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• Numerical instability may occur during the calculation of CSF by using the BIEM/BEM. • The numerical instability of CSF is caused by the degenerate scale. • The mechanism behind numerical instability is a zero denominator. • The three regularization techniques can effectively treat degenerate scale. This paper not only derives an analytical solution for steady-state heat conduction problems in exchanger tubes but also can predict the location of numerical instability due to a degenerate scale in the boundary element method or the boundary integral equation method. Four shapes of the exchanger tubes including concentric annulus, eccentric annulus, confocal ellipses, and elliptical tube with a confocal crack are analytically studied by using degenerate kernels of polar, bipolar and elliptical coordinates, respectively. This work extends our prior research on numerical instability and its treatment for steady-state heat conduction problems in exchanger tubes using the dual boundary element method. Analytical solutions of the temperature field and conduction shape factor can be derived. Two main analytical tools, the degenerate kernel for the closed-form fundamental solution and the generalized Fourier expansion for the boundary densities in the null-field boundary integral equation are required. The analytical derivation process can clearly examine the occurring mechanism of numerical instability due to a zero denominator. The effectiveness of regularization techniques to promote the rank-deficiency by one to a full-rank system can be analytically examined in this paper. [ABSTRACT FROM AUTHOR]

• LaplacianFoam in OpenFOAM® solves the scalar diffusion equation. • Thermal diffusivity may be often incorrectly used in heat conduction problems. • It is tempting to make just a little change from a constant to a scalar field. • To correctly model heat conduction in heterogeneous media, ρ , c p and λ is needed. In the paper "Numerical study with OpenFOAM on heat conduction problems in heterogeneous media" by K. Zhang, C.-A. Wang, J.-Y. Tan, International Journal of Heat and Mass Transfer, Vol. 124 (2018) 1156–1162 the authors modify laplacianFoam from open-source CFD package OpenFOAM® to solve heat conduction problems in heterogeneous media by changing the diffusion coefficient from a constant value to a scalar field. Their paper clearly demonstrates a fundamental, overlooked, and common mistake in rearranging the heat conduction equation, which cannot be replaced with the temperature diffusion equation. In this comment, we provide clear evidence through mathematical derivations and numerical examples calculated in OpenFOAM®. [ABSTRACT FROM AUTHOR]

• Stabilization of boundary conditions obtained from the solution of the inverse problem. • Cooling inside a furnace intended for thermo-chemical treatment. • The impact of the regularizing term on the solution of the inverse problem. Heating and cooling inside a furnace intended for thermochemical treatment is the basis for the execution of processes characterized by lower energy consumption, and, thus, lower costs. Precise control of the thermochemical treatment requires knowledge of the temperature, heat flux, and the heat transfer coefficient (HTC) on the boundaries of the treated elements. The mentioned boundary conditions have been established in this paper for the cooling stage inside the furnace for thermochemical treatment by solving the inverse heat conduction problem. The paper analyzes the impact of regularization of the inverse problem on the stability of the calculated boundary conditions during cooling. Numerical tests were performed for the Tikhonov and Tikhonov-Phillips regularization as well as their modification. The computational method presented in the paper was developed for online control of thermochemical treatment processes. Online control necessitates minimizing computation time. The paper investigated the impact of the regularization term on the solution of the inverse problem with a constant value of the regularization parameter. The choice of regularization method was based on a norm that measures the oscillation of the solution of the inverse problem. The approach presented in the paper allowed for a reduction in computation time and the obtaining of a stable solution to the inverse heat conduction problem for both numerical tests and experimental data. [ABSTRACT FROM AUTHOR]

