Effect Of Heat Conduction Research Articles

Analysis on the internal structure of shock wave-front in a two-phase viscous fluid with heat-conduction

Abstract The present study examined the effect of viscosity and heat-conduction on the internal structure of a plane shock wave in a two-phase gas-solid particles medium. The governing fluid flow equations (i.e., Navier-Stokes equations) are used to obtain the exact solutions supplemented with equations of state and nonlinear thermodynamically consistent constitutive relations. Through this model, the thickness of the shock-front is computed, and thereafter, we analyse the role of viscosity, including the effect of dust-laden parameters (e.g., mass fraction of the mixture, specific density ratio, Prandtl numbers, as well as the strength of shock on the thickness of the shock-front. The asymptotic variations in the thickness of the shock-front due to these flow parameters have been discussed and analysed numerically and graphically. The conclusion of the present study is to figure out the role of viscosity and dust-laden parameters on the width of the shock-front in studying the structure of the shock waves.

Thermal performance analysis of a deep coaxial borehole heat exchanger with a horizontal well based on a novel semi-analytical model

This study introduces a novel semi-analytical model for deep coaxial borehole heat exchanger with a horizontal well(H-DBHE), which incorporates the effects of formation stratification and transient heat conduction within the pipe walls. Initially, the model's validity was checked through a comparison with the results derived from the published numerical models. This semi-analytical approach significantly reduces computational time while ensuring calculation accuracy. Subsequently, the study quantitatively examined the influence of the operation parameters, structural characteristics and the thermal capacity within the borehole on the dynamic heat extraction of H-DBHE. The numerical results demonstrate that the thermal capacity within the borehole significantly influences the heat extraction performance during intermittent operations of H-DBHE. Based on this finding, the study further investigated the effects of intermittent operation and heating time on the heat recovery performance of the system. Additionally, the study compared the long-term operational performance and thermal attenuation between H-DBHE and deep coaxial borehole heat exchanger (DBHE) over a ten-year simulation period. This research introduces a novel semi-analytical model for H-DBHE, which is of significant theoretical guidance for accurately predicting the heat extraction performance of H-DBHE and scientifically designing geothermal utilization systems.

Thermo‐Mechanical Study on Auxetic Shape Memory Periodic Open Cellular Structures—Part I: Characterization of Reentrant Geometry and Effective Heat Conductivity

Periodic open cellular structures (POCS) are additively manufactured supports for heterogeneous catalysts in the field of chemical reaction engineering. Constructed from a repeated unit cell, POCS offer excellent heat transport characteristics due to heat conduction in the continuous solid matrix. However, when inserted into tubular reactors, a loose fit between structure and tube wall results. This considerably hinders heat transfer across the wall. The novel POCS concept presented in this work aims at an intensified wall heat transfer by utilizing a reentrant structure design to ensure auxetic behavior. If the POCS is made of shape memory alloy, it can recover its original shape. Combining these two effects with an initial radial oversize, an interference fit with the tube is established. This contribution comprises the geometric description of reentrant POCS and heat conduction simulations for characterization of the effective heat conductivity, yielding scaling correlations dependent on geometric parameters. Moreover, the effective radial heat conductivity of POCS in cylindrical shape is explicitly investigated. The influencing factor identified is the ratio of tube diameter and cell size: while the ratio increases, the effective radial heat conductivity decreases, but remains well above the effective heat conductivity of the unit cell.

