Effects Of Temperature Dependent Thermal Conductivity Research Articles

Numerical analysis of the Maxwell-Cattaneo-Vernotte nonlinear model

In the literature, one can find numerous modifications of Fourier’s law, the first of which is the Maxwell–Cattaneo–Vernotte heat equation. Although this model has been known for decades and successfully used to model low-temperature damped heat wave propagation, its nonlinear properties are rarely investigated. This paper aims to present the functional relationship between the transport coefficients and the consequences of their temperature dependence, particularly focusing on thermal conductivity. These are the consequences of the second law of thermodynamics. Furthermore, we introduce a particular implicit numerical scheme in order to solve such nonlinear heat equations reliably, free from artificial numerical errors. We investigate the scheme’s stability, dissipation, and dispersion attributes. We demonstrate the effect of temperature-dependent thermal conductivity on two different initial-boundary value problems, including time-dependent boundaries and heterogeneous initial conditions, for which we discuss the nontrivial constraints following irreversible thermodynamics.

Temperature-dependent thermal conductivity and fuel performance of UN-UO2 and UN-X-UO2 (X=Mo, W) composite nuclear fuels by finite element modeling

The temperature-dependent effective thermal conductivity of UN-X-UO2 (X = Mo, W) nuclear fuel composite was estimated. Following the experimental design, the thermal conductivity was calculated using Finite Element Modeling (FEM), and compared with analytical models for 10%, 30%, 50%, and 70% (in mass) uncoated/coated UN microspheres in a UO2 matrix. The FEM results show an increase in the fuel thermal conductivity as the mass fraction of the UN microspheres increases from 1.2 to 4.6 times the UO2 reference at 2,000 K. The results from analytical models agree with the thermal conductivity estimated by FEM. The results also show that Mo and W coatings have similar thermal behaviors, and the coating thickness influences the thermal conductivity of the composite. At higher weight fractions, the thermal conductivity of the fuel composite at room temperature is substantially influenced by the high thermal conductivity coatings approaching that of UN. Thereafter, the thermal conductivity from FEM was used in the fuel thermal performance evaluation during LWR normal operation to calculate the maximum centerline temperature. The results show a significant decrease in the fuel maximum centerline temperature ranging from −94 K for 10% UN to −414 K for 70% (in mass) UN compared to UO2 under the same operating conditions.

Experimental investigation on temperature-dependent effective thermal conductivity of ceramic fiber felt

This paper presents a method to invert the effective thermal conductivity of ceramic fiber felt under high temperatures using experimentally measured specific heat capacity, density, and transient temperature data. The method combines the solution of the heat transfer equation with an inversion method based on real-valued genetic algorithm (GA) optimization, and 11 target parameters can be simultaneously inverted with one experimental dataset. The effective thermal conductivities of ceramic fiber felt were obtained by inversion under ambient pressures of 2 Pa and 100 kPa, compression ratios of 0.8–1.0, and temperature ranges of 295∼1273 K. The results indicates that the effective thermal conductivities of ceramic fiber felt derived from the inversion method are in concurrence with the outcomes of the steady state method. The effective thermal conductivities of the ceramic fiber felt range from 0.069 to 0.321 W m−1 K−1. It is observed that the effective thermal conductivity increases with higher temperature, and decreases with growing compression ratio. The impact of ambient pressure on effective thermal conductivity is linked to the level of compression.

Determination of the temperature-dependent thermophysical properties of polymeric foams using numerical inverse analysis

Polymeric foams used as core materials of sandwich panels undergo severe degradation under high temperatures, making the experimental measurement of their thermophysical properties (thermal conductivity and specific heat) possible only up to 150 °C–200 °C. However, their knowledge at higher temperatures is needed to fully understand their behaviour and to develop advanced numerical models for analysis and design of sandwich structures subjected to fire. This work presents a numerical inverse analysis procedure to determine such effective properties for rigid polyurethane (PUR) and polyethylene terephthalate (PET) foams. Firstly, the campaign used to obtain experimental results is presented and then the proposed numerical inverse analysis procedure is described. This is based on the minimization of a least squares functional and a nonlinear finite element thermal analysis. Next, the numerical results and the effective thermophysical properties obtained for both foams are presented and discussed, and are validated by extending their use to the simulation of the thermal response of a sandwich panel subjected to a standard fire. It is concluded that the numerical procedure is capable of estimating the temperature-dependent effective thermal conductivity and specific heat of PUR and PET foams for temperatures well above those corresponding to their decomposition.

