Heat Conduction Method Research Articles

Development and Investigation of Nitrate Phase Change Filler Material for Solar Process Heating Applications

Thermocline thermal energy storage system is an imperial system for solar process heating applications. The thermal energy storage system comprises filler material and heat transfer fluid. In the present study, the commercial phase change material (PCM) (filler material) solar salt (60%NaNO3+40%KNO3) is synthesized, and it is encapsulated with a 1mm thickness of stainless steel 316L encapsulation with the macro-size of 60mm; the encapsulated PCMs is considered as a single particle in the thermocline thermal energy storage system. The performance of the single encapsulated PCM is studied with a constant heat transfer fluid (Therminol-VP1) flow rate of 0.00015 kg/s during the charging process. The specific heat of the solar salt is measured in Differential Scanning Calorimeter (DSC) in the solid phase is found as 1.381 J/gK, and liquid phase is identified as 1.551 J/g-K, the enthalpy during the phase change process is found as 116.72 J/g. As well, the thermal conductivity of the solar salt is measured in Transient Heat Conduction method, and the thermal conductivity follows the linear relationship of -0.0025(T)+0.4023 (45ºC<T<100ºC) in the sensible region. The temperature variations and the phase change phenomena for the solar salt is identified and the contours are provided. The charging time for the encapsulated solar salt is identified as ~138 minutes. The energy storage cost for the single filler material (Solar Salt + SS316L encapsulation) is identified as Rs.5.93/- (USD 0.071) for the period of charging duration.

Topology optimization method for transient heat conduction using the Lyapunov equation

This study presents a novel topology optimization approach for transient heat conduction during the transition period based on the Lyapunov equation. For the problem under consideration, traditional topology optimization methods face computational challenges due to the time dependence of the transient responses. To address this issue, this article introduces a new optimization formulation that contains a modified governing equation for transient heat conduction and a new objective function. The new formulation aims to simplify the evaluation of transient response performance by utilizing the Lyapunov equation, thereby avoiding time-consuming transient analysis during the optimization iteration process. Additionally, this study employs model reduction techniques to reduce the size of the analysis model and further enhance the efficiency of the optimization process. After comparing two classic methods, the Proper Orthogonal Decomposition (POD) method is selected for its higher efficiency. Numerical examples consider both heat conduction and temperature control problems, employing 2D and 3D models to validate the proposed method's effectiveness. The results of the point-to-point heat conduction example indicate that, compared to the conventional design, the optimized topology design obtained using the proposed method successfully reduce the heating time by approximately 35%. Furthermore, the optimized designs display clear distinguishing features from conventional designs, further emphasizing the significance of implementing transient heat conduction topology optimization.

A new analytical method for transient heat conduction in composite disks applied to thermal plug and abandonment of oil wells

A new hybrid method for transient heat conduction problems is developed and applied to simulate a Plug and Abandonment (P&A) operation of oil wells. An oil well is approximated by concentric disks in a one-dimensional configuration, which allows for use of polar coordinates. The application of the Separation of Variables Method (SVM) is used as the analytical framework for the solution of the conductive heat transfer arising from a volumetric heat source located in the center of the disks. The SVM is able to solve only time-independent boundary conditions. However, using the Duhamel's theorem, the solution determined with the SVM can be used to achieve the solution when both time-dependent boundary conditions and internal heat generation are prescribed. Lastly, for verification purposes, a commercial software that solves the transient temperature field by means of numerical procedures, providing reliability to the analytical method proposed in this work.

Effects of temperature gradients on thermomechanical fatigue of nickel-based superalloy

Temperature-gradient-mechanical fatigue (TGMF) is a significant concern in internal cooling turbine blades. In the present study, the through-thickness temperature gradient was determined by the inverse heat conduction method and investigated in TGMF. Using the continuum damage mechanics, the environmental impact was identified as the primary contributor to the in-phase TGMF damage. A damage accumulation model encompassing fatigue, creep and environmental impact was established and provided satisfactory accuracy in TGMF life assessments. The main conclusion is that temperature gradients do not change the fracture mode but significantly increase stress levels by at least 20%, accelerating oxidation damage and resulting in a TGMF life ca. 10 times shorter than that of TMF.