• An unstructured lattice Boltzmann model is proposed to solve radiative transfer in homogeneous media. • The equilibrium distribution function is reconstructed on the interfaces of the unstructured grids. • The unstructured LB model is stable and accurate for steady and transient radiative transfer in homogeneous media with complex geometries. • The unstructured LB model can greatly reduce the computational time compared to the standard LB model. In the past decades, the lattice Boltzmann method (LBM) has been a great success in convection and heat conduction. Recently, based on its advanced numerical properties, LBM has some progress in radiative transfer. Some lattice Boltzmann (LB) models for radiative transfer have been established successively. However, all these LB models for radiative transfer are standard LB models which are limited to uniform Cartesian grids. The unstructured LB model for radiative transfer is still lacking. The unstructured model is important for radiative transfer problems in complex geometric enclosures. Developing an unstructured LB model for radiative transfer is of great significance. This paper proposes an unstructured LB model for radiative transfer in homogeneous media. We establish this model by using the Chapman-Enskog (CE) analysis and the finite volume discretization. In this model, the equilibrium distribution function is reconstructed on interfaces of unstructured grids. Through the CE analysis, we rigorously derive the radiative transfer equation (RTE) from the proposed unstructured LB model. Several numerical cases are conducted to test the performance of the unstructured LB model. Numerical results show that the present unstructured LB model is stable and accurate for solving steady and transient radiative transfer in homogeneous media with complex geometries. Besides, the proposed unstructured LB model can greatly reduce the computational time compared to the standard LB model due to eliminating the streaming process on the uniform lattice. [ABSTRACT FROM AUTHOR]

• The magnetic fluid heat transfer in biological over a semi-infinite region is investigated. • Absorbing boundary condition is deduced by artificial boundary method. • The superiority of the absorbing boundary condition is discussed. • Important parameters of biological heat transfer and magnetohydrodynamic properties are analyzed. This paper introduces modifications to the classical Pennes' equation through the Cattaneo correction and considers the influence of a magnetic field on the heat generation of the fluid in a semi-infinite region. The traditional method to treat the problem in unbounded regions is to use a large interval to approximate the infinite region, which leads to large deviations of the solution at the truncated boundaries for a long-time numerical simulation. Using the artificial boundary method, the problem in infinite domains can be converted into an equivalent problem in the bounded domains with the absorbing boundary condition, of which the solution would be more physically reasonable and accurate. The governing equation subject to the absorbing boundary condition is discretized using the finite difference method and leads to effective numerical solutions. We analyze the effects of various parameters including the relaxation parameter, heat transfer coefficient, blood perfusion rate, blood tissue density, magnetic fluid concentration, magnitude, magnetic field frequency, and oscillatory boundary condition on the temperature distribution. The study validates the effectiveness of the absorbing boundary condition when addressing problems in unbounded regions. Some important findings are that the relaxation parameter has a delay effect on magnetic fluid heat transfer and magnetic fluid concentration, and the magnetic field strength and magnetic field frequency are directly proportional to magnetic fluid heat production. [ABSTRACT FROM AUTHOR]

• The heat transfer characteristics of different horizontal wires immersed in both liquid and supercritical carbon dioxide were studied by visualization experiments with a schlieren system. • Pseudo film boiling shown the similar heat transfer characteristics and near-wall flow field structure with subcritical film boiling. A correlation based on an integral mean Raleigh number predicted the Nusselt number well. • Experiments with various metal wires revealed distinct self-propagating transition phenomena in boiling modes, driven by the axial heat conduction characteristics. Near-critical and supercritical fluid heat transfer exhibits unique heat transfer characteristics. Pool heat transfer experiments circumvent the drawbacks of traditional flow heat transfer experiments, characterized by numerous factors and challenges in observation, and can offer new insights for the study of heat transfer mechanisms. In this paper, the heat transfer characteristics of different horizontal wires immersed in both liquid and supercritical carbon dioxide were studied by visualization experiments with a schlieren system. The study showed that as approaching the critical point, the pool boiling weakened, resulting in a decrease in the peak heat transfer coefficient. In supercritical cases, heat transfer with low heat flux maintained natural convection, while the cases with high heat flux exhibited similar heat transfer laws and near-wall flow field structures with subcritical film boiling. Meanwhile, experiments with various metal wires revealed distinct self-propagating transition phenomena in boiling modes, driven by the axial heat conduction characteristics. Based on the experiments, a pool heat transfer mechanism of the near-critical and supercritical fluids was proposed. [ABSTRACT FROM AUTHOR]