Effect of temperature-dependent rock thermal conductivity and specific heat capacity on heat recovery in an enhanced geothermal system

The modeling of heat recovery from an enhanced geothermal system (EGS) requires rock thermal parameters as inputs such as thermal conductivity and specific heat capacity. These parameters may encounter significant variations due to the reduction of rock temperature during heat recovery. In the present study, we investigate the effect of temperature-dependent thermal conductivity and specific heat capacity on the thermal performance of EGS reservoirs. Equations describing the relationships between thermal conductivity/specific heat capacity and temperature from previous experimental studies were incorporated in a field-scale single-fracture EGS model. The modeling results indicate that the increase of thermal conductivity caused by temperature reduction accelerates thermal conduction from rock formations to fracture fluid, and thus improves thermal performance. The decrease of specific heat capacity due to temperature reduction, on the contrary, impairs the thermal performance but the impact is smaller than that of the increase of thermal conductivity. Due to the opposite effects of thermal conductivity increase and specific heat capacity decrease, the overall effect of temperature-dependent thermal parameters is relatively small. Assuming constant thermal parameters measured at room temperature appears to be able to provide acceptable predictions of EGS thermal performance.

A finite thin film flow of pseudo-plastic MHD hybrid nanofluid with heat generation and variable thermal conductivity

The primary objective of this article is to get an overview of electrically conductive pseudo-plastic hybrid-nanofluid in a finite thin film over an unsteady, nonlinearly stretching surface. Viscous dissipation, internal heat generation, magnetohydrodynamics, and the temperature-dependent thermal conductivity effects are examined while examining the flow velocity and temperature of the fluid. Different types of hybrid-nanoparticles are assessed, which are the amalgam of , , , and with Carboxy-methyl Cellulose (CMC)-water as base fluid. Further, modified heat conduction of Fourier’s law concerning the power-law model is utilized instead of a classical model. The resolved partial differential equations (PDEs) are transformed into a couple of non-linear ordinary differential equations (ODEs) after using specified transformations. Runge–Kutta technique of order four coupled with shooting method is applied to acquire the numerical solutions. The effects on velocity and temperature profiles due to the behavior of power-law-index, Hartmann number, Prandtl number, and unsteadiness parameter are analyzed and graphically presented. It is observed that and hybrid nanofluid has the most influential impacts on the Nusselt number as compared to the other three combinations. The temperature gets a decline with the increasing power-law index.

Numerical modeling of temperature-dependent effective thermal conductivity of two-phase porous system using square and circular geometries

Two-phase porous materials are extensively employed in industries and their thermal characteristics decide on the overall efficiency of the system. Several dependent parameters such as geometry, its structure, heat transfer mechanism, and contact ratio, strongly influence the effective thermal conductivity (ETC) of the two-phase system. There are various literatures on analytical and experimental prediction of ETC of two-phase porous materials such as packed beds, foams, and sponges. However, numerical studies are limited with the consideration of few influential parameters. This present study has attempted to investigate the thermal behavior of two-phase porous materials numerically using square and circular geometries with the consideration of all primary and secondary criterions at different pressures and elevated temperatures. The numerical results are correlated against the experimental data of different porous insulation materials and packed bed materials. Further, the square and circular models are assessed for their stability in predicting the ETC at higher temperatures. Even at elevated temperatures, the present models hold better accuracy and consistency in prediction.