Experimental research on the thermal performance of the dry conduction plate for multi-point electronic chips

This paper designs a dry conductive heat dissipation method using several parallel heat pipes to solve the difficulty of the thermal management problem of multi-point electronic chips. The heat sources are distributed along the heat pipe, whose heat is efficiently conducted from the middle to the cold plate on the two sides. The effect of gravity, flow rate, and heat source distributions on the heat transfer performance is studied. The testing data indicated that gravity has less effect on the conduction performance of heat pipes for the cooling on two sides. As the heat sources concentrate in the centre, the heat pipe temperature difference between the centre and the side increases under the same transmission power. The results demonstrated that the two-side cooling and multi-point distribution heat conduction method is conducive to improving the thermal management capability under different inclination angles.

The Influence of B4C Film Density on Damage Threshold Based on Monte Carlo Method for X-ray Mirror.

The uniformity and consistency of X-ray mirror film materials prepared by experimental methods are difficult to guarantee completely. These factors directly affect the service life of free electron laser devices in addition to its own optical properties. Therefore, the quality of the film material, especially the density, has a critical effect on its application. Boron carbide film and monocrystalline silicon substrate were suitable examples to explore their influence of density on the damage threshold based on Monte Carlo and heat-conduction methods. Through simulation results, it was found that the change in film density could affect the energy deposition depth and damage threshold. When the film density was 2.48 g/cm3, it had relatively high damage threshold in all energy ranges. And then the specific incident parameter for practical application was investigated. It was found that the damage mechanism of the B4C/Si was the melting of the interface. And the damage threshold was also higher with the film density of 2.48 g/cm3. Therefore, it was recommended to maintain the density at this value as far as possible when preparing the film, and to ensure the uniformity and consistency of the film material.

Coupling transport equations to mechanics in the material point method using an approximate full capacity matrix inverse

Coupling solutions of one or more transport equations to mechanics modeling in the material point method (MPM), extends MPM to a platform for solving multi-physics problems. Unfortunately, the standard MPM approach to transport equations using a lumped transport capacity matrix is prone to large oscillations in particle values especially near interfaces, cracks, or rapid changes in transport value. Switching from lumped capacity matrix methods to an approximate full capacity matrix approach can eliminate those oscillations. Although this switch can cause unwanted numerical diffusion, that problem can be suppressed using periodic or blending options. Several examples illustrate the new methods for heat conduction, solvent transport, poroelasticity, and phase field fracture simulations. In thermal calculations, the new methods improve accuracy for tracking thermodynamics state functions.

Real-Time Data-Driven Inverse Heat Conduction Method for a Reentry Flight Vehicle Based on the Random Forest Algorithm

Real-Time Data-Driven Inverse Heat Conduction Method for a Reentry Flight Vehicle Based on the Random Forest Algorithm

Electrowetting assisted shedding of droplets by a shearing airflow in dropwise condensation

Condensation is a necessary part of most industrial processes dealing with phase change. Efficient condensate removal (shedding) increases the systems’ performance. This study investigated the influence of electrowetting on droplet shedding and heat transfer enhancement during humid air condensation on a horizontal substrate. A mini closed-looped wind tunnel was used to simulate the condensation environment and control condensation parameters. AC electric field with the frequencies of 1 and 10 kHz was applied and compared with the control case (no voltage). The transient inverse heat conduction method was used to determine the heat transfer coefficient, and heat transfer measurements were synchronized to a high-resolution camera to monitor the condensation dynamics. The results show that the area-weighted average droplet radius was increased by 61 % and 84 % for 1 kHz and 10 kHz, respectively, compared to the control case for 1 m/s airflow. At 10 kHz, the shedding time was reduced, particularly at higher airflow velocities. Additionally, the heat transfer coefficient (HTC) exhibited a significant increase at 10 kHz when shedding was present. Notably, the difference in HTC became pronounced at an airflow velocity of 15 m/s, where shedding was prominent. In this scenario, the HTC rose by an impressive 35 % compared to the control case. These findings provide a promising foundation for utilizing EW to enhance heat transfer and improve condensate shedding under shear flow conditions.

