Heat Conduction Research Articles

Tricomi Problem Analogue for a Second Order Mixed Type Equation

In this paper, we investigated an analogue of the Tricomi problem for one equation of parabolic-hyperbolic type of the second order with a heat conduction operator in the parabolicity region and with a degenerate hyperbolic operator of the first kind in the hyperbolicity region. The type change line is characteristic for a parabolic equation and non-characteristic for a hyperbolic one. The problem is studied when the values of the sought function are given on non-characteristic segments of the boundary of a parabolic parabolic equation, and a value is also given on the characteristic of the hyperbolic equation at. Previously, similar problems were the subject of research by many authors, such as, for example, the works of A.~M.~Nakhushev and Kh.~G.~Bzhikhatlova, M.~S.~Salakhitdinov and A.~S.~Berdysheva. In this paper, theorems on the uniqueness and existence of a regular solution to the problem under study are proven. When proving the uniqueness theorem for the solution of the problem, modern methods of the theory of fractional calculus are used, and the existence is proven using the method of integral equations. In the case when the coefficients of the equation under consideration are constant, the solution is found and written out explicitly. The theorems proved generalize the previously obtained results both in terms of sufficiency conditions for the uniqueness of a solution to an analogue of the Tricomi problem, and in terms of the existence theorem.

Thermal boundary conductance enhancement of the Si/diamond interface via atomic transition strategy

Developing multi-chip systems introduces significant thermal management challenges, due to dense vertical stacking and interconnections. Specifically, the increased number of interfaces within the heat conduction path of the chips significantly impedes the effective heat transfer. This study utilizes a series of molecular dynamics simulations to explore how the structure and atomic composition at interfaces affect their thermal conduction abilities. This study initially reveals substantial differences in thermal conduction capabilities between Si/Diamond, SiC/Diamond, and Diamond/Diamond interfaces. Further investigations focus on interfaces between different structures of SiC and diamond, clearly identifying the atomic composition and structure at the interface as key factors influencing thermal boundary conductance (TBC). Based on these findings, the study proposes a strategy for atomic transition that involves inserting SiC into the Si/Diamond interface. Under optimal thickness conditions for the SiC transition layer, a significant increase in theoretical TBC is achieved, from 477.1 MW/m²K to 701.1 MW/m²K, which is twice the value predicted by the existing diffusive mismatch model (DMM) for Si/Diamond interfaces. Lastly, through the developed 3D IC model, the study examines the impact of TBC variations on the peak temperature of the entire device, thereby further emphasizing the importance of enhancing interface thermal conduction capabilities. This series provides strategic guidance for thermal management in 3D ICs and offers a theoretical basis for chip design and material selection.

Validity of Thermal Simulation Models for Different Laser Beam Shapes in Bead-on-Plate Melting

AbstractComputational models that predict melt pool shapes and temperature evolution in laser-based powder bed fusion of metals (PBF-LB/M) can range from simple thermal simulation models to more advanced models that incorporate more detailed physics of the process. While advanced models can accurately predict thermal fields and melt pool fluid dynamics, they are computationally more expensive and, thus, less suited for part-scale simulations or numerical optimization, where repeated model evaluations are necessary. On the other hand, thermal simulations are computationally efficient and attractive for their simplicity, but their accuracy is mainly limited to conduction-dominated processes. Moreover, the conduction model’s validity range is not fully understood for non-Gaussian laser beam shapes. This paper demonstrates that predictions of melt pool depth and width carried out by a heat conduction model are accurate to within 20 % for all investigated laser profiles, provided that the simulated maximum temperature does not exceed a certain threshold value for stainless steel 316L. This is established by thoroughly investigating the validity range of the heat conduction model through comparisons with over 200 single-track experiments on bare plates. The temperature predictions from the model are compared with multi-physics simulations using smoothed particle hydrodynamics (SPH). Through detailed analysis and validation for three laser beam shapes, this contribution provides valuable insights into the accuracy and applicability of heat conduction models in bead-on-plate melting simulations and offers a path to optimize process parameters, such as laser beam shape, scanning strategy, and other processes for diverse applications aimed at PBF-LB/M.