Energy conversion and transport in molecular-scale junctions

Molecular-scale junctions (MSJs) have been considered the ideal testbed for probing physical and chemical processes at the molecular scale. Due to nanometric confinement, charge and energy transport in MSJs are governed by quantum mechanically dictated energy profiles, which can be tuned chemically or physically with atomic precision, offering rich possibilities beyond conventional semiconductor devices. While charge transport in MSJs has been extensively studied over the past two decades, understanding energy conversion and transport in MSJs has only become experimentally attainable in recent years. As demonstrated recently, by tuning the quantum interplay between the electrodes, the molecular core, and the contact interfaces, energy processes can be manipulated to achieve desired functionalities, opening new avenues for molecular electronics, energy harvesting, and sensing applications. This Review provides a comprehensive overview and critical analysis of various forms of energy conversion and transport processes in MSJs and their associated applications. We elaborate on energy-related processes mediated by the interaction between the core molecular structure in MSJs and different external stimuli, such as light, heat, electric field, magnetic field, force, and other environmental cues. Key topics covered include photovoltaics, electroluminescence, thermoelectricity, heat conduction, catalysis, spin-mediated phenomena, and vibrational effects. The review concludes with a discussion of existing challenges and future opportunities, aiming to facilitate in-depth future investigation of promising experimental platforms, molecular design principles, control strategies, and new application scenarios.

Thermal management optimization strategy for lithium-ion battery based on phase change material and fractal fin

In order to solve the problem of temperature control of lithium-ion battery (LB) in electric vehicles, a new battery thermal management system (BTMS) based on phase change material (PCM) coupled fractal fin (FF) was proposed. The effects of latent heat, thickness, and thermal conductivity of PCM (paraffin) on the thermal properties of BTMS were investigated. Subsequently, the fin structure was added to the BTMS to improve the heat transfer capacity, and the number of fins, aspect ratio, material and structure morphology were explored. The results show that when the latent heat of PCM is 200 kJ/kg, the thickness is 2 cm, and the thermal conductivity is 0.8 W/(m·K), the temperature of LB is 34.9 K lower than that of LB without the BTMS at 4C. In addition, the BTMS has the best performance when FF-II with a fin count of 5, aspect ratio of 7:1, and material of carbon steel are used. The temperatures of LB are 301.8 K, 303.9 K, 305.4 K, and 307.3 K at 1 to 4C, respectively, and the temperature difference in BTMS can be controlled within 2.5 K. This study provides some guidance for the optimization of BTMS.

A Review on Sludge Drying after High Pressure Filter Pressing

Sludge drying is a key step in municipal sludge treatment. After mechanical dewatering, the water content of sludge is usually between 50% and 70%, which needs further drying. The main drying technologies include thermal drying, solar drying, ultrasonic drying and microwave drying, among which thermal drying technology is the most mature. Research shows that low-temperature drying technology has obvious advantages in reducing the release of harmful substances, energy consumption and cost. In terms of technology application, domestic sludge drying process is mainly divided into direct drying and indirect drying. Direct drying directly evaporates water through high-temperature gas, while indirect drying makes use of heat conduction effect to contact with high-temperature media. At present, indirect drying technology is mainly used in China, such as paddle type, disc type and thin layer drying. In particular, the low-temperature heat pump drying technology excels in terms of safety, footprint and energy consumption, with its ability to operate at lower temperatures, reduce the release of hazardous gases, and achieve environmental and economic benefits in a closed-cycle mode. This technology is suitable for small and medium-sized wastewater treatment plants and shows clear advantages in cases of budgetary constraints.

Self-similar flow behind a shock wave in a gas under the effect of viscosity, heat conduction, and variable ambient density

Self-similar solutions have been investigated to describe the propagation of planar shock waves in a non-ideal gas generated by a piston under viscous stress and heat flux. The equation of state for non-ideal gas incorporates the correction in pressure and volume of the gas. The piston position and ambient density vary exponentially with time. Newton’s law of viscosity is used for the viscous stress and Fourier’s law of heat conduction is taken for heat flux. The viscosity coefficient is taken as constant whereas the thermal conductivity coefficient varies with temperature and density following the power law. The shock jump conditions have been derived for the viscous non-ideal gas using integral form of conservation laws. The shock Reynolds number Re s has been introduced to study the effect of viscosity on shock propagation in non-ideal gas. It is found that similarity solution exists only in an ideal gas under the condition that the ambient density exponent is equal to twice the shock position exponent. This study shows that shock Reynolds number Re s and heat conduction parameter Γ c can be used to control the variation of the flow variables and piston position significantly. The shock strength decreases with increase in the value of shock Reynolds number Re s but is independent of the heat conduction parameter Γ c . The pressure, density, and adiabatic compressibility have significant deviations from high to low viscous flow of ideal gas but the velocity and heat flux undergo negligible change. The results do not support the claim of negligible effect of viscosity in earlier studies and establish the impact of viscosity and heat flux on shock propagation in an ideal gas.

