Temperature Dependence Of Thermal Conductivity Research Articles

Ablation threshold and temperature dependent thermal conductivity of high entropy carbide thin films

High entropy carbides (HECs) are a promising new class of ultra-high temperature ceramics that could provide novel material solutions for leading edges of hypersonic vehicles, which can reach temperatures > 3,500 �C and experience extreme thermal gradients. Although the mechanical and thermal properties of HECs have been studied extensively at room temperature, few works have examined HEC properties at high temperatures or considered these materials� responses to thermal shock. In this work, we measure the thermal conductivity of a five-cation HEC up to 1200 �C. We find that thermal conductivity increases with temperature, consistent with trends demonstrated in single-metal carbides. We also measure thermal conductivity of an HEC deposited with varying CH4 flow rate, and find that although thermal conductivity is reduced when carbon content surpasses stoichiometric concentrations, the films all exhibited the same temperature dependent trends regardless of carbon content. To compare the thermal shock resistance of HECs with a refractory carbide, we conduct pulsed laser ablation measurements to determine the fluence threshold the HECs can withstand before damaging. We find that this metric for the average bond strength trends with the theoretical hardness of the HECs as expected.

Теплопроводность SiC: расчет изотопического эффекта из первых принципов

The thermal conductivity temperature dependence kappa(T) of a hexagonal 2H-SiC silicon carbide crystal was calculated using the first-principle approach for the orientation of the heat flux in the basal plane and along the hexagonal axis c in the temperature range from 100 to 500 K. The effect of silicon and carbon isotopic disorder on thermal conductivity is considered. It was found that, at a temperature of 300 K, the thermal conductivity of isotopically pure 2H-SiC containing 100% 28Si and 100% 12C is higher by 15.2% and 12.4% for directions along and across the basal plane, respectively, than that of crystals with a natural composition of silicon and carbon isotopes. For crystals with a natural mixture of carbon isotopes natC, the isotope effect for silicon is 14.5% and 11.9% for these directions.

SiC thermal conductivity: calculation of the isotope effect from first principles

The thermal conductivity temperature dependence kappa(T) of a hexagonal 2H-SiC silicon carbide crystal was calculated using the first-principle approach for the orientation of the heat flux in the basal plane and along the hexagonal axis c in the temperature range from 100 to 500 K. The effect of silicon and carbon isotopic disorder on thermal conductivity is considered. It was found that, at a temperature of 300 K, the thermal conductivity of isotopically pure 2H-SiC containing 100% 28Si and 100% 12C is higher by 15.2% and 12.4% for directions along and across the basal plane, respectively, than that of crystals with a natural composition of silicon and carbon isotopes. For crystals with a natural mixture of carbon isotopes textnatC, the isotope effect for silicon is 14.5% and 11.9% for these directions. Keywords: single crystal, thermal conductivity, silicon carbide, first principle calculation.

Functional estimation of space and time varying thermal properties using modified conjugate gradient method

Estimation of thermal properties is essential for composite or newly invented materials used in various industries such as nuclear, aerospace, chemical, medical etc. In this work, the conjugate gradient method (CGM) with adjoint problem has been applied for the functional estimation of space and time varying thermal properties. No prior knowledge of the functional form of thermal properties is available. To overcome the divergence issue and relatively low derivative value during the start of CGM algorithm, a scaling factor based on Levenberg-Marquardt method (LM) has been applied. To test the efficacy of the proposed method for estimating thermal properties in actual applications, a numerical experiment with added artificial Gaussian error (noise) in simulated temperature measurements of standard deviation (θ) 0.01 °C and 0.1 °C is carried out. Three test cases of estimation have been considered in this study: (1) function estimation of space and time varying (temperature-dependent) thermal conductivity (k(T)) with known specific heat (c(T)) (2) function estimation of c(T) with known k(T) and (3) simultaneous function estimation of k(T) and c(T). The Root Mean Square (RMS) error is calculated for evaluating the accuracy of modified CGM. The RMS error for the individual estimation of k(T) and c(T) with θ = 0.1 °C is 0.1527 W/m°C and 4.0933 J/kg°C, respectively. While, when k(T) and c(T) are estimated simultaneously the RMS error with θ = 0.1 °C is 0.3531 W/m°C for k(T) and 5.2252 J/kg°C for c(T).