A three-dimensional analytical model for performance evaluation of thermoelectric generators

A three-dimensional (3D) theoretical model for thermoelectric generators (TEGs) has been developed in this paper, yielding analytical solutions for power output and energy conversion efficiency. The model comprehensively considers convective heat transfer between the thermoelectric legs and their ambient environment, as well as 3D heat conduction within the ceramic substrates. Numerical results reveal the significant influence of convective heat loss from the legs' surfaces on efficiency, especially for taller legs or higher heat convection coefficient, while having a minimal impact on power output for the constant temperature boundaries. It is shown that neglecting 3D heat conduction within the ceramic substrates leads to a substantial overestimation of TEG performance. Additionally, the complex 3D heat conduction problem for TEGs can be simplified into a more manageable 1D model with only minor adjustments to classical TEG theory. This is achieved by introducing analytical expressions for a dimensionless impact factor to quantify convective heat loss from the legs’ surfaces and the effective thermal conductance of the ceramic substrates. The proposed model serves as a valuable tool for simplifying the modeling process and optimizing the design of actual TEGs.

A Lagrangian for Compressible Flow Focusing on Dissipation due to Thermal Conduction

ABSTRACTWith the aim of describing compressible viscous flows by means of a variational principle that takes into account heat conduction, a recently proposed Lagrangian is subjected to a detailed linear wave analysis that stems directly from the Lagrangian. The accompanying thermodynamic equation of state employed leads to a natural decomposition of the conduction term into three contributions, with the importance of each accessed through a detailed analysis employing a recently developed perturbation methodology giving rise to a favorable system of governing Jacobi equations. In addition to the model Lagrangian itself, three potential model scenarios—based on different combinations of the contributions forming the Lagrangian—are rigorously evaluated and appraised, regarding the occurrence, or otherwise, of dissipation recognizable by an attenuation of harmonic waves. Results reveal that two of the four models are suitable candidates, and suggest one in particular.

Analysis of the effect of the heat stabilizer outer surface finning on soil cooling efficiency

Relevance. The construction of buildings and structures in permafrost conditions is associated with the problem of soil thawing. To prevent this phenomenon, heat stabilizer have proven themselves good in practice. Their successful use is difficult without preliminary modeling of heat flows in the soil–heat stabilizer system. The most effective design of a passive heat stabilizer is an installation with two-phase of refrigerant. An additional increase in the efficiency of using a two-phase heat stabilizer is possible due to the finning of the outer surface of the outer pipe of it. Aim. To calculate the efficiency of using a heat stabilizer with and without finning of the outer surface. Objects. Heat stabilizer, refrigerant, heat transfer, frozen soil. Methods. The mathematical model for describing the processes of heat and mass transfer in the heat stabilizer–frozen soil system is considered in an axisymmetric formulation. There are three subtasks: the movement of liquid refrigerant in the inner tube of the heat stabilizer, the two-phase convective flow of refrigerant in the gap between the inner and outer tubes and conductive heat exchange in the system of the heat stabilizer–frozen soil. The influence of the finning of the outer surface of the heat stabilizer is considered within the framework of the modified concept of the skin factor. Results and conclusions. The authors have obtained the pressure and temperature distributions along the length of the heat stabilizer. It was found that the presence of fins on the outer surface of the external pipe of the heat stabilizer increases the heat flow from the soil by 10%. It is determined that the soil is effectively cooled within 1 m from the heat stabilizer; this distance is recommended as optimal for the placement of an adjacent heat stabilizer.

The moderate electron-spin interaction in Fe-intercalated NbSe2

Abstract The interaction between charge and spin degrees of freedom has always been the central issue of condensed matter physics, and transition metal dichalcogenides (TMDs) provide an ideal platform to study it benefiting from their highly tunable properties. In this article, the influence of Fe intercalation in NbSe2 was elaborately investigated using a combination of techniques. Magnetic studies have shown that the insertion of Fe atoms induces an antiferromagnetic state in which the easy axis aligned out of the plane. The sign reversal of the magnetoresistance across the Neel temperature can be satisfactorily explained by the moderate interaction between electrons and local spins. The Hall and Seebeck measurements reveal a multi-band nature, and the contribution of various phonon scattering processes is discussed based on the thermal conductivity and specific heat data.

