Temperature Dependence Of Heat Conductivity Research Articles

An analytical study of thermal environment’s effect on the free vibration of FGM double curved FG shells

The main objectif of this work is to examine the thermal environment’s effect of on the free vibration of double curvature shells made of functionally graded materials. A new mathematical model based on higher order shear deformation theory, is developed to incorporate the influence of dependent and independent thermal stresses, which can be uniform, linear, nonlinear, or sinusoidal on the mechanical properties of the double curvature shell. Two material couples, ( S i 3 N 4 / SUS 304 , ZrO 2 /Ti‐6Al‐4V ) , are considered as progressive materials, accounting for temperature-dependent and temperature-independent heat conduction and material properties in the thickness direction. The temperature field is assumed to be uniform across the shell surface but varies only in the thickness direction. The accuracy of the analytical results is validated by comparing them with existing literature results for functionally graded material (FGM) shells with infinite radii under dependent and independent temperature conditions. The study aims to demonstrate the thermal effects on material composition, as well as various specific geometric shapes such as plates, cylinders, spheres and ellipses and how different temperature laws influence the frequencies of vibrating double curvature FGM shells. Both existing theories accurately predict temperature-independent and temperature-dependent vibration responses of the shells. By verifying and comparing the results with the literature, a better agreement is achieved, thereby paving the way for further research in this field.

An analytical study of thermal environment’s effect on the free vibration of FGM double curved FG shells

The main objectif of this work is to examine the thermal environment’s effect of on the free vibration of double curvature shells made of functionally graded materials. A new mathematical model based on higher order shear deformation theory, is developed to incorporate the influence of dependent and independent thermal stresses, which can be uniform, linear, nonlinear, or sinusoidal on the mechanical properties of the double curvature shell. Two material couples, ( S i 3 N 4 / SUS 304 , ZrO 2 /Ti‐6Al‐4V ) , are considered as progressive materials, accounting for temperature-dependent and temperature-independent heat conduction and material properties in the thickness direction. The temperature field is assumed to be uniform across the shell surface but varies only in the thickness direction. The accuracy of the analytical results is validated by comparing them with existing literature results for functionally graded material (FGM) shells with infinite radii under dependent and independent temperature conditions. The study aims to demonstrate the thermal effects on material composition, as well as various specific geometric shapes such as plates, cylinders, spheres and ellipses and how different temperature laws influence the frequencies of vibrating double curvature FGM shells. Both existing theories accurately predict temperature-independent and temperature-dependent vibration responses of the shells. By verifying and comparing the results with the literature, a better agreement is achieved, thereby paving the way for further research in this field.

Free vibration analysis of FGM spherical and elliptical shells under nonlinear thermal environments

The thermo-mechanical effects of the free vibration of functionally graded (FG) spherical and elliptical shells under nonlinear temperature distributions (NTD) are investigated. The geometries of the FG spherical and elliptical shells are expressed in terms of the surface fundamental form, and the displacement function is derived based on higher-order shear deformation theory (HSDT). Temperature-dependent (TD) material and heat conduction are investigated based on Voigt's micromechanical model. The equation of motion of the thermo-elastic FG shells is formulated using the classical Hamilton's principle. Numerical results are obtained using the finite element method with quadrilateral Lagrangian isoparametric elements. A comparison of the results for the free vibration of FG shells based on the FSDT and HSDT approaches is presented. The first fundamental mode is the axisymmetric mode for the circular plate and oblate shell, but the results are otherwise for spherical and prolate shells. The torsional mode occurs in the seventh mode within the first ten vibrational modes for the prolate shell. In addition, the frequency parameter in the torsional mode is independent of the different support conditions. Parametric studies show that the non-dimensional frequency parameters of the FG shells decrease quickly, then slowly, as the volume fraction index increases. Finally, the frequency parameters decrease when the temperature at the top of the FG shell surface increases.

