–Stokes system with constant viscosity and heat conductivity [Kazhikhov, Siberian. Math. J. 23, 44–49 (1982)] to the planar MHD compressible flow with nonlinear viscosity and degenerate heat-conductivity, which means no shock wave, vacuum, or mass or heat concentration will be developed in finite time, although the interaction between the magnetodynamic and hydrodynamic effects is complex and the motion of the flow has large oscillations.

Влияние зависимости коэффициента теплопроводности от температуры на физические закономерности объемного синтеза интерметаллида

Two-dimensional model of high-temperature synthesis of chemical compounds and alloys in a dynamic thermal explosion mode when a powder compact is heated in a steel cylindrical mold by an induction heat source are proposed. The complex of chemical reactions is described by a total reaction with effective formal kinetic parameters. The kinetic law takes into account strong retardation of the reaction by the layer of the synthesized product that prevents the interaction of the reagents. The model makes it possible to investigate the macroscopic physical laws of the synthesis of a composite with a change in the heating rate and reactor dimensions. It is made a comparison of the results obtained for a constant heat conductivity coefficient and a temperature-dependent heat conductivity coefficient. It is revealed that taking into account the temperature dependence of the heat conductivity coefficient can lead to a numerical change in the ignition delay time and to a qualitatively different temperature distribution in the reactor bulk.

Global existence of strong solutions to compressible Navier–Stokes system with degenerate heat conductivity in unbounded domains

In one‐dimensional unbounded domains, we prove the global existence of strong solutions to the compressible Navier–Stokes system for a viscous and heat conducting ideal polytropic gas, when the viscosity is a constant and the heat conductivity is proportional to a positive power of the temperature. Note that the conditions imposed on the initial data are the same as those of the constant heat conductivity case (Kazhikhov, A. V. Siberian Math. J. 23 [1982], 44‐49) and can be arbitrarily large. Therefore, our result generalizes Kazhikhov's result for the constant heat conductivity case to the degenerate and nonlinear one.

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.

Global large solutions to the planar magnetohydrodynamics equations with constant heat conductivity

This paper is concerned with global existence of large solutions to the initial-boundary value problem of the planar magnetohydrodynamic compressible flow. Under the assumptions that viscosity and heat conductivity coefficients are constants, magnetic diffusion is a function of the specific volume, we obtain the global existence of strong solutions. Some new methods are developed to deal with the complex interaction between the hydrodynamic and magnetodynamics effects.

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.

Shock wave structure in a non-ideal gas under temperature and density-dependent viscosity and heat conduction

The structure of a shock wave is investigated using the continuum hypothesis for steady one-dimensional flow of a viscous non-ideal gas under heat conduction. The coefficients of viscosity and heat conductivity are assumed to be directly proportional to a power of the temperature and density of the gas. The simplified van der Waals equation of state for the non-ideal gas has been assumed in this work. Qualitative analysis of shock wave structure has been done in terms of singularity analysis, isoclines, and integral curves. The exact and numerical solutions of shock structure equations are obtained under the quantitative analysis. The validation of solution is established by comparing the results in the literature (Iannelli in Int J Numer Methods Fluids 72(2):157–176, 2013). The variation of normalized gas velocity, viscous stress, heat flux, and shock thickness have been investigated across shock transition zone with the non-idealness of the gas, temperature, and density exponents in the viscosity and heat conductivity of the gas and initial Mach number. It is found that gas velocity decreases significantly with the increase in non-idealness parameter, temperature, and density exponent in the viscosity of the gas. Shock wave thickness decreases with the increase in the non-idealness of the gas under constant viscosity and heat conductivity but increase under variable gas properties. The thickness of a shock wave decreases with the increase in the temperature exponent and increases with the increase in the density exponent.

Nonlinearly exponential stability of compressible Navier-Stokes system with degenerate heat-conductivity

We study the large-time behavior of strong solutions to the one-dimensional, compressible Navier-Stokes system for a viscous and heat conducting ideal polytropic gas, when the viscosity is constant and the heat conductivity is proportional to a positive power of the temperature. Both the specific volume and the temperature are proved to be bounded from below and above independently of time. Moreover, it is shown that the global solution is nonlinearly exponentially stable as time tends to infinity. Note that the conditions imposed on the initial data are the same as those of the constant heat conductivity case (Kazhikhov-Shelukhin (1977) [18]; Kazhikhov (1981) [17]) and can be arbitrarily large. Therefore, our result can be regarded as a natural generalization of the Kazhikhov's ones for the constant heat conductivity case to the degenerate and nonlinear one.

Global Well-Posedness of the One-Dimensional Compressible Navier--Stokes Equations with Constant Heat Conductivity and Nonnegative Density

In this paper we consider the initial-boundary value problem to the one-dimensional compressible Navier--Stokes equations for ideal gases. Both the viscous and heat conductive coefficients are assu...

Three-dimensional thermo-visco-elasticity with the Einstein-Debye $(\theta^3+\theta)$-law for the specific heat. Global regular solvability

A three-dimensional thermo-visco-elastic system for the Kelvin-Voigt type material at small strain is considered. The system involves the constant heat conductivity and the specific heat satisfying the Einstein-Debye $(\theta^3+\theta)$-law. Such a nonlinear law, relevant at relatively low temperatures, represents the main novelty of the paper. The existence of global regular solutions is proved without the small data assumption. The crucial part of the proof is the strictly positive lower bound on the absolute temperature $\theta$. The problem remains open in the case of the Debye $\theta^3$-law. The existence of local in time solutions is proved by the Banach successive approximations method. The global {\em a priori} estimates are derived with the help of the theory of anisotropic Sobolev spaces with a mixed norm. Such estimates allow to extend the local solution step by step in time.

