Heat Conduction Research Articles

An innovative subdivision collocation algorithm for heat conduction equation with non-uniform thermal diffusivity.

This paper presents a subdivision collocation algorithm for numerically solving the heat conduction equation with non-uniform thermal diffusivity, considering both initial and boundary conditions. The algorithm involves transforming the differential form of the heat conduction equation into a system of equations and discretizing the time variable using the finite difference formula. The numerical solution of the system of heat conduction equations is then obtained. The feasibility of the algorithm is verified through theoretical and numerical analyses. Additionally, numerical and graphical representations of the obtained numerical solutions are provided, along with a comparison to existing methods. The results demonstrate that our proposed method outperforms the existing methods in terms of accuracy.

Research on surface integrity of titanium alloy in V-groove micro-textured ball-end milling cutter

In order to realize chip guiding control in titanium alloy machining, reduce the negative influence of unstable chip flow direction on the milling environment, and improve the performance and reliability of parts, this article adopts the V-groove micro-texture carbide tool as the research object and takes the laser preparation of the V-groove micro-texture as a breakthrough point, analyzes the influence of laser parameters on the aspect ratio of V-groove micro-texture, and optimizes the laser parameters. The titanium alloy milling test platform was built to analyze the influence of the micro-texture parameters of the V-groove on the surface integrity of the workpiece, reveal the action mechanism, and optimize the relevant parameters based on the artificial bee colony algorithm. The results show that laser power has the largest influence on the aspect ratio of the groove. The power determines the melt content in the groove and influences the width and depth of the micro-texture. The optimized laser combination parameters are: laser power 42.5 W, scanning speed 10 mm/s scanning times nine times, scanning frequency 30 kHz, and spot diameter 30 μm. The V-groove micro-texture on the tool surface can change the chip flow direction, reduce the contact area of the chip, accommodate the cutting particles, and improve heat conduction, reducing cutting resistance and friction, thereby optimizing cutting control distance, thereby improving the surface integrity of the workpiece becomes. The optimized V-groove micro-texture parameters are as follows: V-groove angle X = 46.2°, V-groove height H = 175 μm, radial spacing L = 259.4 μm, circumferential angle J = 2.1°, and distance from the edge K = 120 μm.

Efficient ecological function analysis and multi-objective optimizations for an endoreversible simple air refrigerator cycle

Abstract Combining finite time thermodynamics and exergetic analysis, analogous to the definition of ecological efficient power for heat engines, this paper proposes a unified performance indicator for various cycles, exergy-based efficient ecological function (E ɛ ) which is defined as product of exergy-based ecological function and coefficient of performance, and introduces it into performance optimization of endoreversible simple air refrigerator cycle coupled to constant-temperature heat reservoirs. Relations among E ɛ , pressure ratio (π) and heat conductance distribution ratio (u) are derived by using numerical method. The cycle performance indicators which include cooling load (R), coefficient of performance (ɛ), and exergetic loss rate (E out/T 0) under the different maximum objective criteria are compared. Taking π as optimal variable, and taking R, ɛ, cooling load density (r), E ɛ and their combinations as optimization objectives, multi-objective optimizations, totally 15 optimization combinations, are performed by using NASG-II algorithm. The results demonstrate that, the maximum E ɛ criteria can better reflect the compromise among R, ɛ and E out/T 0. The Pareto solution sets are majorly distributed in 2.5–20 when quadru-objective optimizations are performed. The option selected by LINMAP decision-making method is closer to ideal solution when bi-objective optimization of ɛ and r is carried out.

Enhancing directional thermal conductivity in hexagonal boron nitride reinforced epoxy composites through robust interfacial bonding