Effects of temperature-dependent thermal conductivity with variable Biot number on a fully developedflow in a porous channel using LTNE (local thermal nonequilibrium) model

The thermal conductivity of the porous materials is dependent on the temperature in a range of applications, including nuclear reactors and fossil fuel sources. The LTNE (local thermal nonequilibrium) model is widely used to study the thermal interactions between solid and fluid phases inside the porous media. The majority of the prior LTNE models assumed the constant thermal conductivities of both the fluid and solid phases, but in actual practice, the thermal conductivities depend on the temperature variations. In the current study, the effective thermal conductivities of the fluid and solid phases in the porous channel are considered as the functions of the respective temperatures by implementing the LTNE model. The Biot number is assumed to vary linearly, quadratically and sinusoidally along with the channel height. The thermal conductivity variation parameter [Formula: see text], porosity [Formula: see text] the ratio of fluid and solid phase thermal conductivities [Formula: see text] and heat generation parameter [Formula: see text] are considered as the main operating parameters. A system of ordinary differential equations has been derived and solved numerically under the above-mentioned conditions which is the generalization of the constant thermal conductivities of both the phases. The present results are validated with the already published results for the constant thermal conductivity and variable Biot number with the LTNE model. The obtained results show that the maximum heat transfer between the two phases is observed by taking [Formula: see text] as the linear increasing function of [Formula: see text] i.e., [Formula: see text] and correspondingly, it provides the highest values of Nusselt number. The Nusselt number increases with the decrement in thermal conductivity variation parameter [Formula: see text], heat generation parameter [Formula: see text] and ratio of fluid to solid phase conductivities [Formula: see text] A complex relationship has been observed between the porosity and the Nusselt number.

Estimation of Temperature-Dependent Effective Thermal Conductivity and Specific Heat of Thermally Bonded High Bulk Nonwoven Exposed to Sub-Zero Temperature

Abstract In this work, temperature-dependent effective thermal conductivity and specific heat of high bulk thermally bonded polyester nonwovens (composed of four fibers, namely, 1.4 denier solid, 3 denier hollow, 6 denier hollow, and 15 denier hollow individually) are estimated for the sub-zero condition where the temperature drops up to 213 K (−60 °C). Experiments are performed in a custom-made climatic chamber for measurement of the transient sensor temperature data placed at a different location inside the fiber web. The test chamber can achieve and maintain the temperature in the range of 213–310 K. The properties are estimated using theoretical relations available in the literature. Heat transfer through the fiber web is assumed to be a one-dimensional coupled conduction-radiation problem. Effective thermal conductivity is calculated at a different ambient temperature ranging from 213 K to 273 K, and specific heat is calculated at an ambient temperature of 213 K. Experimental temperature profiles compare well with numerical temperature profiles and thus justify the numerical methodology adopted in this work. It can be seen from the results that effective thermal conductivity and specific heat decreases with a decrease in temperature which is favorable in providing more insulation in an extremely cold climate.

Thermophysical Properties of a Subsoil Drill Core for Geothermal Energy Applications

Urban heat islands (UHI) occur especially in inner-city areas due to small green areas, an excess of high solar heat, and low air circulation. One solution is the “harvesting” of excess solar urban heat through shallow absorber ducts, which are then used in borehole heat exchanger (BHE) fields for later use for heat or cold storage. Knowing the thermophysical properties of the subsurface as accurately as possible is of great importance in the design and configuring of a borehole heat exchanger field as a thermal energy storage system. In this study, a subsoil drill core from a BHE, with a depth of 80 m, was used to determine temperature dependent effective thermal conductivity based on the heat flow meter method, the specific heat capacity based on differential scanning calorimetry, and thermal expansion based on dilatometry in moist and dry states. The results have shown that the actual moisture content of the subsoil sample has a strong impact on the thermal conductivity, as well as on the heat capacity. Thermal expansion measurements have shown the influence of the drying process on the shrinkage of drill core samples and the low thermal expansion of the dry subsoil itself.

Nonlinear heat transfer analysis of spines using MLPG method

In the current article, an analysis of heat transfer in the spine of different profiles is carried out. A nonlinear differential equation that includes the effect of temperature-dependent thermal conductivity, variable heat transfer coefficient, and surface radiation is solved using a predictor-corrector scheme and the meshless local Petrov-Galerkin (MLPG) method. The moving least square (MLS) method is employed for the approximation of unknown function and the penalty parameter method is used to impose essential boundary conditions. Temperature variation along the length of the spine and rate of heat transfer in steady-state, under convective and convective-radiative environment has been obtained and explained. Performance of the spine under the above conditions is evaluated. Further, the study is extended to calculate volume adjusted performance which presents a comparative thermal performance of different profiles.