On initial boundary value problems for the compressible Navier–Stokes system with temperature dependent heat conductivity

On initial boundary value problems for the compressible Navier–Stokes system with temperature dependent heat conductivity

The Influence of Physical Properties on the Membrane Morphology Formation during the Nonisothermal Thermally Induced Phase Separation Process.

The physical properties of a polymer solution that are composition- and/or temperature-dependent are among the most influential parameters to impact the dynamics and thermodynamics of the phase separation process and, as a result, the morphology formation. In this study, the impact of composition- and temperature-dependent density, heat capacity, and heat conductivity on the membrane structure formation during the thermally induced phase separation process of a high-viscosity polymer solution was investigated via coupling the Cahn-Hilliard equation for phase separation with the Fourier heat transfer equation. The variations of each physical property were also investigated in terms of different boundary conditions and initial solvent volume fractions. It was determined that the physical properties of the polymer solution have a noteworthy impact on the membrane morphology in terms of shorter phase separation time and droplet size. In addition, the influence of enthalpy of demixing in this case is critical because each physical property showed a nonhomogeneous pattern owing to the heat generation during phase separation, which in turn influenced the membrane morphology. Accordingly, it was determined that investigating spinodal decomposition without including heat transfer and the impact of physical properties on the morphology formation would lead to an inadequate understanding of the process, specifically in high-viscosity polymer solutions.

On Some Types of Initial-Boundary Value Problems for the Compressible Navier–Stokes Equations with Temperature-Dependent and Degenerate Heat Conductivity

On Some Types of Initial-Boundary Value Problems for the Compressible Navier–Stokes Equations with Temperature-Dependent and Degenerate Heat Conductivity

Thermo-metallurgical-mechanical modeling of FG titanium-matrix composites in powder bed fusion

The build-up of residual stress plays a crucial role in the formation quality of as-built parts fabricated by powder bed fusion (PBF). However, the comprehensive understanding of residual stress and distortion fields in PBF-printed functionally graded titanium matrix composites (FGTMCs) has not been achieved. Furthermore, the effect of metallurgical transformation on thermo-mechanical behavior of these materials during the PBF remains unclear. In this paper, considering the phase transition effect due to thermal evolution in the PBF process, a thermo-metallurgical-mechanical coupled model of printed FGTMCs is developed. The equivalent temperature-dependent elastic modulus and heat conductivity of FGTMCs are calculated based on the homogenization method. The differential quadrature method is first employed to efficiently predict the temperature, residual stress, and distortion distributions of PBF-printed FGTMCs. The accuracy of the proposed model is verified by a comparison with predictions in the literature. Furthermore, the effect of crucial process and geometrical parameters on the thermo-mechanical behaviors of FGTMCs is analyzed. The results indicate that the residual stress and vertical distortion of FGTMCs increase as the laser penetration, energy densities, and power index increase, while decreasing significantly with the increased ceramic content, preheating temperature, and layer thickness. These results provide valuable insights for guiding the process optimization of additively manufactured FGTMCs.

Asymptotic Behavior of the Solution to Compressible Navier–Stokes System with Temperature-Dependent Heat Conductivity in an Unbounded Domain

This paper concerns the one-dimensional compressible Navier–Stokes system with temperature-dependent heat conductivity in R with large initial data. We prove that velocity and temperature are uniformly bounded from below and above in time and space when the heat conductivity coefficient takes κ=κ¯(1+θb) for all b>52. In addition, we show that the global solution is asymptotically stable as time tends to infinity.

Global Existence to Cauchy Problem for 1D Magnetohydrodynamics Equations

Magnetohydrodynamics are widely used in medicine and biotechnology, such as drug targeting, molecular biology, cell isolation and purification. In this paper, we prove the existence of a global strong solution to the one-dimensional compressible magnetohydrodynamics system with temperature-dependent heat conductivity in unbounded domains and a large initial value by the Lagrangian symmetry transformation, when the viscosity μ is constant and the heat conductivity κ, which depends on the temperature, satisfies κ=κ¯θb(b>1).