Thermal and multi-boiling analysis of a rectangular porous fin: A spectral approach

Abstract Fins are commonly utilized to enhance (dissipate) heat in various engineering systems that include heat exchangers. In the present investigation, the impact of multi-boiling and thermo-geometric factors on a convective–radiative rectangular porous fin subjected to the temperature-dependent thermal conductivity of linear and non-linear variations is discussed extensively. The governing equations describing the problem were formulated with the aid of Darcy law. Similarity variables were employed to reduce the models to non-dimensional form. The solution of the governing dimensionless equation is approximated using the RK4 and spectral local linearization methods. Before parametric analysis, the agreement between the two numerical methods was established. Findings reveal that the non-linear variation of thermal conductivity shows better thermal efficiency than the linear variation. An improvement in the multi-boiling heat transfer parameter retards the temperature distribution of the fin. Furthermore, increasing the thermo-geometric parameter will result in a progressive decrease in the temperature of the fin. The results obtained in this work will aid in the design of heat exchangers and other heat transfer equipments.

Particle swarm optimization based numerical study for pressure, flow, and heat transfer over a rotating disk with temperature dependent nanofluid properties

In the era of nanotechnology and advanced manufacturing, many industrial applications involve the flow control over the rotating disk. Rotating machineries, computer storage devices, dynamic filtration processes, gas turbine engines, bio inspired electro-catalysis processes are a few of them. Considering the wide applications of flow over rotating permeable disks, this paper presents the investigation of flow, temperature and pressure characteristics of water-based titanium oxide nanofluid with temperature dependent properties. The quadratic Boussinesq approximation is considered to incorporate the density variations due to temperature change. The numerical computation is carried out using metaheuristic based hybrid shooting technique. Temperature dependent dynamic viscosity and thermal conductivity models for nanofluid are considered and the numerical results for velocity components, pressure and temperature distributions are investigated. The investigation unveiled reduction in skin friction and heat transfer rate with increasing value of quadratic convection parameter. The suction parameter is found to be very significant in terms of increasing heat transfer rates. An 80% increase in local Nusselt number is observed for a small change in suction parameter from −1 to −1.5.

Low Temperature Thermal Properties of Nanodiamond Ceramics

The temperature dependence of thermal conductivity and specific heat for detonated nanodiamond ceramics is investigated on specially designed experimental setups, implementing the uniaxial stationary heat flow method and the thermal relaxation method, respectively. Additionally, complementary studies with a commercial setup (Physical Property Measurement System from Quantum Design operating either in Thermal Transport or Heat Capacity Option) were performed. Two types of samples are under consideration. Both ceramics were sintered at high pressures (6–7 GPa) for 11–25 s but at different sintering temperatures, namely 1000 °C and 1600 °C. The effect of changing the sintering conditions on thermal transport is examined. In thermal conductivity κ(T), it provides an improvement up to a factor of 3 of heat flow at room temperature. The temperature dependence of κ(T) exhibits a typical polycrystalline character due to hindered thermal transport stemming from the microstructure of ceramic material but with values around 1–2 W/mK. At the lowest temperatures, the thermal conductivity is very low and increases only slightly faster than linear with temperature, proving the significant contribution of the scattering due to multiple grain boundaries. The specific heat data did not show a substantial difference between detonated nanodiamond ceramics obtained at different temperatures unlike for κ(T) results. For both samples, an unexpected upturn at the lowest temperatures is observed—most likely reminiscent of a low-T Schottky anomaly. A linear contribution to the specific heat is also present, with a value one order of magnitude higher than in canonical glasses. The determined Debye temperature is 482 (±6) K. The results are supported by phonon mean free path calculations.