Review of Temperature Dependence of Thermal Properties in Steam-Assisted Gravity-Drainage Process: Mathematical Formulation

Summary Steam-assisted gravity drainage (SAGD) is the preferred thermal-recovery method used to produce bitumen from Athabasca deposits in Alberta, Canada. In SAGD, heat energy is transferred from steam to the reservoir, which reduces bitumen viscosity, and enables the bitumen to flow toward the horizontal production well under gravity forces. Conduction is the main heat-transfer mechanism at the edge of the steam chamber. It is controlled by reservoir thermal conductivity and heat capacity. Both factors are temperature dependent and neglecting such dependency can cause errors that should be evaluated in one study. In this study an analytical SAGD model is discussed that includes temperature dependency in the prediction of the temperature evolution ahead of the interface, oil-production rates, and steam/oil ratio (SOR). Such a model is used to evaluate the importance of temperature dependency in different operational conditions. The results of the presented analytical model reveal that the oil rate can be calculated ignoring temperature dependency, suggesting thermal conductivity and specific heat calculated at a dimensionless temperature ratio between 0.75 to 0.8 and between 0.37 to 0.41, respectively. For both laterally expanding and angularly expanding reservoirs, the SOR is independent of the thermal conductivity. Unlike the effect of temperature-dependent thermal conductivity on SOR, temperature dependency on heat capacity significantly affects SOR. Such errors are larger for higher injection pressures (hence, higher steam-chamber temperatures). This study provides a modified Butler analytical SAGD model that combines independently calculated modification factors for thermal conductivity and heat capacity into a modification factor (CT). Interestingly, the modification factor is identical with the TANDRAIN factor that is suggested by Butler to reduce the overestimated rates from the original theory. Such a finding is important because it addresses modifications such as in TANDRAIN and LINDRAIN estimations that are a result of ignoring the temperature dependency in analytical formulation.

Effect of Thermophysical Property Variation on Entropy Generation towards Micro-Scale

AbstractIn this work, the effect of temperature-dependent thermal conductivity (k(T)) and viscosity (\mu (T)) variation on entropy generation in circular channels with an approach from macro- to micro-scale is numerically investigated. Thermally as well as hydrodynamically fully developed flow of water through the fixed length channels with constant total heat flow rate and total mass flow rate is considered. The effects of k(T) variation and \mu (T) variation on entropy generation are analyzed individually as well as collectively. It is observed that in the case of Constant Property Solutions (CPS) {S_{\mathit{gen},\mathit{tot}}} is maximum at the macro-level; however, in the case of combined k(T) and \mu (T) variations it is maximum at the micro-level. The Bejan number (\mathit{Be}) and irreversibility distribution ratio (φ) are also calculated for asserting the dominance of frictional irreversibility and conduction heat transfer irreversibility. Additionally, the optimum diameter ({D^{\ast }}) corresponding to the optimum number of channels is calculated at minimum total entropy generation. It is observed that {D^{\ast }} is minimum for k(T) variation followed by CPS, \mu (T) variation, and combined k(T) and \mu (T) variations.

Thermal rectification mechanism of one-dimensional composite structure with interface thermal contact resistance