• Micromechanical modelling of the thermal conductivity of gas-solid mixture medium with imperfect interface. • Eshelby's ellipsoidal inhomogeneity problem. • Green's function technique and integral equation, • Ellipsoidal harmonics method for the thermal conduction inside gas-solid mixture medium. • Analytical expressions of local mean intensity and effective thermal conductivity. The present paper deals with the micromechanical modeling of the thermal conductivity of two-phase gas-solid mixtures with ellipsoidal inhomogeneities. In some structural morphologies, when the characteristic size of the gas-filled inhomogeneity is comparable to the mean path of the gas molecule, the classical heat conduction theory is no longer applicable to the regions very close to the solid interfaces. The present work assumes a sliding flow regime and a Knudsen number such that: 0 < K n ≪ 1. K n = λ / l where λ is the mean path of the gas molecule and l is the size of the inhomogeneity. In this situation, the thermal behavior of the gas can be described by the classical thermal conductivity with modified boundary conditions, considering discontinuities in the local heat flux and temperature fields across gas-solid interfaces. Within this framework, the solution of two problems involving a gaseous ellipsoidal inhomogeneity immersed in a solid matrix, and conversely a solid ellipsoidal inhomogeneity suspended in a gas, is developed. For the first problem, the proposed micromechanical approach is based on the use of Green's function technique and the integral equation established in the general case of anisotropic thermal conductivity per phase. For the second issue, the solution is obtained directly by solving the Fourier equation describing heat transfer in the heterogeneous medium. Then, the Mori–Tanaka (MT) method and the Differential (DS) Scheme are employed to express the effective thermal conductivity of the gas-solid mixture media. [ABSTRACT FROM AUTHOR]

Efficiently enhancing heat conduction through optimized distribution of a limited quantity of high thermal conductivity material is paramount in cooling electronic devices and numerous other applications. This paper introduces a target-driven all-at-once approach for PDE-constrained optimization and derives a splitting smoothed particle hydrodynamics (SPH) method for optimizing the distribution of thermal conductivity in heat conduction problems. In this method, the optimization iteration of the system is split into several easily addressed steps. A targeting step is employed to progressively enforce the direct target, which potentially leads to increased PDE residuals. Then, these residuals are recovered through an evolution step of the design variable. After this, a PDE solution step is carried out to further decrease the PDE residuals, and the system is ready for the next iteration. Unlike the simulation-based approaches, the present method does not rely on the adjoint state equation and converged state variable field in each iteration, and the optimization process is significantly simplified and accelerated. With the utilization of an implicit SPH splitting operator and a general numerical regularization formulation, the information propagation is further accelerated and the numerical stability is greatly enhanced. Typical examples of heat conduction optimization demonstrate that the current method yields optimal results comparable to previous methods and exhibits considerable computational efficiency. Moreover, the optimal results feature more moderate extreme values, which offers distinct advantages for the easier selection of appropriate material with high thermal conductivity. • The optimization of the heat conduction is split into several easily addressed weakly coupled steps. • The target is directly imposed on the temperature, and fields only converge at the termination. • The splitting SPH method is employed to implicitly update temperature and thermal conductivity. • General regularization formulation is proposed to guarantee numerical stability. • Optimal results with moderate peak values of thermal conductivity are obtained with good efficiency. [ABSTRACT FROM AUTHOR]