Hybrid Trefftz finite element method for heat conduction in cylindrical composite laminates

Laminated composites are made of continuous fibers and matrix which can provide required engineering properties. This paper proposed a hybrid Trefftz finite element method for the analysis of conductive heat transfer in cylindrical composite laminates by assuming two independent temperature fields. The non-conforming intra-element field which is approximated by a linear combination of T-complete solutions satisfying the governing equation and undetermined coefficients is defined within the element domain, while the auxiliary conforming frame field which is interpolated by standard one-dimensional shape functions is defined on the element boundary. Due to the fabrication characteristics of laminates, each layer can be treated as an orthotropic medium for which the hybrid functional is employed to enforce the continuity of temperature and heat flux across the interface of adjacent elements. The proposed method is tested on three numerical examples and compared with exact or ABAQUS solutions. It was found that the proposed method exhibits low sensitivity to mesh distortion and achieves more acceptable results compared with ABAQUS.

Hyperbolic lattice Boltzmann method for three-dimensional non-Fourier heat conduction with phase change

The study described the simulation of 3D non-Fourier heat conduction with phase change using a hyperbolic lattice Boltzmann method (HLBM). The equilibrium distribution function was modified for the temperature to develop a new approach for handling the latent-heat source term. Unlike the commonly used lattice Boltzmann method (LBM), the hyperbolic collision operator was used in the HLBM process. The approach enabled the recovery of the enthalpy conservation equation and avoided the need for iteration stages or solving groups of linear equations. This suggests that the approach is more efficient and accurate than previous methods. Overall, the study demonstrates the potential of using HLBM for simulating complex thermal processes, particularly those involving phase change. The method could be useful in various applications, such as in the design of efficient heat exchangers or in understanding the behavior of materials during phase transitions.

Multi-source directional heat conduction method based on coordinate transformation

Based on the optical transformation theory, the formal invariance of the heat conduction equation was used to realize the transformation of constitutive parameters of heat conducting materials through coordinate transformation, so as to control the distribution of heat flow in physical space. In addition, based on the research on the control method of heat flow propagation path, a multi-heat source directional heat conduction method with complex boundary was studied for the case where the object is affected by a variety of internal and external heat sources, and the temperature field is uneven, resulting in irregular deformation. Based on translation transformation and compression transformations, the thermal conductivity distribution of the material was derived for the directional heat conduction structure. And the controllable propagation of heat flow from high temperature region to low temperature region was realized. By analyzing three distributions of multiple heat sources, applicable directional heat conduction structures with multiple sources and complex boundaries were designed to realize passive control of temperature field. The performance of directional heat conduction structures in transient state was analyzed by Comsol software simulation, where the direction of the heat flow is observed through the temperature cloud. Then, from the comparison graph of the average temperature of different sides of the heat conduction structure after 60 min, it can be concluded that the difference between the average temperature of different areas decreases, and the temperature field of the structure becomes more uniform.

Study of flow boiling in a vertical mini-channel with surface structuring: Heat transfer analysis using inverse method

Using a boiling fluid to cool components is a very efficient process, which is often used in micro/mini channel flows. A proposed application is the direct contact liquid cooling of lithium-ion battery cells, where a dielectric fluid is required and where the effects a cell thermal runaway could be mitigated by a convective boiling flow between the cells. For such applications, better designs require both to understand confined convective boiling with coupled flow phenomena and to quantify the local heat transfer accurately. The present paper introduces new experimental results of flow boiling heat transfer of a dielectric fluid, the HFE-7100, in a vertical rectangular 1 mm deep, 30 mm wide and 120 mm long mini-channel. The test section is an aluminum block instrumented with three lines of five K-type thermocouples located all along the flow. The experiment mainly aims at determining the heat transfer coefficient and CHF and at characterizing both the flow regimes and the dry-out phenomenon. Measurements are carried out from start of boiling to dry-out, at different mass fluxes (140, 390 and 648 kg/(m2.s)) and at a pressure of 1.1 bar. These tests were performed on a reference unmodified surface and compared to two biphilic surfaces including coating techniques. 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. This approach uses a numerical Finite Difference Method (FDM) for the spatial discretization and a Tikhonov's method for regularization. The inverse 2D method permits to follow the evolution of the heat transfer coefficient along the channel with the visualized flow pattern. The experimental results show a small sensitivity of the mass flux on the heat transfer coefficient and a predominance of nucleate boiling. On the other hand, there is a significant sensitivity of the mass flux on the dry-out occurrence. Finally, the sensitivity of two techniques of biphilic surface coating on boiling and on the dry-out occurrence is quantified and discussed.