Impact of electron-phonon interactions on phonon transport in diamond and c-BN

Diamond and cubic polymorph of boron nitride (c-BN) are two promising next-generation ultrawide bandgap semiconductor materials owning superior thermal properties. Although lattice vibration is the dominant mechanism of heat conduction in semiconductors, electron-phonon interactions exist and may affect phonon transport in doped semiconductors; yet such effects in wide bandgap materials have not received much attention. In this study, we explore the effects of electron-phonon interactions on the lattice thermal conductivity and phonon transport in electron-doped Si, diamond, and c-BN under various electron concentrations and in a wide temperature range from 300 K to 900 K based on the first-principles calculation. It is found that the electron-phonon interactions will bring down the thermal conductivity of doped materials, and the depletion impact increases as the electron concentration increases but decreases as the temperature increases. This depression effect in ultrawide bandgap diamond and c-BN is apparent, though it is not as severe as in Si. At room temperature with a high electron concentration of 10 21 cm −3 , the reduction of thermal conductivity reaches 36 % in Si, and 17.4 % and 16.1 % in diamond and c-BN, respectively. • Thermal effect of electron-phonon interactions in doped c-BN and diamond is revealed. • Temperature and electron concentration dependent lattice thermal conductivity is quantified. • Thermal depletions exist in doped c-BN and diamond, but not as severe as in doped Si. • Depletion lessens as temperature rises, but increases with increasing electron concentration. • Ultrawide bandgap materials have great potentials in high-power high-temperature electronics.

Unsteady axisymmetric flow of nanofluid on nonlinearly expanding surface with variable fluid properties

The physical phenomena of nanofluid at high temperature motivate us to analyze problems with temperature-reliant fluid properties, like viscosity and thermal conductivity. Since in glass blowing, viscosity and thermal conductivity of the fluid may gets affected in such high temperature. This communication deals with the unsteady flow of nanofluid generated by nonlinear expansion of the surface. Temperature-dependent fluid viscosity and thermal conductivity are considered in the investigation of the problem. The flow of nanofluid is modeled using famous the Buongiorno's two-phase model, which includes the simultaneous effect of Brownian motion and thermophoresis diffusion. Appropriate transformations are adopted to obtain the ODEs from governing PDEs. Then MATLAB ‘bvp4c’ computation is used to solve the problem and to get a clear insight of the influences of various parameters. Graphical comparisons are made to check the accuracy of used numerical method. The study explores that heat transfer rate significantly enhances by the index of nonlinearity, variable viscosity and thermal conductivity parameters. Unsteadiness of the flow can be used as a controlling parameter to reduce the surface drag, heat and nano-mass transfer rate. Variable viscosity parameter leads to enhance the velocity near the surface and reducing the concentration of the nanoparticles. The thermal and concentration boundary layer thickens with thermal conductivity parameters. Nanofluid temperature and concentration of nanoparticles decay with nonlinear expanding index.

Graded Longitudinal Fins Having Spatially Varying Temperature-Dependent Thermophysical Properties

This paper reports transient responses of graded longitudinal fins subject to step change in base temperature and base heat flux wherein the graded fin materials are theorized to have spatial- and temperature-dependent thermal conductivity. Microstructure variations in graded materials (GMs) are addressed by axially varying the thermal conductivity; because GMs are potentially high-temperature application materials, consequently, thermal conductivity and heat generation are, respectively, assumed as polynomial and linear functions of temperature. Additionally, most of the applicable pragmatic fluid regimes are accounted for using the power law convection coefficient. The numerical solution of a typical nonlinear governing differential equation is obtained by using a particle tracking-based method called the lattice Boltzmann method (LBM). The LBM is a mesoscopic-based simulation method centered around the principles of kinetic theory and statistical mechanics. The LBM formulation accompanied with the in-house MATLAB code of the aforesaid problem with varying parameters is reported; also, it is validated with a previously available solution. The foregoing analysis is carried out to enhance the performance of a fin by using the superior thermomechanical property of graded materials. Furthermore, the inclusion of temperature-dependent thermophysical properties and heat generation will provide more accurate design data. The reported graph reveals that, even though a linear GM fin tip possesses thermal conductivity that is 25% less in magnitude in comparison to the Type-II homogeneous material (HM-2), the GM fin always yields a higher fin tip temperature because of grading. In addition, the tip temperature deficits between GMs and HM-2 proportionally increase from 0.4 to 2.1% for values of increasing from 0.1 to 2.0, respectively, for step changes in temperature; whereas in the case of the step change base flux, the deficits increase from 8.72 to 12.1% for values of decreasing from 3.0 to 1.0, respectively.