• HFE-7100 boiling curves from the onset of boiling to dry-out, in a vertical and rectangular mini-channel. • Local heat transfer coefficient (HTC) calculated with an inverse heat conduction method. • Influence of subcooling and pressure on heat transfer, pressure drop and flow patterns. • Increasing pressure improves the critical heat flux (CHF) and HTC, delays the dry-out, and reduces pressure drops. • Increasing subcooling improves CHF and HTC, delays the dry-out, and modifies the flow pattern. The background of this study is the problem of thermal runaway in the battery cells of electric vehicles. Increasingly powerful and compact battery packs require highly efficient thermal management. One potential solution is the direct liquid cooling of lithium-ion battery cells using a dielectric liquid which boils over a safety limit temperature. This approach intends to prevent in a first step the cell thermal runaway and if it fails in a second step its propagation to its neighbors: the liquid boiling helps to mitigate the cell temperature rise and to transport and spread the heat. The arrangement of the cells in the pack and their close spacing induce a scientific problem of convective boiling in a mini-channel. To enhance designs using this solution, a comprehensive understanding of flow boiling and a precise local heat transfer quantification is essential. The HFE-7100 has been selected as a working fluid for its attractive thermophysical properties and a suitable saturation temperature. The present paper introduces new experimental results of flow boiling dielectric fluid, the HFE-7100, in a vertical rectangular mini-channel. Measurements are carried out from start of boiling to dry-out. Boiling curves are obtained for a mass flux of 391 kg/(m².s), at different pressures (0.7, 1, 1.5 bar) and at different subcoolings (Δ T s u b = 0 ; 15 ; 30 ; 45 ∘ C). The test section is an aluminum block instrumented with three lines of five K-type thermocouples located all along the flow. The visualization of the flow is achieved through a glass pane with a high-speed camera to identify different flow patterns. The local heat transfer coefficient is calculated by a resolution of a 2D inverse heat conduction method. The experiment mainly aims at determining the heat transfer coefficient, the critical heat flux (CHF) and the pressure drop and at characterizing both the flow regimes and the dry-out phenomenon. The influence of subcooling and pressure on flow boiling is analyzed. An increase in subcooling enhances the CHF and the heat transfer coefficient, and delays the dry-out. Subcooling has an impact on the flow pattern and modifies the type of CHF. In the operating conditions tested, a decrease in pressure enhances CHF and delays dry-out. On the other hand, the heat transfer coefficient increases with rising pressure. Similarly, pressure drops are lower with higher pressure. [ABSTRACT FROM AUTHOR]

This paper analyzes the influence of the anomalous diffusive effects caused by micro-scale heterogeneity and kinetic and inertial thermal relaxations on the optically induced thermoelastic bending component of the photoacoustic response. We calculated the temperature distribution for a one-dimensional heat transfer problem with planar and periodic excitation, neglecting the influence of thermoelastic strains on the temperature profile. Thermoelastic bending was evaluated using a theoretical approximation of a thin plate, while pressure fluctuations in the photoacoustic cell were obtained by assuming adiabatic changes in the closed air. The model analysis shows that the relaxation processes could significantly affect the mechanical piston component of the photoacoustic response at frequencies higher than the minima of the inverse of two thermal relaxation times, while the influence of micro-scale heterogeneity is observable in the whole frequency range. • The hyperbolic DPL model enhances accuracy of thermoelastic effect at higher frequencies. • Sensitivity to fractional order of DPL model emphasizes precision in TE control. • Anomalous DPL heat diffusion shifts and attenuates the peak of the hyperbolic result. • Maximum damping occurs to identical kinetic and thermal relaxation times. [ABSTRACT FROM AUTHOR]

• Application of MCrAlY coating to increase heat transfer during water spray cooling. • The use of the coating intensifies heat transfer compared to the uncoated surface. • The thickness of the coating affects the intensity of the heat removal. The main purpose of the paper was to determine the influence of NiCoCrAlY coating application and its thickness on the heat transfer during water spray cooling under surface boiling conditions. The scope of the research included: sensor preparation, measurements of the sensor temperature during cooling, and numerical calculations to determine the intensity of sensor cooling. The intensity of heat removal was determined by the average values of the heat flux on the cooled surfaces. The inverse method for the heat conduction equation was used to determine the heat transfer boundary conditions. Temperature measurements during cooling were carried out for an initial sensor temperature of 500°C, 700°C and 900°C and a liquid pressure 0.1 MPa, 0.2 MPa. Due to this, it was possible to select a coating thickness that contributed to the greatest extent to the increase in the intensity of heat dissipation from the hot surface. The highest values of the heat flux were obtained during the cooling of the sensor with a 134.5 μm coating. [ABSTRACT FROM AUTHOR]