Model-based analysis of the effective pressure on effective thermal conductivity of porous media

Accurate characterization of the effective thermal conductivity (ETC) of porous media is crucial for analyzing heat transfer involved in the scientific, technological, and engineering fields. For example, ETC is a fundamental parameter for characterizing energy exploitation and utilization, such as the coupled thermo-hydro-mechanical-chemical process. During the energy extraction from the deep subsurface, the effective pressure (the difference between the confining pressure and the pore pressure) will alter the microstructure of the porous medium, which will then change its ETC value. In light of the intrinsic randomness and disorder in the distribution of grains and pores in the deep subsurface, many researchers have focused on heat conduction to develop theoretical models of ETC. Less attention has been paid to the thermal and mechanical coupling processes. In this paper, a novel analytical model was derived to study the effect of effective pressure on ETC of porous materials based on fractal theory, Laplace′s equation and the theory of elastic mechanics. The newly developed ETC model considered the effective pressure, the liquid saturation, and the microstructure parameters. The model has also been validated against the experimental results. The model demonstrated that effective pressure increases the ETC of a given porous medium. Moreover, there is a larger change in ETC in porous materials with a smaller initial porosity compared to porous materials with a larger initial porosity. This work constitutes a comprehensive investigation of pressure-dependent ETC, which is a key issue in heat transfer in porous media.

Main Heat Transfer Mechanisms in Hot Stamping Processes: a Review

Objectives: The article reviews heat transfer mechanisms in the hot stamping process, highlighting models to calculate the interfacial heat transfer coefficient (IHTC), crucial for optimizing the cooling and quality of formed products. Theoretical Framework: In hot stamping of high-strength steels, the IHTC is affected by variables such as contact pressure, roughness and temperature. Cooling efficiency directly impacts the temperature distribution and martensitic microstructure of the material, essential for structural strength. Method: The review compares IHTC calculation methods, such as inverse heat conduction analysis and Newton's law of cooling, detailing the convection, radiation and conduction mechanisms at each stage of the process: transfer, positioning and forming. Results and Discussion: The inverse heat conduction analysis proved to be the most accurate for determining the IHTC, compared to the finite element method (FEM). The study suggests that efficient cooling channels and high conductivity materials in the matrix reduce cooling time and improve the quality of the final product. Research Implications: Findings provide a basis for improving thermal management in hot stamping, reducing cycle time and increasing productivity. Originality/Value: This work contributes a comprehensive reference on IHTC, assisting researchers and engineers in optimizing heat transfer and production efficiency in the manufacture of automotive components.

A Physics‐Driven GraphSAGE Method for Physical Field Simulations Described by Partial Differential Equations

AbstractPhysics‐informed neural networks (PINNs) have successfully addressed various computational physics problems based on partial differential equations (PDEs). However, while tackling issues related to irregularities like singularities and oscillations, trained solutions usually suffer low accuracy. In addition, most current works only offer the trained solution for predetermined input parameters. If any change occurs in input parameters, transfer learning or retraining is required, and traditional numerical techniques also need recomputation. In this work, a physics‐driven GraphSAGE approach (PD‐GraphSAGE) based on the Galerkin method and piecewise polynomial nodal basis functions is presented to solve computational problems governed by irregular PDEs and to develop parametric PDE surrogate models. This approach employs graph representations of physical domains, thereby reducing the demands for evaluated points due to local refinement. A distance‐related edge feature and a feature mapping strategy are devised to help training and convergence for singularity and oscillation situations, respectively. The merits of the proposed method are demonstrated through a couple of cases. Moreover, the robust PDE surrogate model for heat conduction problems parameterized by the Gaussian random field source is successfully established, which not only provides the solution accurately but is several times faster than the finite element method in the experiments.