Crack propagation arrest by the Joule heating in micro/nano-sized structures

The Joule heating technique is utilized to arrest the crack propagation so to protect some important structures being further damaged. In this approach there are created compression stresses at the crack tip vicinity due to a specific temperature distribution induced by the electric current. The Joule heating is amulti-physical problem which is applied here to micro/nano-sized structures. The size-effects are considered for description of both the elastic and the thermal fields. The heat conduction can’t be well described by classical Fourier’s law in nano-sized structures. A novel gradient theory is developed in such structures adopting the size effect of heat conduction. Besides, the strain gradients and double stresses are introduced into the constitutive laws. Then, the governing equations are given by partial differential equations with order of derivatives being higher than in classical theory. The principle of virtual work is the base of weak formulation and derivation of the discretized finite element equations for ageneral 2d boundary value problem with cracks. The collocation mixed FEM with large strain gradients is developed for numerical solution, where the C0 continuous approximation is applied independently to displacements and strains and also to temperature and temperature gradients. Kinematic constraints between strains and displacements are satisfied by the collocation method at selected interior points. The collocation mixed FEM is applied to solve 2D crack problems with Joule heating.

Asymptotic solution of electromagnetic heating of skin tissue with lateral heat conduction

We study the temperature evolution in the three-dimensional skin tissue exposed to an electromagnetic beam of millimeter wavelength. The skin absorption coefficient of the beam frequency determines how deep the electromagnetic energy penetrates into the skin tissue, which gives a sub-millimeter penetration depth for a 94 GHz wave. In contrast, in the lateral directions perpendicular to the depth, the beam size is usually much larger than the penetration depth. Based on this separation of length scales, we establish an asymptotic formulation in which each term has separable dependences on the depth coordinate and on the lateral coordinates. We solve it analytically to obtain a two-term asymptotic solution of the temperature distribution in the three-dimensional skin tissue. This closed-form analytical solution provides a practical and accurate way of predicting the temperature. When the beam size is moderately larger than the penetration depth (a ratio of 20), the effect of lateral heat conduction is well captured in the asymptotic solution with maximum error less than 0.0017 in the normalized temperature of magnitude well above 1.

Thermodynamically consistent Cahn–Hilliard–Navier–Stokes equations using the metriplectic dynamics formalism

Cahn–Hilliard–Navier–Stokes (CHNS) systems describe flows with two-phases, e.g., a liquid with bubbles. Obtaining constitutive relations for general dissipative processes for such systems, which are thermodynamically consistent, can be a challenge. We show how the metriplectic 4-bracket formalism (Morrison and Updike, 2024) achieves this in a straightforward, in fact algorithmic, manner. First, from the noncanonical Hamiltonian formulation for the ideal part of a CHNS system we obtain an appropriate Casimir to serve as the entropy in the metriplectic formalism that describes the dissipation (e.g. viscosity, heat conductivity and diffusion effects). General thermodynamics with the concentration variable and its thermodynamics conjugate, the chemical potential, are included. Having expressions for the Hamiltonian (energy), entropy, and Poisson bracket, we describe a procedure for obtaining a metriplectic 4-bracket that describes thermodynamically consistent dissipative effects. The 4-bracket formalism leads naturally to a general CHNS system that allows for anisotropic surface energy effects. This general CHNS system reduces to cases in the literature, to which we can compare.