Frequency Tuning of In-Plane Comb Drive MEMS Resonators Due to VO2 Phase Transition

This letter reports the thermal-mechanical tuning capability of an in-plane comb drive resonator using VO2 phase transition material. By inducing the insulator-to-metal transition (IMT) using a heat conduction method, a shift of approximately 2% was observed. The frequency tuning was attributed to the induced stresses during the IMT. [2022-0200]

Solutions of one-dimensional inverse heat conduction problems: a review

Estimations using the inverse conduction approach to predict temperature and heat flux at the exposed surface lead to indirect measurements away from the exposed surface within the solid. The approach is extremely useful when access to direct measurements is not possible due to various working conditions, and thereby provides estimates without disturbing the flow under the real flow condition over the surface. The approach is useful not only for heat transfer applications but also for numerous engineering applications, including fluid mechanics and furnace applications. The approach requires the time history of effective parameters at the strategic locations away from the exposed surface to be known. In the present paper, a review of sequential development of various inverse heat conduction methods is presented to get solutions in different geometries.

Analytical modelling of transient thermal characteristics of precision machine tools and real-time active thermal control method

Thermal error is one of the primary factors affecting the machining accuracy of precision machining tools. Therefore, it is important to study the transient thermal characteristics of machine tools and the thermal-error control strategies. Thus far, a transient analytical modelling method for characterising the thermal characteristics of machine tools was proposed and an active error control strategy was provided. First, temperature-field modelling was conducted using an analytical method based on the Fourier series method and partial differential equations of heat conduction. Second, using the derived temperature field, the thermal deformation field was calculated based on finite element theory. Subsequently, the continuous real-time effect of the thermal power per unit heat source on the temperature and deformation fields of precision machine tools was studied. The proposed analytical modelling method not only predicts the machine tool heat deformation based on the working conditions of the heat source, but also matches the thermal control source power with the demand of the machine tool heat deformation. The optimal real-time power of the thermal control source is dynamically iterated and matched, such that the thermal deformation caused by the heat and thermal control sources can be balanced in real time at the displacement control point. Finally, the volumetric thermal error was actively controlled by adjusting the temperature field of the machine tool.The simulated and experimental results indicate that the transient analytical model can accurately predict the real-time thermal characteristics of the machine tool and that the real-time active thermal control method can effectively reduce volumetric thermal errors. Using active thermal control, the squareness error in the YZ-plane was reduced by approximately 45%, the spindle thermal elongation was reduced from 23 μm to 7 μm, and the volumetric thermal error in the X, Y, and Z directions were reduced by approximately 16, 14, and 17 μm, respectively.

Experimental investigation of heat transfer characteristics of polyethylene glycol (PEG) based quench media for industrial heat treatment

Aqueous polymer quenchants are now increasingly used in the quench hardening of steels. The inverse solubility property of polymer media leads to polymer film encapsulation of the quenched component, followed by an instantaneous rupture of the polymer film. The film boiling stage is absent, thus improving heat transfer uniformity. In the present investigation, the effect of molecular weight of Polyethylene glycol (PEG) on heat transfer characteristics of PEG/water quenchants with concentrations of 5, 10, and 20 vol% was studied. The cooling curve analysis is performed to assess the cooling characteristics. Spatially dependent surface heat flux transients are estimated using the inverse heat conduction method. The rewetting kinematics is analyzed by videography and acoustic analysis of polymer film rupture during quenching. The results indicated that an increase in the molecular weight of PEG from 200 to 6000 changed the rewetting kinematics from a local wetting front movement to an instantaneous rupture of the polymer film. The change in the rewetting kinematics is reflected in the surface heat flux, indicating an increased uniformity of heat transfer. The film rupture acoustics showed that the polymer film's instantaneous breakup had a higher sound intensity than the one showing wetting front motion.