• The chemical source term is the main control factor of thermal runaway. • The higher the temperature intensity, the shorter the explosion delay time. • The critical temperature of thermal runaway for AP/HTPB propellant is 458 K. • If the propellant is thick enough, the temperature distribution remains constant. For the safe use of solid rocket motors, it is crucial to investigate the thermal effect of AP/HTPB propellants. Transient high temperature may cause AP/HTPB propellants to burn or explode, resulting in serious damage. The fundamental equations that describe the thermal effect of AP/HTPB propellants are the heat conduction differential equation and Arrhenius law. In this paper, the thermal safety of AP/HTPB at transient high temperature is obtained by solving the heat conduction differential equation. The results show that the chemical source term S (T) is the main control factor of thermal runaway. When the action duration of the external high-temperature is short (ms-s magnitude), the first explosion occurs closest to the high-temperature source. When the action duration of the external high-temperature action is long (min-h magnitude), the first explosion occurs inside the propellant. The higher the high-temperature intensity of external action, the shorter the explosion delay time, but the explosion temperature does not change accordingly. The critical temperature of thermal runaway is 458 K under the condition of no shell and a high-temperature action duration of 2 h. At high-temperature intensities of 458 K, 459 K, and 500 K, the propellant explosion temperatures are 533 K, 539 K, and 540 K, and the explosion delay time is 1592s, 1102s, and 160 s, respectively. The critical duration of thermal runaway is 430 ms, 650 ms, 1350 ms, and 9820 ms, and the stable explosion delay time is 450 ms, 680 ms, 1400 ms, and 9920 ms, respectively, under the conditions of 2000 K, 1500 K, 1000 K, and 600 K without the shell. The propellant explosion temperature remains constant as the shell thickness grows while the explosion delay time gradually increases. When the propellant is thick enough, the temperature distribution of the system remains constant. The results of this study may be useful as a guide for assessing the thermal safety of AP/HTPB propellant. [ABSTRACT FROM AUTHOR]

• A novel numerical framework is developed for transient heat conduction problems. • The present method is of arbitrary order of accuracy in both space and time. • The developed method allows for the utilization of large time step sizes. • The present method exhibits high stability, rendering it well-suited for long-time simulations. This paper presents an arbitrary order numerical approach for achieving highly accurate solutions in transient heat conduction problems. In this framework, the arbitrary order Krylov deferred correction method (KDC) is first utilized to discretize the temporal direction of the problems, ensuring high-accuracy results by selecting an adequate number of Gaussian nodes. During each time iteration, a boundary value problem in terms of the inhomogeneous modified Helmholtz equation is generated by utilizing the KDC methodology. Subsequently, the arbitrary order GFDM is introduced to solve the boundary value problem, allowing for flexible selection of the Taylor series expansion order to improve spatial accuracy. Consequently, the present numerical framework is of arbitrary order of accuracy and very stable through integrating advantages of the arbitrary order KDC and the arbitrary order GFDM. The developed numerical framework is ultimately verified for its characteristic of high accuracy and stability through two numerical examples in two-dimensions and three numerical examples in three-dimensions. The results highlight the significant improvement in numerical accuracy achieved by the present arbitrary-order numerical approach for long-time simulations. [ABSTRACT FROM AUTHOR]

• Semi-analytic methods are used to solve 3D DPL problems. • Compared with FEM, the semi-analytic method has higher computational efficiency. • The phase lag of heat flow and the phase lag of temperature gradient have influence on the temperature response speed and the formation of temperature field. With the development of picosecond laser technology, the dual-phase-lagging (DPL) model is more suitable to describe the heat transfer problem with micro-scale effect and micro-time effect. In this paper, a three-dimensional dual-phase-lagging heat transfer model for picosecond laser processing is established. Then Fourier transform (FT) and Laplace transform (LT) are used to derive the frequency response functions (FRFs) of the problem in the frequency domain, and the inverse Laplace transform (ILT) and discrete-convolution fast Fourier transform (DC-FFT) algorithm are used to solve the temperature field. The calculation accuracy of this method is verified and the effect of phase lag constants on temperature field is studied. The results show that the semi-analytical method has a high accuracy for solving the dual-phase-lagging heat conduction model, and the phase lag of heat flux will affect the heating rate in the heating stage, and the phase lag of temperature gradient will delay the formation of temperature field. The effect of phase lag constants on temperature-time history is investigated and the related phenomena are explained by using the two-step heat transfer theory. This semi-analytical method provides a new approach to solve the problem of three-dimensional dual-phase-lagging heat transfer. [ABSTRACT FROM AUTHOR]