A sizing model for a tube in tube sensible thermal energy storage heat exchanger with solid storage material

Sensible thermal energy storage (STES) systems are generally the most affordable and least complex type of thermal energy storage systems available. The main question when modeling STES systems is the outlet state of the heat transfer fluid for a given inlet condition. Traditional heat exchanger design methods such as the logarithmic mean temperature difference method do not apply to TES systems since these systems do not operate in steady state. Other design methods are only applicable to specific cases such as packed bed systems with a thermocline. The present paper proposes a novel framework for STES system design with solid, stationary storage material. The framework is validated based on the case of a tube in tube STES system. The novel design model characterizes the local conductive heat transfer in the Laplace domain. This local behavior is integrated over the surface of the heat exchanger using three methods: a height split, a height lumped and a fully lumped approach. Each method corresponds to a different assumption regarding the temperature gradient in the storage material and will therefore be applicable to different cases. By numerically inverting the Laplace transform, a prediction is obtained of the outlet temperature of the HTF in the time domain. The solution is compared to the result of a computational fluid dynamics (CFD) reference model for five selected cases, with the CFD requiring calculation times in the order of days on a dedicated server while the novel model requires seconds on a laptop. This difference in calculation time is the result of the need of the CFD model to discretize the domain in space and apply a time stepping algorithm. The transfer function approach requires neither discretization nor time stepping but it does require a numerical inverse Laplace transform. The transfer function approach has a good fit with the CFD predictions. Furthermore, the quality of the fit and the behavior of the system is predicted based on the Biot number, the thermocline width ratio and the cross conduction number where the latter two numbers are derived in the present paper. The novel approach can provide a method to obtain sizing models for STES systems with a solid storage material.

Method for predicting conductive heat transfer topologies based on Fourier neural operator

This paper presents an iterative topology optimizer for conductive heat transfer structures based on the Fourier neural operator (FNO). A data-driven model based on FNO is trained to predict the temperature under different material distributions, different boundary conditions, and different thermal loads. A new method is used to generate data, which makes the modeling process of temperature predictor completely independent of the traditional optimization method. Then by coupling the trained temperature predictor with the solid isotropic material with penalization (SIMP) method, a new iterative topology optimizer is formed. Numerical experiments demonstrate that the proposed method can generate heat transfer structures with good performance, and can apply the model trained on low-resolution data to the structural topology optimization with high resolution, which greatly improves the optimization efficiency. In addition to the heat conduction structure optimization problem, the method developed in this paper is expected to be applied to other optimization problems or coupled with other conventional optimization methods

Interaction between vapor bubbles during flow boiling heat transfer in microchannels

Microchannel flow boiling is an efficient cooling solution for high-power-density miniaturized systems. Many studies on microchannel flow boiling focused on the dynamics of single vapor bubbles, while neglecting the interaction between bubbles, which is important in relevant applications. Here, numerical simulations are carried out to study the interaction between multiple vapor bubbles in microchannel flow boiling. The results show that for different numbers of bubbles in the microchannels with the same initial size and position of leading bubbles, the bubble size in a single-bubble microchannel is larger compared to the leading bubble of multiple-bubble cases because of heat absorption by the vaporization at the rear bubbles. As the initial volume ratio between the leading bubble and the rear bubble decreases, the leading bubble size in the downstream becomes smaller because of the reduced contact with the superheated thermal boundary layer. With increasing the Reynolds number, both the leading and the trailing bubbles increase slightly in size in the upstream of the heated region, because the bubbles at higher Reynolds number move faster and firstly get in contact with the superheated fluid. The increase in the bottom wall thickness increases the growth rate of the multiple bubble sizes with earlier bubble coalescence because of the higher upstream wall temperature by heat conduction in the solid wall.