Thermal rectification refers to the phenomenon that heat fluxes or equivalent thermal conductivities are different under the same temperature difference when temperature gradient directions are different. The nature of the thermal rectification is that the structure has different effective thermal conductivities in different directions. Most of previous studies focused on thermal rectification of temperature-dependent thermal conductivity materials or variable cross section area structure, and the effect of thermal contact resistance at the interface was investigated very rarely. In the present paper we present the analytical and finite element numerical solution of temperature field and thermal rectification ratios of a composite structure with variable cross section area and thermal conductivity under different interface thermal contact resistances. The prescribed temperature boundary condition is introduced by penalty method, and the temperature jump condition at the interface is implemented by the definition of thermal contact resistance directly. The nonlinear heat conduction problem caused by temperature-dependent thermal conductivity and interface thermal contact resistance is then solved with a direct iteration scheme. Comparisons between experimental results and the present theoretical and numerical results show the feasibility of the proposed model. Then parameter investigations are also conducted to reveal the effect of some key geometric and material parameters. Numerical results show that thermal contact resistance plays an important role in the temperature field and thermal rectification ratio of the two-segment thermal rectifier. With the increase of the length ratio, thermal ratification ratio increases first and decreases then, and the optimal length ratio varies with both thermal contact resistance and cross-section radius change rate of the two segments. In general, the existence of thermal contact resistance can increase the total thermal resistance of the rectifier and magnify the distinction of the heat flux in forward and reverse cases. However, if the thermal contact resistance is too large, this distinction will decrease and correspondingly the thermal rectification ratio becomes low. With the increase of the boundary temperature difference, thermal rectification ratio increases due to the effect of temperature-dependent thermal conductivity. In the present study, we propose a theoretical and numerical approach to designing and optimizing the length ratio, cross-section radius change rate, thermal conductivity, boundary temperature difference and interface thermal contact resistance to obtain the maximal thermal rectification ratio of a bi-segment thermal rectifier, as well as the manipulation of thermal flux in engineering applications.

Effect of thermal radiation on MHD Casson fluid flow over an exponentially stretching curved sheet

This paper presents the flow and heat transfer characteristics of an electrically conducting Casson fluid past an exponentially stretching curved surface with convective boundary condition. The fluid motion is assumed to be laminar and time dependent. The effects of temperature-dependent thermal conductivity, Joule heating, thermal radiation, and variable heat source/sink are deemed. Suitable transformations are considered to transform the governing partial differential equations as ordinary ones and then solved by the numerical procedures like shooting and Runge–Kutta method. Graphs are outlined to describe the influence of various dimensionless parameters on the fields of velocity and temperature and observe that there is an enhancement in the field of temperature with the radiation, temperature-dependent thermal conductivity, and irregular heat parameters. Also, the Casson parameter has a tendency to suppress the distribution of momentum but an inverse development is noticed for the curvature parameter. Attained outcomes are also compared with the existing literature in the limiting case, and good agreement is perceived.

Effective conductivity of porous ceramics in a radiative environment

The knowledge of the effective thermal conductivity, taking into account conduction and radiation, is crucial for the accurate prediction of the thermal behavior of porous foams, especially in an environment where radiation is dominating. We present a combined experimental-numerical method for the quantification of the temperature-dependent effective thermal conductivity of porous ceramics. The experiments include transient and spatially-resolved temperature measurements of ceramic foam samples with porosities between 75% and 92%, exposed to high radiative fluxes (peak of 1500 kW.m−2). Maximum surface temperatures of 1900K for high purity alumina samples and of 1500K for alumino-silicate (AS) samples were measured, and nonlinear temperature profiles through the sample along the main temperature gradient direction were measured. A 3D numerical model based on an OpenFOAM toolbox was developed and used to determine the thermal conductivity, using the experimental temperature measurements as input. We quantified the effective thermal conductivities (ETCs) in a temperature range of 288–1473K and showed that the ETC of AS samples can significantly increase in the presence of incoming and internal radiation. Alumina with 2 to 5 times smaller typical pore sizes (80 μm vs 190 μm, 230 μm, and 400 μm) exhibited an ETC dominated by conduction and relatively unaffected by radiation. This work illustrates that the ETC of porous materials exposed to radiative fluxes do not only depend on material properties or morphology but also on the operational conditions.

A molecular dynamics simulation on the static calibration test of a revised thin-film thermopile heat-flux sensor

A revised thin-film thermopile heat-flux sensor with cooper-based heat sink is calibrated at a static calibration system that provides a stable heat flux source in the range of 0.1–10.0 MW/m2. The calibration results show that sensitivity coefficients (SCs) of the revised heat-flux sensor are quadratically dependent on surface temperatures, which is different from the linear SCs of original heat-flux sensors. A molecular dynamics simulation is applied to predict the thermal conductivity (TC) of thin-film thermal resistance layer and the interfacial thermal resistivity at the interface with film thickness and substrate material being considered. With the aid of the molecular dynamics simulation and finite element method, the reason for such a difference is analyzed to be the coupled effect of temperature-dependent thermal conductivity (TC) of thin-film thermal resistance layer and the interfacial thermal impedance at the interface.