AbstractEstablishing a robust interfacial bond between hexagonal boron nitride (h‐BN) plates and the epoxy matrix is essential for enhancing heat transfer, which is difficult because of h‐BN's low‐surface energy, tendency to clump together, and the chemical inertness of the epoxy matrix. This research shows different techniques for treating the surface of h‐BN fillers by applying acids and thermal processes to activate the surface. The silanization process was used to increase the silane content on the surface of activated h‐BN in order to make it more compatible with the epoxy matrix. X‐ray photoelectron spectroscopy analysis revealed silicon peaks (Si2s peak at 150.1 eV and Si2p peak at 100.3 eV) in the spectrum of silane‐treated samples. Heat treatment resulted in the production of more oxygen molecules on the shell of h‐BN compared to the acid treatment. Here, the primary focus was on examining how surface treatment affects thermal conductivity (TC) performance in both in‐plane and through‐thickness paths. There was an increase in the epoxy's TC perpendicular to the plane, going from 0.21 to 0.47 (W/mK), showing a remarkable 123.8% enhancement by adding 10 wt% of silane‐modified‐thermal treated h‐BN particles. The improvement resulted from effectively silanizing the exterior boundary of h‐BN particles, enhancing connection and distribution in the epoxy matrix. Surface modification of h‐BN‐epoxy composites improves TC, leading to better heat conduction in thermal management systems, benefiting industries like aerospace, automotive, and energy systems.Highlights Silanization of h‐BN for better filler‐matrix bonding leading to improved heat transfer Boosting thermal conductivity in the through‐thickness direction with surface‐modified h‐BN Significant improvement in through‐thickness thermal conductivity with treated h‐BN. Thermal treatment of h‐BN produced better oxygenation than acid treatment. Application in aerospace and automotive through improved heat transfer.

Chaotic self-beating of left ventricle modeled by liquid crystal elastomer

Self-vibration systems using active materials generate sustained vibrations spontaneously through synergistic actions between internal structure and external environment. Therefore, the self-vibration systems have a wide application prospect in bionic design and soft robots. Inspired by the human left ventricle, a novel chaotic self-beating system modeled by an electrothermal responsive liquid crystal elastomer balloon is proposed. To study the self-beating characteristics of the liquid crystal elastomer left ventricle, a simplified theoretical framework is formed by combining the electric joule heat conduction model, the left ventricle circulatory system model and the dynamic principle. The numerical results show that the left ventricle has two typical self-beating modes: periodic beating and chaotic beating. The mechanisms of periodic beating and chaotic beating are elucidated by analyzing the balance between the work done by each force on the left ventricle. In addition, the effects of key system parameters on self-beating behavior are investigated in detail. This research will promote the application of chaotic dynamics in artificial hearts and medical devices, while providing a new perspective for the study of chaotic behavior and mechanism in biology.

Enhanced Thermoelectric Performance of Bi0.5Sb1.5Te3 through Precise Pb Doping: Analysis Using the Single Parabolic Band Model

This study investigates the thermoelectric properties of Pb-doped p-type Bi0.5Sb1.5Te3 alloys using the Single Parabolic Band (SPB) model, focusing on optimizing room-temperature performance. We systematically analyze the effects of Pb doping (0, 0.49, 0.65, 0.81, 0.97, and 1.3 at%) on key parameters including density-of-states effective mass (md *), non-degenerate mobility (μ0), weighted mobility (μw), and the thermoelectric quality factor (B-factor) at 323 K. The results reveal that md * reaches a maximum of 1.37 me at 0.97 at% Pb doping, representing a 22.25 % increase over the pristine sample. The highest μ0 of 234.5 cm2 V-1 s-1 is achieved at 0.65 at% Pb, highlighting the complex relationship between doping and carrier mobility. Notably, 0.97 at% Pb doping optimizes thermoelectric performance, yielding the highest μw, power factor, and B-factor. This composition also minimizes lattice thermal conductivity (k1) by 44.93 % compared to the undoped sample, significantly reducing phonon heat conduction. The Callaway-von Baeyer model corroborates these findings, indicating maximized point defect scattering at 0.97 at% Pb. A theoretical peak figure-of-merit (zT) of 1.74 is thus predicted at this doping level, demonstrating a possible substantial enhancement in thermoelectric efficiency upon appropriate carrier concentration tuning. The observed trends in Seebeck coefficient, Hall carrier concentration, and Hall mobility with increasing Pb content provide insights into the underlying mechanisms of performance enhancement. This comprehensive study highlights the critical role of precise Pb doping in optimizing the thermoelectric properties of Bi0.5Sb1.5Te3 alloys for room-temperature applications and establishes a framework for future investigations into similar material systems.