Effective heat conductivity of composites with stochastic microstructure using asymptotic homogenization

This contribution presents a comprehensive methodology aimed at determining the effective heat conductivity of composites with stochastic microstructure by analyzing micro Computerized Tomography (μCT) images. We revisit asymptotic homogenization for multiscale analysis of transient heat problems and derive systems of partial differential equations (PDEs) governing the homogenized problem and two new cell problems, which are solved numerically using the Finite Element (FE) method to identify the effective thermal conductivity. The methodology does not require enforcing Dirichlet Boundary Conditions (BCs) on the interfaces, making it well-suited for analyzing stochastic microstructures with irregular interfaces. Following image preprocessing and segmentation to identify the pores (void) and the solid matrix, the workflow transforms the segmented image into a periodic computational domain suitable for the upscaling procedure to identify the effective thermal conductivity tensor. We employ the open-source computing platform FEniCSx, along with its Multi-Point Constraints (MPC), to solve the computational problems and enforce the periodic boundary condition (PBC), eliminating the need for one-by-one mapping of inlet and outlet computational nodes. To validate the methodology, we apply it to model a bi-laminated composite and compare the obtained results with analytical values. This is followed by statistical descriptions of μCT images of several samples, together with a comprehensive representativity analysis using multiple RVE realizations approach. We find the results of statistical descriptions useful to guide us in selecting suitable RVE sizes.

A temperature field model based on energy flow analysis of wet clutch sliding interface

A fluid-solid convective heat transfer model is constructed according to the velocity distributed calculation of lubricant in clutch groove cavity. Considering the characteristics of circumferential alternation of heat dissipation and generation area on separator plate surface,the effective energy flow characterization equations of convective hear transfer and heat generation at sliding interface are established. The non-heat source temperature field is proposed by effective convective heat transfer and heat conduction. Following the target constraint of continuous contact temperature, the temperature field change is solved during actual dynamic heat flux partition period. The tests with different intensity of heat generation and dissipation are designed, which indicates the reliability of model. The research provides a new method for the temperature field calculation of clutch.

Effect of heat conduction on viscoelastic lubricant behavior during heat-assisted magnetic recording (HAMR): A numerical study

Heat-assisted magnetic recording (HAMR) is one of the critical technologies to overcome the areal density limitations of hard disk drives. In order to reveal the behavior of viscoelastic lubricants under HAMR conditions, the coupled physical field model of disk Fourier heat conduction model and viscoelastic lubricant model is established. The effects of Fourier heat conduction model and Gaussian distribution model on the disk temperature distribution and viscoelastic lubricant behavior are investigated. The lubricant deformation calculated by the Fourier heat conduction model is more accurate. The laser power overshoot method is proposed to improve the efficiency of HAMR writing process. The lubricant recovery ratio calculated by the Fourier heat conduction model is greater than that calculated by the Gaussian distribution model. The smaller the laser radius is, the greater the deformation of the lubricant is, and the lower the recovery ratio is.

A calorimetric evaluation method for beam targets with IR imaging: Implementation for the negative ion source BATMAN Upgrade

A comprehensive calorimetric evaluation method is presented for the beam target installed in the testbed BATMAN Upgrade (BUG). BUG hosts the prototype RF-driven negative ion source for the ITER Neutral Beam Heating System. In nominal conditions BUG features an array of negative ion beamlets (5 horizontal × 14 vertical) with 20 mm spacing among them. Each beamlet is accelerated electrostatically up to a maximum of 45 kV and transports currents in the range from 0.01 to 0.05 A. BUG has two beam targets at different distances from the beam acceleration system. The furthest (2.08 m downstream) is a water-cooled diagnostic CW-calorimeter, which can measure the heat flux distribution of the beam with a resolution of 20 × 20 mm² over a surface of 600 (H) × 800 (V) mm² and water calorimetry. The closest (0.86 m downstream) beam target with sub-millimetric resolution consists of a (376 × 142 × 20 mm³) tile made of a composite anisotropic material with carbon fibers oriented in the thickness direction (1D-CFC). It can only be exposed to beams for limited time, therefore it is retractable. Infrared (IR) imaging of beam targets yields time-resolved high-resolution spatial temperature footprints. A simple algorithm is proposed to reconstruct the heat flux at the front of a beam target, from the IR footprints at the rear. The reconstructed heat flux profiles are lower and broader due to heat conduction effects in the beam target. A correction algorithm is proposed through simulation-based inference of 2D axisymmetrical FEM simulations that reduces the power and shape fit errors over an order of magnitude, to a few percent. The calorimetric evaluation method is applied to experimental shots and two advanced heat flux distribution analysis are shown. The most relevant error sources are discussed and quantified to assess systematic errors. Finally, the method is validated in BUG comparing total beam power estimations with the two calorimetric diagnostics from the CW-calorimeter, showing good agreement.