Effect of h-BN addition on thermo-physical properties and phonon mechanisms of C/C-BN composites

C/C-BN composites containing different contents of h-BN particles were prepared by chemical vapor infiltration (CVI), presenting different microstructures and pyrolytic carbon (PyC) textures. The effects of different microstructures and PyC textures on the thermo-physical properties and their phonon mechanisms at 30–900 °C were investigated. The temperature dependence of heat capacity follows Debye's phonon theory, especially in the low-temperature section (30–300 °C) and the temperature dependence of thermal conductivity is determined by heat capacity and mean free length of phonon. Due to the higher texture of h-BN and regenerative laminar PyC (ReL-PyC), h-BN addition causes higher Debye temperature (ΘD) and high sensitivity of thermal conductivity to temperature. Besides, h-BN addition significantly changes the microstructure of composites such as pore structure, PyC morphology, crack distribution and fiber/PyC interface bonding state, causing the transformation of thermal conductivity from anisotropy to isotropy. Finally, based on the different microstructures of composites, the microstructure model and thermal resistance formulas of composites were established and coincident with the experimental results.

Flow characteristics of non-Newtonian hybrid nanofluid under shear rate and temperature-dependent viscosity and thermal conductivity

Background and purpose: Thermal conductivity and viscosity are significant properties that determine the characteristics of heat and mass transfer. These properties of a hybrid nanofluid are a strong function of the type of nanoparticles, concentration, base fluid, and temperature. By considering these facts, the models of properties are developed for different ranges of temperatures and solid concentrations and further used in the current fluid flow problem. Design of model: A homogenous hybrid nanofluid is considered and synthesized by dispersing hybrid nanomaterial and with an equal ratio in the solution of ethylene glycol and water. The mathematical model of this hybrid nanofluid is designed through developed properties and modified non-Newtonian power-law models. Findings: The simplified equations of the problem are solved by a numerical method. The results are obtained as velocity and temperature profiles. The velocity profile is decreased and increased by increasing solid concentration and operating temperature, respectively. On the other hand, the temperature profile is increased with the variation of both parameters. Originality: The model of the physical problem is developed through modified thermophysical properties that are functions of nanoparticle concentration and operating temperature. This type of model is not used before in heat and mass flow problems.

Convective Heat Transfer in Magneto-Hydrodynamic Carreau Fluid with Temperature Dependent Viscosity and Thermal Conductivity.

This study is aimed to explore the magneto-hydrodynamic Carreau fluid flow over a stretching/shrinking surface with a convectively heated boundary. Temperature-dependent variable thermophysical properties are utilized to formulate the problem. The flow governing equations are obtained with boundary layer approximation and constitutive relation of the Carreau fluid. The shooting method is utilized to obtain graphical and numeric outcomes. Additionally, initial guesses are generated with the help of Newton's method. The effect of Weissenberg number, Magnetization, stretching ratio, Prandtl number, suction/blowing parameter, and Lewis number is obtained on velocity, temperature and species continuity profile and analyzed. Shear stress rates and Nusselt number outcomes under body forces influences are present in tabulated data and discussed. It is observed that in absence of magnetization force, B = 0 and strong mass suction 5≤S≤7.5 effect high rates of Nusselt number is obtained. It is concluded that under the influence of power law index and non-linearity parameter maximum heat transfer and reduced shear stress rates are obtained.