Natural convection and variable fluid properties of tangent hyperbolic nanofluid flow with Cattaneo-Christov theories and heat generation

The main aim behind this work is that we have to determine the enhancement that happens in thermal conductivity by using the Buongiorno model of nanofluid when the nanofluid particles are added to the tangent hyperbolic base fluid moving above the stretched surface. The viscosity of tangent hyperbolic nanofluid is assumed to be temperature-dependent. The modified form of the Fourier law of heat conduction motivated us; therefore, the Cattaneo-Christov heat and mass flux model is considered to observe its significance for heat and mass transport. The chemical reaction and heat generation are also considered to determine their influence on temperature and concentration gradients. This study is crucial because of its application in industrial manufacturing processes such as the coating of wire, the thinning of copper, the production of paper, photographic films, hot rolling, and the purification of crude oil. In electronic cooling systems, the efficient dissipation of heat in smartphones, computers, and data centers is critical to preventing overheating. Nanofluids, with their enhanced thermal properties, can significantly improve heat transfer rates, ensuring better performance, stability, and energy savings. The partial governing equations arising from fluid flow, mass, and heat transfer are transformed into ordinary differential equations via appropriate similarity variables. The obtained ordinary differential equations are solved numerically by using the Runge-Kutta Fehlberg method in the MATLAB software. The effects of the emerging parameters are represented through graphs. According to the results, the velocity profile upsurges due to the natural convection parameters and curvature parameter, while the power law index declines the velocity profile. As the Brownian motion coefficient rises, the concentration profile diminishes while the temperature profile increases. Both the concentration and temperature profiles increase for larger values of the thermophoresis parameter. The concentration profile declines for larger values of chemical reaction parameters, and enhancement happens in the temperature region.

Impact of Acoustic and Optical Phonons on the Anisotropic Heat Conduction in Novel C-Based Superlattices.

C-based XC binary materials and their (XC)m/(YC)n (X, Y ≡ Si, Ge and Sn) superlattices (SLs) have recently gained considerable interest as valuable alternatives to Si for designing and/or exploiting nanostructured electronic devices (NEDs) in the growing high-power application needs. In commercial NEDs, heat dissipation and thermal management have been and still are crucial issues. The concept of phonon engineering is important for manipulating thermal transport in low-dimensional heterostructures to study their lattice dynamical features. By adopting a realistic rigid-ion-model, we reported results of phonon dispersions ωjSLk→ of novel short-period XCm/(YC)n001 SLs, for m, n = 2, 3, 4 by varying phonon wavevectors k→SL along the growth k|| ([001]), and in-plane k⟂ ([100], [010]) directions. The SL phonon dispersions displayed flattening of modes, especially at high-symmetry critical points Γ, Z and M. Miniband formation and anti-crossings in ωjSLk→ lead to the reduction in phonon conductivity κz along the growth direction by an order of magnitude relative to the bulk materials. Due to zone-folding effects, the in-plane phonons in SLs exhibited a strong mixture of XC-like and YC-like low-energy ωTA, ωLA modes with the emergence of stop bands at certain k→SL. For thermal transport applications, the results demonstrate modifications in thermal conductivities via changes in group velocities, specific heat, and density of states.

Simulation of solidification for saving energy with using nanomaterial involving conduction heat transfer

The current article studies the improvement of the discharging rate in cold storage systems by modifying the tank configuration and incorporating additives. Specifically, the study inspects how varying the diameter (dp) and fraction (ϕ) of nano-powders affects the process duration. The governing equations, derived under the assumption of negligible slip velocity of nanoparticles and convection terms, were solved using the Galerkin method. The computational grid was modified owing to location of the ice front, and unsteady terms were discretized using an unconditionally stable approach. The results indicate that initially, increasing dp decreases the process duration by approximately 20.01 %, but further increases in dp lead to a 49.53 % rise in the duration. As the process time increases, the amount of ice produced also increases, with nanoparticle loading resulting in a significantly higher ice yield. Specifically, the incorporation of nanoparticles enhances the storage rate by approximately 41.37 %.