Generalized thermoelastic damping in micro/nano-ring resonators undergoing out-of-plane vibration

Micro/nano-ring or ring-based resonators are popular core components of sensors and actuators. Accurately predicting the quality factor (Q) based on thermoelastic damping (TED) is intensively crucial for designing high-performance micro/nano-ring resonators. In this work, adopting the modified-couple-stress (MCS) and nonlocal-dual-phase-lagging (NDPL) models, analytical TED expressions are developed for circular cross-section micro/nano-rings undergoing out-of-plane vibration for the first time. Multiple effects are considered in the modeling procedure, which are size-dependence effects in the mechanical and thermal fields, the non-Fourier effect of heat conduction, and three-dimensional temperature gradients in the circumferential, radial, and tangential directions. Therefore, the proposed TED models are more comprehensive compared to existing TED models. The coefficients (CC and CM) associated with the out-of-plane vibration mode are examined from an energy-ratio perspective. Moreover, the investigation is focused on the impacts of the MCS and NDPL non-Fourier effects on the fluctuation temperature and TED spectra. The results indicate as CC and CM approach one, the bending energy emerges as the predominant component of the stored energy. Notably, the NDPL non-Fourier effect significantly affects the fluctuation temperature within the ring operated in high-order modes. In special, the distributions of fluctuation temperature in the circumferential direction exhibit periodic patterns that are closely correlated with the modal order. Furthermore, TED can be suppressed by the MCS size-dependence effect. Meanwhile, the behavior of TED at high frequencies is simultaneously determined by the dimension of heat conduction, phase-lagging times, and nonlocal thermal-length parameter.

Time-Fractional Heat Conduction Effects on the Dynamic Response of a Magneto-Thermoelastic Half-Space Subjected to a Thermal Shock

Time-Fractional Heat Conduction Effects on the Dynamic Response of a Magneto-Thermoelastic Half-Space Subjected to a Thermal Shock

Analysis to the dynamic response of a functionally graded spherical microshell in consideration of fractional-order dual-phase-lag heat conduction and nonlocal effect

Functionally graded materials (FGMs) stand as one of the most representative composite materials due to the superior thermal resistance in non-isothermal environment. On another front, the applicability of integer-order heat conduction models is increasingly questionable because the heat transfer shares the history-dependent property at time microscale. It is noted that the small-scale effect of elastic deformation has become significant due to the development of micro-devices. To capture the small-scale effect of elastic deformation and the memory-dependent effect of heat conduction in the FGM microstructures, as a first attempt, the present study focuses on developing a thermoelastic model by incorporating the fractional-order dual-phase-lag (FODPL) heat conduction model and the Eringen’s nonlocal model. Moreover, the extension of the Caputo definition, i.e., the Tempered-Caputo (TC) definition of fractional derivative ruling out singular kernel is adopted to depict the memory-dependent effect of the heat conduction. Then, the modified model is used to investigating the dynamic response of a FGM spherical microshell subjected to a sinusoidal thermal-mechanical loading. The corresponding governing equations are formulated and then solved by Laplace transform techniques. Some parametric results are demonstrated to display the influences of the fractional-order parameter, the nonlocal parameter and the power-law index on the considered physical quantities.