THE EFFECT OF REPETITIVE METAL CASTING ON THE TENSILE STRENGTH OF DENTURES

Background: Dentures or prostheses function to replace chewing and dental arch structures. Denture plates used in dentistry are made with acrylic resin, metal, or a combination of acrylic and metal. Metals are shiny, opaque chemical substances and good conductors of heat and can be polished. Recycling or reusing used metal is an option in making prostheses because the price of new metal is increasing, and metal recycling is quite effective. Purpose: To determine the effect of repeated metal casting on the strength of the metal frame denture base. Method: The current research is a laboratory study with a tensile test in the form of dumbbells with iso 22674 with a length of 15 ± 1 mm and a diameter of 3 ± 1 mm. This research used 18 CoCr metal samples divided into three groups, namely 100% new metal group (control), 50% new + 50% repeated composition group, and 100% repeated group. Result: The mean strain of the new 100% CoCr metals group was 0.133%, strain mean of the new 50% CoCr + 50% repeated metals group was 0.1%, and the strain of the 100% repeated CoCr metals group was 0.066%. The average modulus of elasticity (MPa) for the new 100% CoCr metals group is 7866, or 711 MPa, the new 50% CoCr + 50% repeat metals group is 7538, or 833 MPa, the 100% CoCr metals group is 6659, or 336 MPa. Conclusion: The new 100% CoCr metal group has a higher average tensile strength value than the 50% new CoCr metal + 50% repeated group, and the lowest is the 100% repeated CoCr metal group.

Neural network analysis of bioconvection effects on heat and mass transfer in Non-Newtonian chemically reactive nanofluids

Using artificial neural networks, this study sought to investigate the magneto Williamson two-phase nanofluid, taking into account chemical reactions and the motion of gyrotactic motile microorganisms. Fluid flow behavior is influenced by chemical reactions, magnetic effects, Brownian motion, and thermophoresis, according to the study. Thermal transmission is enhanced in non-Newtonian fluids as a result of their propensity to thin under shear, increased turbulence, and superior convective heat transfer. As a result of the fluid's increased thermal conductivity, the incorporation of nanoparticles enhances heat conduction. Additionally, epidermis friction, Nusselt and Sherwood numbers, and the quantity of motile microorganisms were assessed in the study. The overall Absolute Errors lies in the range of 10−2to10−10.The mean squared error generated by Neural Networks lies in the range of 10−02−10−10, and 10−02−10−09 respectively. Suction or injection parameter and Prandtl number have an inverse relation with fluid temperature, while Thermophoretic parameter have a direct relation. Thermophoretic parameter, Schmidt number and suction or injection parameter have an inverse relation with the concentration of nanofluid and gyrotactic microorganisms' density, while micro-organisms density have a direct relation with the microorganisms. Engineering and medicine have utilized bioconvection, a process involving heat transfer and microorganism motion, in the development of nanomedicine, pharmacokinetics, drug delivery, and biosensors, among others. Solvers utilizing stochastic numerical computing include nonlinear networks, atomistic physics, thermodynamics, astrometry, fluid mechanics, nanobiology. As a result, variant scenarios are then tested, trained, and validated, in order to prove its accuracy.

Stability and thermo-physical characteristics of EG/H2O-based nanofluid with graphene nanoplatelets for secondary coolant applications

In the present article, the thermophysical properties of an EG-H2O dispersed with GNP nanofluid are studied. The graphene nanoplatelets were dispersed in a 50:50 volume ratio (1113.2:1000 by mass in g per litre) of EG and H2O along with Gum Arabic surfactant to create the stable nanofluid dispersions by varying vol% of GNP from 0.1% to 0.5% in steps of 0.1%. The stability of proposed GNP-EG/H2O nanofluid was found using the zeta potential distribution method. A thermal properties analyzer, densitometer and rheometer were used to measure the thermal conductivity (k) (heat conduction), specific heat capacity (Cp), density (ρ) and viscosity (µ) of the nanofluid. All the properties were measured with various temperatures ranging from −15 °C to 15 °C with interval of 5 °C. The outcomes of steadiness test performed and reveal that the GNP-EG/H2O nanofluid was stable and exhibits a zeta potential distribution of −33.7 mV at 0.5 vol% of GNP. The thermal conductivity and thermal diffusivity of nanofluid enhanced by about 8.6% and 10.43% respectively when compared to the base fluid while the specific capacity decreased by 8.96% at 15 °C for 0.5 vol%. The proposed nanofluid favorable for all volume concentration under laminar flow regime while it was favorable up to 0.1% under turbulent regime which observed from the predicted effectiveness.