Thermal and thermo-mechanical post-buckling analysis of GNP-reinforced composite laminated plates

This research utilizes isogeometric analysis (IGA) method to analyze buckling and post-buckling responses of composite laminated plates embedded with graphene nanoplatelets (GNPs) subjected to three-dimensional (3D) conduction of heat or combined 3D heat conduction and mechanical edge compression. A formulation to determine temperature profile produced by 3D conduction of heat in the GNP-reinforced laminate is established, and a new function with smooth transition form of GNP volume fraction across the thickness is presented for dictating the volume fraction of layer. Shear deformable quasi-3D theory with the von Kármán type nonlinearity which takes initial geometric deformation and thermal effect into consideration is employed to construct the nonlinear equilibrium states. Four types of GNP arrangements encompassing uniform, O, X and V shapes are considered. The IGA approach presented, through the benchmark test, is evidenced to estimate the thermal buckling temperature accurately and to successfully trace the thermal post-buckling path. Additional parametric study is carried out to scrutinize the thermal and the thermo-mechanical post-buckling features of the GNP-reinforced composite laminated plates, and the new findings are sure to be served as the benchmark solutions.

Enhancing interfacial heat conduction in diamond-reinforced copper composites with boron carbide interlayers for thermal management

In this work, we have synthesized a copper/boron carbide/diamond composite structure via magnetron sputtering. Surface roughness of the diamond layers was characterized using atomic force microscopy (AFM), and interfacial thermal conductance (ITC) between copper and diamond was experimentally measured by the Time-domain Thmoreflectance (TDTR) technique. Molecular dynamics (MD) simulations were conducted to investigate the influence of the <010> crystal plane thickness of boron carbide and interface roughness on the ITC. The results indicate a significant increase in ITC with the incorporation of a <010>-oriented boron carbide interlayer. The ITC initially rose and then fell as the boron carbide layer thickness increased, reaching a maximum of 286.52 MW m−2 K−1 for a three-layer (approximately 2 nm) interlayer, which is 14.1 times higher than that of the unmodified interface. Additionally, by creating a three-dimensional sinusoidal rough interface, we observed that increasing interface roughness can further enhance heat transfer efficiency up to a certain threshold, beyond which a saturation in phonon heat conduction is anticipated. The simulation outcomes are in good agreement with the experimental data, confirming the reliability of our findings.

Parametric and optimization analyses of a dynamic trombe wall incorporating PCM to save heating energy under cold climate zones

The Trombe wall system incorporating a dynamic PCM layer (DTWPS) has been recognized as a viable envelope to reduce the energy demand for heating effectively. However, properly selecting PCMs in the DTWPS is complicated and much less studied. Therefore, parametric and optimization analyses of the PCM thermal properties of a DTWPS are carried out for heating energy saving under cold climate zones using a validated CFD model, multiple linear and nonlinear regression models, and the particle swarm optimization (PSO) algorithm. The results show nonlinear relationships between the four critical PCM thermal properties and the energy saving, time lag, and thermal comfort. Moreover, the optimal values of the melting point, latent heat, density, and thermal conductivity of the PCM are 26.4 °C, 200 kJ/kg, 2080 kg/m3, and 1.34 W/(m·K), respectively. Meanwhile, the energy saving for the test room equipped with the DTWPS with optimal thermal properties could reach 100 % compared to that for the traditional reference Trombe wall. With available PCMs, heating energy consumption can be saved by up to 90 % or more. Further, the DTWPS demonstrates a reduced PCM mass compared to other passive walls.

Jute-reinforced hybrid biocomposite incorporated with low thermal conductive silica aerogel for improved resistance to conductive and radiative heat

This study aims to develop jute-reinforced polypropylene composites by incorporating low-heat conductive silica aerogel for enhanced thermal performance, envisioning their utilization as heat-insulating panels in buildings. The fabrication of hybrid composites using a heat press molding technique showed a significant improvement in thermal properties due to incorporating aerogel into the material. The lowest obtained thermal conductivity of hybrid composite was 0.0986 W/m·K, which was almost halved (0.1704 W/m·K) to the material without aerogel. The radiative heat resistance of hybrid composites was also improved with the aerogel in the material. Additionally, composites with higher amounts of aerogel showed superior flame resistance and thermal stability at high temperatures. The hybrid composites, however, demonstrated a decrease in tensile strength due to the presence of aerogel particles at the interface of composites. The composite without aerogel displayed the highest tensile strength of 64.67 MPa, which was the lowest (47.87 MPa) for the material with the maximum amount of aerogel. The fractographic investigation also revealed the existence of aerogel particles and their random distribution at the interface of the material. The low water absorption owing to reduced interfacial vacuities and the existence of super-hydrophobic aerogel in the interior of composites indicated their durability in humid conditions without deteriorating the dimensional stability. The outcomes of the study revealed a considerable effect of aerogel on the thermal performance of composites and ascertained their excellence as a prospective heat-insulating material for conserving thermal energy by minimizing heat transfer from inside to outside of the building and vice versa.