Anomalous thermal response of bulk diamond to uniaxial (100) strain: A first-principles prediction

Diamond, a material that exhibits ultrahigh thermal conductivity with a sensitive thermal response to stress, is an ideal heat-sink material in the embedded cooling paradigm. This study uses first-principles calculations with the phonon Boltzmann transport equation to predict the variation rules of the thermal conductivity of diamond along the $\ensuremath{\langle}100\ensuremath{\rangle}$ crystal direction under strains at three orders of magnitude: 0.1%, 1%, and 10.5%. Density functional theory is used to predict the stress--strain dependence of diamond and the temperature-dependent thermal conductivity of unstrained diamond. The predictions are in good agreement with the experimental results. The calculated uniaxial strain--thermal conductivity dependence results reveal that the thermal conductivity of diamond abnormally increases by approximately 15% under small-scale uniaxial strain because of the weakened anharmonic interatomic force constants. Under large-scale strain, the thermal conductivity considerably decreases because of reduced phonon group velocities and increased numbers of phonon scattering channels. The findings in this study will guide analyses of the dependence of thermal conductivity on strain in other diamondlike structures, such as Group IV element-based materials. The abnormal thermal response at small strain is expected to lead to the realization of an artificial thermal conduction channel.

Heat transfer performance of temperature-dependent Xue and Yamada–Ota hybrid nanofluid flow models past a curved stretching sheet with generalized Fourier law

In this exploration, temperature-dependent Yamada–Ota and Xue hybrid nanoliquid models are investigated over a curved stretchable surface embedded in an absorbent media. Hybrid nanofluids are formed by the combination of single and multi-walled carbon nanotubes (CNTs) as nanoparticles with engine oil as base fluid. The goal of this study is to interpret how the modified Fourier law combined with temperature-dependent thermal conductivity, Newtonian heating and variable heat source/sink enhances thermal performance. A mathematical formulation of the problem is illustrated in the curvilinear coordinates. Highly nonlinear dimensionless ODEs are solved numerically by engaging the bvp4c approach. The impression of the key parameters is illustrated graphically. Drag force coefficient and Nusselt number are highlighted through tables. It is comprehended that the fluid velocity decays on augmenting the velocity slip parameter while elevates on amplifying the curvature parameter. Furthermore, an enhancement in the temperature field is noted for the conjugate parameter. A significant correlation with the existing outcomes is perceived when a comparison with the existing literature is made.

Time-dependent finite-difference model for transient and steady-state analysis of thermoelectric bulk materials

A mathematical model of coupled thermoelectricity is presented to investigate the transient and steady-state behaviour of thermoelectric bulk material. Governing partial differential equations (PDEs) for the coupled thermal and electrical behaviour of the thermoelectric model are discretised using the explicit finite-difference method. Differencing schemes like Upwind and Lax–Wendroff methods are employed to obtain solutions for the first-order hyperbolic PDEs, whereas FTCS (Forward Time, Centred Space) scheme is employed to solve second-order parabolic PDEs. Courant-Friedrichs-Lewy and Von Neumann stability analyses are done to ensure the stability and convergence of the model. The model considers the temperature dependency of thermal conductivity, electrical conductivity, and Seebeck coefficient of the P/N materials separately. and accounts for the Seebeck, Peltier, and Joule-Thomson effects in thermoelectric materials. The new model is practically useful to predict the transient and steady-state behaviours of a thermoelectric device with multiple P-N elements. The results of the presented finite-difference model are proven to agree well with experimental values as well as 3D simulations with ANSYS®.