Approximation of Composition and Temperature Dependent Heat Conductivity and Optimization of Thermoelectric Energy Conversion in Silicon–Germanium Alloys

We analyze the efficiency as thermoelectric energy converter of a silicon–germanium alloy with composition and temperature dependent heat conductivity. The dependency on composition is determined by a non-linear regression method (NLRM), while the dependency on temperature is approximated by a first-order expansion in the neighborhood of three reference temperatures. The differences with respect to the case of thermal conductivity depending on composition only are pointed out. The efficiency of the system is analyzed under the assumption that the optimal energy conversion corresponds to the minimum rate of energy dissipated. The values of composition and temperature which minimize such a rate are calculated as well.

Local Strong Solutions to the Full Compressible Navier--Stokes System with Temperature-Dependent Viscosity and Heat Conductivity

Local Strong Solutions to the Full Compressible Navier--Stokes System with Temperature-Dependent Viscosity and Heat Conductivity

Thermal Response of Magnetic Refrigerants: Combined Effect of Temperature Dependent Specific Heat and Thermal Conductivity

Device optimization plays a paramount role in current research on magnetic refrigeration. Solid state refrigerants have been characterized and numerical simulations assume a critical relevance in the development of magnetocaloric technology to have alternatives to vapour-compression systems whose operating elements have high global warming potential. Experimental studies have shown that the thermal properties of several magnetocaloric materials considerably change around their Curie temperatures (TC) and that this temperature dependency should not be dismissed. Current numerical research does not fully predict the complete thermal response of such materials, due to inaccuracies from neglecting the impact of combining both thermal conductivity (k) and specific heat (Cp) dependence on temperature. In this study, a simple unidimensional model includes k(T) and Cp(T) functions as input parameters, highlighting the relevance of considering temperature dependent thermophysical properties’ inputs when simulating the magnetic refrigerant’s heat transfer processes. The obtained results evidence that neglecting the temperature dependence of the magnetocaloric material thermophysical properties, namely its thermal conductivity and its specific heat, affects its temperature response, what may strongly affect the results after a succession of (hundreds or thousands) cycles.

Finite element approximation and preconditioning for anisothermal flow of implicitly-constituted non-Newtonian fluids

We devise 3-field and 4-field finite element approximations of a system describing the steady state of an incompressible heat-conducting fluid with implicit non-Newtonian rheology. We prove that the sequence of numerical approximations converges to a weak solution of the problem. We develop a block preconditioner based on augmented Lagrangian stabilisation for a discretisation based on the Scott–Vogelius finite element pair for the velocity and pressure. The preconditioner involves a specialised multigrid algorithm that makes use of a space decomposition that captures the kernel of the divergence and non-standard intergrid transfer operators. The preconditioner exhibits robust convergence behaviour when applied to the Navier–Stokes and power-law systems, including temperature-dependent viscosity, heat conductivity and viscous dissipation.

Evolution of the parent body of enstatite (EL) chondrites

Chondrites stem from undifferentiated asteroidal parent bodies that nevertheless experienced a certain degree of metamorphism after their formation in the early solar system. Maximum temperatures of metamorphism depend mainly on formation time and the abundance of the main heating source, which is short-lived 26Al (half life 720 000 yr).Enstatite chondrites formed under reducing conditions and include many strongly metamorphosed members of petrologic type 6. We model the thermal evolution of the parent body of the low metal enstatite chondrite class (EL). The model takes into account accretion, heating, sintering and compaction by hot pressing of the initially porous material, temperature dependent heat conductivity, and insulation effects by the remaining regolith layer.A fit of key parameters of the parent body comprising formation time, radius, and porosity is achieved by fitting thermal histories of EL6 chondrites (LON 94100, Neuschwanstein, Khairpur, Blithfield, Daniel’s Kuil) constrained mainly by I–Xe and Ar–Ar ages and their respective closure temperatures. Viable fits are obtained for parent bodies with 120–210 km radius, formed c. 1.8–2.1 Ma after Ca,Al rich inclusions (CAIs), and an initial porosity of 30%, relatively independent on initial disk temperatures. Optimised models with parent body formation-times >1.95 Ma after CAIs imply central core temperatures below incipient plagioclase silicate melting.Thermal histories of the different EL6 chondrites are indistinguishable and so are their burial depths. While the exact layering depth is somewhat model dependent (c. 12–20 km), the thickness of the layer from which all five EL6 chondrites stem is <1 km. Hence, an origin from a quite small asteroidal fragment is possible, particular as most excavation ages inferred from cosmic ray exposure data are compatible with a separation as metre sized meteoroids from a small Apollo asteroid 33 Ma ago.