The heating effect analysis of electromagnetic induction heating system based on the multi objective optimization strategy

Lithium-ion battery heating in cold weather is necessary to ensure its low-temperature performance and lifetime, so the multi objective optimization heating strategy based on the non-dominated sorting genetic algorithm II is introduced to improve the heating effect of electromagnetic induction heating system, in which the generated Pareto frontier as the research sample is input in K-medoid algorithm in order to reduce the feasible range of solution sets and then get the optimal induction coil parameters combination, and the temperature rise and terminal voltage output performance of battery are characterized by the electrochemical-thermal coupling model. Firstly, under the optimal parameters combination (N = 180, f = 9 kHZ, IA = 6 A), the battery can be heated from 243.15 K to 293.15 K in 1430 s with the temperature difference of 2.74 K, and the temperature field is mainly generated by the heat conduction from active material to mandrel during the heating process due to skin effect and material property. Secondly, the internal resistance is decreased by more than 3 times after the heating, giving rise to the substantial improvement of energy output ability. Finally, neither noticeable discharging capacity retention loss nor apparent voltage output difference is founded after the 200 repeated heating cycles, as compared with the normal charging-discharging cycle at 293.15 K, so the heating strategy has almost no effect on the battery aging and lifetime deterioration. Therefore, the proposed heating strategy can realize a suitable tradeoff among temperature-rising effect, lifespan and low-temperature operating performance, which has substantial potential to be a feasible method for improving the applicability of electric vehicles in a cold weather.

Investigating the impact of fin configuration on phase change material melting in square cells: A numerical study

This investigation thoroughly explores the effects of different fin arrangements on the melting behavior of phase change materials (PCMs), specifically paraffin wax (RT42), within a 50 × 50 mm2 square cell. Three distinct cases are considered: Case 1 involves no fins, Case 2 incorporates straight rectangular fins, and Case 3 employs undulated fins. To simulate real-world thermal energy storage conditions, the PCM container is thermally insulated, preventing external heat leakage. The primary objective is to identify the optimal fin arrangement to enhance latent heat storage system efficiency by improving both melting and solidification processes. The novelty of this research lies in the detailed analysis of various undulated fin geometries and their placements, which have not been extensively explored in previous studies. Numerical simulations were conducted using the ANSYS FLUENT solver. The progression of PCM melting was evaluated via the ANSYS design modeler based on the finite volume method, incorporating transient heat conduction and free convection. The results demonstrate that optimized undulated fin configurations can significantly enhance the melting process by promoting uniform temperature distribution and improving heat transfer rates, thereby reducing melting time. This study provides valuable insights for designing efficient latent heat energy storage systems, contributing to advancements in energy management and sustainable technologies.

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.

Effect of plant fibers on the physical properties of slurry-processed reconstituted tobacco.

The primary function of plant fibers in reconstituted tobacco is to enhance the physical strength, and it can quite modify their physical properties. This study demonstrated the effect of various plant fibers and their beating degrees on the physical properties of reconstituted tobacco. Tensile index, burst index, uniformity, tensile stiffness orientation, and thermal conductivity coefficient were examined. The result revealed that the mechanical properties of reconstituted tobacco varied according to the type and beating degree of the fibers. The mechanical properties of softwood, cotton, and bast fibers showed an initial increase followed by a decrease with increasing beating degree, while bamboo fiber showed a continuous improvement in mechanical properties proportional to the beating degree. Conversely, hardwood fiber displayed an inverse relationship with its beating degree. Under identical beating conditions, reconstituted tobacco containing softwood fibers showed the greatest improvement in tensile properties, achieving the highest tensile strength, thermal conductivity, and specific heat capacity. In particular, when softwood fibers were beaten to 50 °SR, the physical properties of the reconstituted tobacco peaked, with longitudinal and transverse tensile indices improving by 42.48% and 12.11%, respectively. Additionally, the bursting resistance index increased by 61.93%, and the thermal conductivity coefficient increased by 5.94%.