Numerical simulation of fire vortex

The article considers the numerical simulation of the swirling flow of air around the smoothly heated vertical cylindrical domain in the conditions of gravity and Coriolis forces action. The solutions of the complete system of Navie-Stocks equations are numerically solved at constant viscosity and heat conductivity factors. Along with the proposed initial and boundary conditions, these solutions describe the complex non-stationary 3D flows of viscous compressible heat conducting gas. For various instants of time of the initial flow formation stage using the explicit finite-difference scheme the calculations of all gas dynamics parameters, that is density, temperature, pressure and three velocity components of gas particles, have been run. The current instant lines corresponding to the trajectories of the particles movement in the emerging flow have been constructed. A negative direction of the air flow swirling occurred in the vertical cylindrical domain heating has been defined.

Numerical analysis of ion temperature effects to the plasma wall transition using a one-dimensional two-fluid model. I. Finite Debye to ionization length ratio.

A one-dimensional, two-fluid, steady state model is used for the analysis of ion temperature effects to the plasma-wall transition. In this paper, the model is solved for a finite ratio ε between the Debye and the ionization length, while in Part II [T. Gyergyek and J. Kovačič, Phys Plasmas 24, 063506 (2017)], the solutions for [Formula: see text] are presented. Ion temperature is treated as a given, independent parameter and it is included in the model as a boundary condition. It is shown that when the ion temperature larger than zero is selected, the ion flow velocity and the electric field at the boundary must be consistent with the selected ion temperature. A numerical procedure, how to determine such "consistent boundary conditions," is proposed, and a simple relation between the ion temperature and ion velocity at the boundary of the system is found. The effects of the ion temperature to the pre-sheath length, potential, ion temperature, and ion density drops in the pre-sheath and in the sheath are investigated. It is concluded that larger ion temperature results in a better shielding of the plasma from the wall. An attempt is made to include the ion heat flux qi into the model in its simplest form [Formula: see text], where [Formula: see text] is a constant heat conduction coefficient. It is shown that inclusion of such a term into the energy transfer equation introduces an additional ion heating mechanism into the system and the ion flow then becomes isothermal instead of adiabatic even in the sheath.

A new boundary meshfree method for calculating the multi-domain constant coefficient heat conduction with a heat source problem

ABSTRACTA new high-precision boundary meshfree method, namely virtual boundary meshfree Galerkin method (VBMGM), for calculating the multi-domain constant coefficient heat conduction with a heat source problem is given. In the paper, the radial basis function interpolation is used to solve the virtual source function of virtual boundary and the heat source within each subdomain. Simultaneously, the equation of VBMGM for multi-domain constant coefficient heat conduction with a heat source problem is obtained by the Galerkin method. Therefore, the proposed method has common advantages of the boundary element method, meshfree method, and Galerkin method. Coefficient matrix of this specific expression is symmetrical and the specific expression of VBMGM for the multi-domain constant coefficient heat conduction with a heat source problem is given. Two numerical examples are given. The numerical results are also compared with other numerical methods. The accuracy and feasibility of the method for the multi-domain constant coefficient heat conduction with a heat source problem are proved.

Convection in axially symmetric accretion discs with microscopic transport coefficients

The vertical structure of stationary thin accretion discs is calculated from the energy balance equation with heat generation due to microscopic ion viscosity {\eta} and electron heat conductivity {\kappa}, both depending on temperature. In the optically thin discs it is found that for the heat conductivity increasing with temperature, the vertical temperature gradient exceeds the adiabatic value at some height, suggesting convective instability in the upper disc layer. There is a critical Prandtl number, Pr = 4/9, above which a Keplerian disc become fully convective. The vertical density distribution of optically thin laminar accretion discs as found from the hydrostatic equilibrium equation cannot be generally described by a polytrope but in the case of constant viscosity and heat conductivity. In the optically thick discs with radiation heat transfer, the vertical disc structure is found to be convectively stable for both absorption dominated and scattering dominated opacities, unless a very steep dependence of the viscosity coefficient on temperature is assumed. A polytropic-like structure in this case is found for Thomson scattering dominated opacity.

Zirconium Carbide Produced by Spark Plasma Sintering and Hot Pressing: Densification Kinetics, Grain Growth, and Thermal Properties.

Spark plasma sintering (SPS) has been employed to consolidate a micron-sized zirconium carbide (ZrC) powder. ZrC pellets with a variety of relative densities are obtained under different processing parameters. The densification kinetics of ZrC powders subjected to conventional hot pressing and SPS are comparatively studied by applying similar heating and loading profiles. Due to the lack of electric current assistance, the conventional hot pressing appears to impose lower strain rate sensitivity and higher activation energy values than those which correspond to the SPS processing. A finite element simulation is used to analyze the temperature evolution within the volume of ZrC specimens subjected to SPS. The control mechanism for grain growth during the final SPS stage is studied via a recently modified model, in which the grain growth rate dependence on porosity is incorporated. The constant pressure specific heat and thermal conductivity of the SPS-processed ZrC are determined to be higher than those reported for the hot-pressed ZrC and the benefits of applying SPS are indicated accordingly.