Numerical simulation for transient flow of Williamson fluid with multiple slip model in the presence of chemically reacting species

PurposeThe purpose of this paper is to analyze a mathematical model for the time-dependent flow of non-Newtonian Williamson liquid because of a stretching surface. The mathematical formulation of the current model is accomplished from the momentum, energy and concentration balances by assuming a laminar, two-dimensional and incompressible flow subjected to a variable magnetic field. The study further aimed at discovering the possible effects of temperature-dependent thermal conductivity on the heat transfer characteristics.Design/methodology/approachIn addition, a first-order chemical reaction is considered between the fluid and chemically reacting species. The governing transport model for Williamson fluid has been altered to ordinary differential equations via appropriate dimensionless parameters. These basic non-dimensional partially coupled differential equations of fluid motion are solved by an efficient Runge–Kutta–Fehlberg integration scheme along with the Nachtsheim–Swigert shooting technique.FindingsIt is found that the velocity slip parameter has a reducing impact on the skin friction coefficient. Moreover, we noticed that the Hartmann number and variable thermal conductivity parameters show prominent impacts on the velocity and temperature fields. It is also perceived that the fluid temperature shows an increasing trend with uplifting values of variable thermal conductivity.Originality/valueNo such work is yet published in the literature.

Magnetohydrodynamic flow of nano Williamson fluid generated by stretching plate with multiple slips

PurposeThe purpose of this paper is to present an exploration of multiple slips and temperature dependent thermal conductivity effects on the flow of nano Williamson fluid over a slendering stretching plate in the presence of Joule and viscous heating aspects. The effectiveness of nanoparticles is deliberated by considering Brownian moment and thermophoresis slip mechanisms. The effects of magnetism and radiative heat are also deployed.Design/methodology/approachThe governing partial differential equations are non-dimensionalized and reduced to multi-degree ordinary differential equations via suitable similarity variables. The subsequent non-linear problem treated for numerical results. To measure the amount of increase/decrease in skin friction coefficient, Nusselt number and Sherwood number, the slope of linear regression line through the data points are calculated. Statistical approach is implemented to analyze the heat transfer rate.FindingsThe results show that temperature distribution across the flow decreases with thermal conductivity parameter. The maximum friction factor is ascertained at stronger magnetic field.Originality/valueIn the current paper, the magneto-nano Williamson fluid flow inspired by a stretching sheet of variable thickness is examined numerically. The rationale of the present study is to generalize the studies of Mebarek-Oudina and Makinde (2018) and Williamson (1929).

Infinite speed behavior of two-temperature Green–Lindsay thermoelasticity theory under temperature-dependent thermal conductivity

The present work attempts to analyze the effects of temperature-dependent thermal conductivity on thermoelastic interactions in a medium with a spherical cavity under two-temperature Green–Lindsay thermoelasticity theory. An attempt is made to compare the results with the corresponding results under other three thermoelastic models. The thermal conductivity of the material is assumed to be depending affinely on the conductive temperature. It is assumed that the conductive temperature is prescribed at the stress-free boundary of the spherical cavity. Assuming spherical symmetry motion, the resulting thermoelastic system in one space dimension is solved by using the Kirchhoff transformation, Laplace transform technique and expansion in modified Bessel functions. The paper concludes with numerical results on the solution of the problem for specific parameter choices. Various graphs depict the behavior of the conductive and thermodynamic temperature, the displacement and two nonzero components of stress. A detailed analysis of the results is given by showing the effects of the assumed temperature dependence of the material property. The effect of employing the two-temperature model is discussed in detail. We observe an infinite domain of influence under the two-temperature model as compared to the classical Green–Lindsay model, which we hope will be a useful insight.