Convective radiative moving fin with temperature-dependent thermal conductivity, internal heat generation and heat transfer coefficient

Convective radiative moving fin with temperature-dependent thermal conductivity, internal heat generation and heat transfer coefficient

Prediction of Thermal Distribution in an Internally Heated Radiative-Convective Moving Porous Fin with variable Thermal Conductivity using Homotopy Perturbation Method

Thermal distribution of a rectangular moving convective-radiative porous fin with temperature-dependent thermal conductivity and internal heat generation is analyzed in this work homotopy perturbation method. With the aid of the analytical solutions, the impacts of the model parameters on the thermal behaviour of the fin are investigated. The parametric analysis reveals that increase in porosity and convective parameters, the rate of heat transfer from the fin increases and consequently improves the efficiency of the fin. The values of the temperature distribution in the fin increase as the Peclet number increases. However, as thermal conductivity and internal heat generation increase, the rate of heat transfer from the fin decreases. Therefore, the operational parameters of the fin must be carefully selected to ensure that the fin retains its primary purpose of removing heat from the primary surface.

Analysis of Reciprocal Thermal Conductivity on Free Convection Flow along a Wavy Vertical Surface

The effects of thermal conductivity which depend on temperature are conversely proportional with the linear function of temperature on free convective flow where the fluid is viscous and incompressible along a heated uniform and the vertical wavy surface has been examined in this study. The boundary layer equations with the associated boundary conditions that govern the flow are converted into a nondimensional form by using an appropriate transformation. In the domain of a vertical plate that is flat, the resulting method of nonlinear PDEs is mapped and then worked out numerically by applying the implicit central finite difference technique with Newton’s quasilinearization method, and the block Thomas algorithm is well known as the Keller-box method. The outputs are obtained in the terms of the heat transferring rate, the frictional coefficient of skin, the isotherms, and streamlines. The outcomes showed that the local heat transferring rate, the local skin friction coefficient, the temperature, and the velocity all are decreasing, and both the thermal layer of boundary and velocity become narrower with the rising values of reciprocal variation of temperature-dependent thermal conductivity. On the other hand, the friction coefficient of skin, the velocity, and the temperature decrease where the friction coefficient of skin and velocity decrease by 43% and 64%, respectively, but the heat transfer rate increases by 61% approximately, and both the boundary layer thermal and velocity become thinner when the Prandtl number increases.

Piloted ignition of vertical polymethyl methacrylate (PMMA) exposed to power-law increasing radiation

• Temperature-dependent thermodynamics is determined by inverse modelling. • Top ignitor shortens ignition time compared to center ignitor. • Volatile concentration at top ignitor is 2.5 – 3.5 times of that at center ignitor. • Thermal boundary layer remains invariant at ignition time with changing heat flux. • Ignition criteria of center ignitor are larger than those of top ignitor. Piloted ignition of vertically mounted solid induced by time-dependent radiation, which is frequently encountered in practical scenarios, is barely examined in existing studies. This contribution experimentally addresses piloted ignition of vertically mounted polymethyl methacrylate (PMMA) heated by five power-law increasing heat fluxes. Susceptibility feature of ignition to ignitor position was examined by selecting two ignitor locations (top and center). A condensed phase analytical model and a solid-gas numerical solver were established to analyze experimental results. Temperature-dependent thermal conductivity and specific heat of PMMA were determined by inversely modelling measured surface temperature and mass loss rate at an intermediate radiation level. Meanwhile, simulated evolutions of surface temperature, mass loss rate, pyrolyzate concentration, streamlines as well as thermal, species and velocity boundary layers were demonstrated and discussed. The results show that top ignitor shortens ignition time due to buoyancy-induced accumulation effect of volatiles, which consequently leads to lower critical temperature and critical mass loss rate. The numerical model successfully predicts measured experimental results, but the analytical model overestimates surface temperatures and underpredicts ignition times owing to the neglect of pyrolysis. At ignition time, the thermal boundary layer remains approximately unchanged with varying heat fluxes. Measured critical temperatures for center and top ignitors are 651 K and 641 K, while the corresponding critical mass loss rates are 10 g m −2 s −1 and 4.5 g m −2 s −1 , respectively.