A comprehensive study on the roles of viscosity and heat conduction in shock waves

Shock waves are of great interest in many fields of science and engineering, but the mechanisms of their formation, maintenance and dissipation are still not well understood. While all transport processes existing in a shock wave contribute to its compression and irreversibility, they are not of equal importance. To figure out the roles of viscosity and heat conduction in shock transition, the existence of smooth shock solutions and the counter-intuitive entropy overshoot phenomenon (the specific entropy is not monotonically increasing and exhibits a peak inside the shock front) are theoretically and numerically investigated, with emphasis on the effects of viscosity and heat conduction. Instead of higher-order hydrodynamics, the Navier–Stokes formalism is employed for its stability and simplicity. Supplemented with nonlinear thermodynamically consistent constitutive relations, the Navier–Stokes equations are adequate to demonstrate the general nature of shock profiles. It is found that heat conduction cannot sustain strong shocks without the presence of viscosity, while viscosity can maintain smooth shock transition at all strengths, regardless of heat conduction. Hence, the critical role in shock compression is played by viscosity rather than heat conduction. Nevertheless, the dispensability of heat conduction would not compromise its essential role in the emergence of an entropy peak. It is the entropy flux resulting from heat conduction that neutralises the positive entropy production and thus prevents the decreasing entropy from violating the second law of thermodynamics. This mechanism of entropy overshoot has not been addressed previously in the literature and is revealed using the entropy balance equation.

Regular reflection of shock waves in steady flows: viscous and non-equilibrium effects

Numerical analysis of a steady monatomic gas flow about the point of the regular reflection of a strong oblique shock wave from the symmetry plane is conducted with the Navier–Stokes–Fourier (NSF) equations, the regularized Grad 13-moment (R13) equations and the direct simulation Monte Carlo (DSMC) method. In contrast to the inviscid solution to this problem completely defined by the Rankine–Hugoniot (RH) relations, all three models predict a complicated flow structure with strong thermal non-equilibrium and a long wake with flow parameters not predicted by the RH relations. The temperature $T_y$ related to thermal motion of molecules in the direction normal to the symmetry plane has a maximum inside the reflection zone while in a planar shock wave the maximum is observed for the $T_x$ temperature. The R13 equations predict these features much better than the NSF equations and are in good agreement with the benchmark DSMC results. An analysis of the flow with the conservation equations was conducted in order to evaluate the effects of various processes on a fluid element moving along the symmetry plane. In contrast to the shock wave where effects of viscosity and heat conduction are one-dimensional with zeroth net contribution to the fluid-element energy across the shock, the flow across the zone of the shock reflection is dominated by two-dimensional effects with positive net contribution of viscosity and negative contribution of heat conduction to the fluid-element energy. These effects are believed to be the main source of the wake with parameters deviating from the RH values.

Feasibility Study on Biodegradable Black Paper-Based Film Solidified Using Cooked Tung Oil

New biodegradable paper-based films are a hot research topic in the development of green agriculture. In this study, a black paper-based film coated with cooked tung oil with excellent mechanical properties, a hydrophobic surface, high heat transfer and strong weather resistance was prepared by spraying high-pigment carbon black solution on the surface of base paper. The results showed that the surface-solidified oil film had a rough structure produced via the brush coating process using cooked tung oil. The base film of the black paper had a given hydrophobic structure, and the contact angle reached 98.9°. Cooked tung oil permeates into the inside of the paper base, and after curing, it forms a multi-dimensional network film structure. The maximum tensile stress of the black paper base film is about 123% higher than that of the original paper base film. The coloring of carbon black gives the black paper base film a heat conduction effect, and the average heat transfer rate reaches 15.12 °C/s. Cooked tung oil is combined with the paper-based fiber high-toughness layer to form a stable system. The existence of a cured film improves the basic mechanics and hydrophobicity, and the resistance to ultraviolet radiation and hot air is greatly improved. This study provides a feasible scheme for the application of a black paper base film coated with cooked tung oil.