On globally large smooth solutions of full compressible Navier–Stokes equations with moving boundary and temperature-dependent heat-conductivity

The global existence and uniqueness of smooth solution to the vacuum free boundary problem of full compressible Navier–Stokes equations with large initial data and radial symmetry is established in this paper, when the fluid connects to vacuum continuously. The main difficulty lies in the fact that, the system is strongly nonlinear with unknown boundary variables, and degenerate near the free boundary separating the fluid and vacuum, thus general theory does not apply to this case. To overcome this trouble, we establish the point-wise estimates on the upper and lower bounds of the deformation variable ηx, the refined estimate for the temperature, and also the uniform-in-time weighted energy estimates for the solutions with high regularity, by careful analysis. Moreover, the expanding rate of the free interface is also proved. The main ingredient of this paper is that the high regularity of the solution is always up to the free boundary. Previous results are only for weak solutions, or the case that the fluids connect to the vacuum with a jump. The assumption on the heat conductivity coefficient κ≈1+θq,q≥2 is also improved to be q>0.

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.

Recovering temperature-dependent heat conductivity in 2D and 3D domains with homogenization functions as the bases

The paper solves the parameters identification problem in a nonlinear heat equation with homogenization functions as the bases, which are constructed from the boundary data of the temperature in the 2D and 3D space-time domains. To satisfy the over-specified Neumann boundary condition, a linear equations system is derived and then used to determine the expansion coefficients of the solution. Then, after back substituting the solution and collocating points to satisfy the governing equations, the space-time-dependent and temperature-dependent heat conductivity functions in 2D and 3D nonlinear heat equations are identified by solving other linear systems. The novel methods do not need iteration and solving nonlinear equations, since the unknown heat conductivities are retrieved from the solutions of linear systems. The solutions and the heat conductivity functions recovered are quite accurate in the entire space-time domain. We find that even for the inverse problems of nonlinear heat equations, the homogenization functions method is easily used to recover 2D and 3D space-time-dependent and temperature-dependent heat conductivity functions. It is interesting that the present paper makes a significant contribution to the engineering and science in the field of inverse problems of heat conductivity, merely solving linear equations and without employing iteration and solving nonlinear equations to solve nonlinear inverse problems.

Global strong solutions for viscous radiative gas with degenerate temperature dependent heat conductivity in one-dimensional unbounded domains

In one-dimensional unbounded domains, we prove the global existence of strong solutions to the compressible Navier–Stokes system for a viscous radiative gas, when the viscosity μ is a constant and the heat conductivity κ is a power function of the temperature θ according to κ(θ)=κ̃θβ, with β ≥ 0 and κ̃&amp;gt;0. Our result generalizes Zhao and Liao’s result [Y. K. Liao and H. J. Zhao, J. Differ. Equations 265, 2076–2120 (2018)] to the degenerate and nonlinear heat conductivity. In particular, the constant coefficients’ case (μ and κ are positive constants) is also covered in our theorem.

Local classical solutions to the full compressible Navier–Stokes system with temperature-dependent heat conductivity

Local classical solutions to the full compressible Navier–Stokes system with temperature-dependent heat conductivity

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.