Effective thermal conductivity simulations of suspensions containing non-spherical particles in shear flow

Suspensions of oblate spheroid particles can have different thermal characteristics from suspensions of spherical particles based on its orthotropic geometry. However, the effective thermal conductivity of non-spherical particle suspensions under shear flow conditions has not been reported yet. In a first step dilute suspensions are considered ignoring particle-particle interactions, and a representative volume is observed containing one single oblate spheroid rotating at the center coupled to the shear flow. The fluid-side convective heat and mass transfer is computed by the Lattice Boltzmann Method (LBM). And the Discrete Element Method (DEM) accounts for particle dynamics, while the Finite Element Method (FEM) for heat conduction inside particles. Three codes are coupled together. As predicted by Maxwell’s model and the model of Nan et al., the effective thermal conductivity of a water suspension would saturate if the conductivity of the particle exceeds 20∼30W/(mK) at stagnant state, because the thermal resistance of the particles becomes negligible in comparison to the fluid thermal resistance. The simulation results in this study confirm such saturation also to a shear flow. Besides, another saturation mechanism exists for spherical particles if the shear rate is increased to a point where particle rotation induces convective transport that supersedes conductive transport within the particle. However, this is not the case for the oblate ellipsoidal particles due to different rotating states. And comparing different rotating states, if the particle’s thermal conductivity is higher than the base fluid, the shear-induced rotation around the oblate minor axis (log-rolling) results in a higher effective thermal conductivity than around the oblate major axis (tumbling) or the rotation of a spherical particle of equivalent volume fraction. The results provide a design guideline for particle in suspensions with better heat transfer behaviors.

Investigation of reacting fuel jets in hot vitiated crossflow

Near-wall reacting jets can occur in different engineering applications, such as rocket combustion chambers and in gas turbine combustors and turbines. This work presents results of experimental investigations of reacting gaseous fuel jets (hydrogen, methane, propane) injected normally into a hot oxygen-rich cross-flow using OH laser-induced fluorescence and OH* chemiluminescence diagnostics. RANS CFD simulations with EDC combustion model are performed for comparison. To determine the surface heat fluxes, the inverse heat conduction method was applied using measured wall temperature data as input. It was observed, that hydrogen jets ignite directly at the injection location and caused a higher surface heat flux than the hydrocarbon jets, where jet-like diffusion flames emerged. With the latter fuels, a significant ignition delay length was observed. Operation with methane fuel showed the least stability, least reactivity and the lowest surface heat flux. Increasing the jet momentum ratio led to a reduced ignition delay length due to enhanced jet-crossflow interaction, and to a reduction of surface heat flux as the reacting jet detached more from the surface. CFD results using the Eddy-Dissipation Concept (EDC) combustion model predicted ignition delay lengths and reaction zone shapes in qualitative agreement with the experiment but with a trend of overestimating combustion temperatures.

Heat Transfer Characteristics of Fullerene and Titania Nanotube Nanofluids under Agitated Quench Conditions.

Distilled water and aqueous fullerene nanofluids having concentrations of 0.02, 0.2, and 0.4 vol % and titania (titanium dioxide, TiO2) nanofluids of 0.0002, 0.002, and 0.02 vol % were analyzed for heat transfer characteristics. Quenching mediums were stirred at impeller speeds of 0, 500, 1,000, and 1,500 RPMs in a typical Tensi agitation system. During the quenching process, a metal probe made of ISO 9950 Inconel was used to record the temperature history. The inverse heat conduction method was used to calculate the spatial and temporal heat flux. The nanofluid rewetting properties were measured and matched to those of distilled water. The maximum mean heat flux was 3.26 MW/m2, and the quickest heat extraction was 0.2 vol % fullerene nanofluid, according to the results of the heat transfer investigation.