Enhanced physics-informed neural networks without labeled data for weakly and fully coupled transient thermomechanical analysis

In this paper, a series of enhanced physics-informed neural networks (PINN) models without labeled data is proposed to solve the weakly and fully coupled thermomechanical problems. In these models, to better predict the thermal and mechanical responses, PINNs consisting of different deep neural networks (DNN) representing temperature, displacement, and stress are specifically constructed. Furthermore, to elevate the accuracy and avoid possible training failure, several advanced algorithms are developed to ensure the effectiveness of imposing boundary conditions, refining sampling distributions, and enhancing training strategy. A notable aspect of the enhanced PINNs is their independence from expensive, labeled data, relying solely on the temporal and spatial information embedded within the sampling points. The effectiveness and accuracy of the enhanced PINNs are validated through extensive numerical examples, including heat conduction and both weakly and fully coupled thermomechanical problems. The comparation between original PINN and enhanced PINN illustrates the necessity of involving these enhanced methods. The results demonstrate the significant potential of PINN methodologies in engineering areas involving complex thermomechanical processes.

Aero-thermodynamic responses of a novel FGM sector disks using mathematical modeling and deep neural networks

Composite sector disks have extensive applications in aerospace industries, particularly when exposed to challenging conditions such as supersonic airflow and thermal environments. These applications leverage the superior properties of composite materials, including high strength-to-weight ratios, enhanced durability, and excellent thermal resistance, to meet the stringent requirements of aerospace operations. Multi-directional functionally graded (MD-FG) materials due to high-temperature resistance and other amazing properties in each direction have gotten plenty of attention recently. So, in this research, a thermoelasticity solution has been presented to study fundamental frequency traits of an MD-FG sector disk in supersonic airflow via both mathematics simulation and deep neural networks technique. For obtaining exact displacement fields, along with defining the changes of transverse shear strains along the system's thickness, the refined zigzag hypothesis is utilized. For obtaining the temperature-dependent equations, heat conduction relation and thermal boundary conditions of the MD-FG structure are presented. A coupled quasi-3D new refined theory (Q3D-NRT) and generalized differential quadrature method (GDQM) are presented for obtaining and solving the partial differential equations in the time-displacement domain. After obtaining the mathematics results, appropriate datasets are made for testing, training, and validation of the deep neural networks technique. Finally, the results have shown that aerodynamic pressure, temperature changes, Mach number, free stream speed, and air yaw angle have a major role in the stability/instability analyses of the thermally affected MD-FG sector disk in supersonic airflow. As an amazing outcome, increasing the sector angle, FG indexes, and temperature change lead to the reduction of the critical Mach number, and aerodynamic pressure associated with the flutter phenomenon.

Random Walk Modeling of Conductive Heat Transport in Discontinuous Media

AbstractWe consider heat transport within a discontinuous domain by relying on the modeling approach proposed by Baioni et al. Such approach has been specifically designed to address diffusive processes in media with discontinuous physical properties and generalized boundary conditions at the discontinuities. Three algorithms are here applied to estimate the conductive heat transport in a bimaterial medium. The algorithms undergo testing using two test cases that share the same computational domain but differ in terms of their initial conditions. According to the numerical results all the algorithms ensure the conservation of thermal energy and preserve thermal equilibrium under steady state conditions. The Generalized Uffink Method (GUM) and Generalized HYMLA demonstrate sensitivity to the choice of the time step, whereas the Generalized Skew Brownian Motion appears to be unaffected by the value of $$\Delta t$$ Δ t . The GUM algorithm presents an optimal trade-off between accuracy and computational time.

Pore Network Modeling of Intraparticle Transport Phenomena Accompanied by Chemical Reactions.

In this work, a 3D pore network model (PNM) is introduced for modeling reaction-diffusion phenomena, with and without coupled heat transfer, in a spherical porous catalyst particle. The particle geometry is generated by packing thousands of microspheres inside a large sphere to represent the 3D geometry, porosity, and tortuosity of a spherical catalyst particle. A pore-network representation is extracted from this geometry, and a PNM for diffusion-reaction and heat conduction is constructed. This newly proposed particle-scale PNM allows for the application of realistic 3D nonuniform boundary conditions on the particle's surface, which is commonly encountered in slender packed-bed reactors. Concentration profiles inside the particle, and effectiveness of the reactions, is analyzed.

Microencapsulated phase change material in 3D-printable mortars

The present study investigates the potential of replacing sand with microencapsulated phase change materials (MEPCM) in 3D-printable mortar to provide a promising way to improve thermal performance in 3D-printed buildings. Adding MEPCM significantly enhanced the rheological properties and early hardening evolution of cementitious mortar for 3D printing applications without the need for viscosity modifier agents. In hardened mortars, microstructural analysis and thermal cycling experiments confirmed that MEPCM remained intact and stable within the cementitious environment. The thermal properties of the treated mortars, including latent heat and thermal conductivity, were improved for energy-saving applications. Despite this, the compressive strength of the mortars dropped considerably by increasing the concentration of MEPCM while a strength of above 20 MPa was maintained. Simulation results from 3D Finite Element Method (FEM) and 1D reduced order model (ROM) closely matched the experimental data from printed walls in a thermal setup, validating the use of 1D ROM simulations for long-term predictions. In a case study, a printed wall where MEPCM replaced 80 % of the sand showed a ∼40 % reduction in energy consumption compared to mortar without MEPCM under real weather conditions.

In Situ Conductive Heating for Thermal Desorption of Volatile Organic-Contaminated Soil Based on Solar Energy

A novel conductive heating method using solar energy for soil remediation was introduced in this work. Contaminated industrial heritage sites will affect the sustainable development of the local ecological environment and the surrounding air environment, and frequent exposure will have a negative impact on human health. Soil thermal desorption is an effective means to repair contaminated soil, but thermal desorption is accompanied by a large amount of energy consumption and secondary pollution. Therefore, a trough solar heat collection desorption system (TSHCDS) is proposed, which is applied to soil thermal desorption technology. The effects of different water inlet temperature, water inlet velocity and soil porosity on the evolution of soil temperature field were discussed. The temperature field of contaminated soil can be numerically simulated, and a small experimental platform is built to verify the accuracy of the numerical model for simulation research. It is concluded that the heating effect is the best when the water entry temperature is the highest, at 70 °C, and the temperature of test point 4 is increased by 50.71% and 1.42%, respectively. When the inlet water flow rate is increased from 0.1 m/s to 0.2 m/s, the heating effect is significantly improved; when the inlet water flow rate is increased from 0.5 m/s to 1.5 m/s, the heating effect is not significantly improved. Therefore, when the flow rate is greater than a certain value, the heating effect is not significantly improved. The simulation analysis of soil with different porosity shows that larger porosity will affect the thermal diffusivity, which will make the heat transfer effect worse and reduce the heating effect. The effects of soil temperature distribution on the removal of petroleum hydrocarbon C6–C9 and trichloroethylene (TCE) were studied. The results showed that in the thermal desorption process of petroleum hydrocarbon C6–C9-contaminated soil, the removal rate of pollutants increased significantly when the average soil temperature reached 80 °C. In the thermal desorption of trichloroethylene-contaminated soil, when the thermal desorption begins, the soil temperature rises rapidly and reaches the target temperature, and a large number of pollutants are removed. At the end of thermal desorption, the removal of both types of pollutants reached the target repair value. This study provides a new feasible method for soil thermal desorption.

A weakly coupled system of p-Laplace type in a heat conduction problem

Abstract Given is a bounded domain Ω ⊂ ℝ n {\Omega\subset\mathbb{R}^{n}} , and a vector-valued function defined on ∂ ⁡ Ω {\partial\Omega} (depicting temperature distributions from different sources), our objective is to study the mathematical model of a physical problem of enclosing ∂ ⁡ Ω {\partial\Omega} with a specific volume of insulating material to reduce heat loss in a stationary scenario. Mathematically, this task involves identifying a vector-valued function 𝐮 = ( u 1 , … , u m ) {\mathbf{u}=(u^{1},\dots,u^{m})} ( m ≥ 1 {m\geq 1} ) that represents the temperature within Ω and gives rise to a free boundary, somehow reminiscent of, but not equivalent to, the Bernoulli free boundary problem.