Values Of Thermal Contact Resistance Research Articles

Inverse Estimation of Thermal Contact Resistance Between Two Layers of Cylindrical Wall

This study presents a method for estimating the space-dependent thermal contact resistance between the two-layer walls of a furnace using the boundary element method (BEM) and conjugate gradient method (CGM) for the heat conduction problem. The global solution equation in matrix form is derived using the interface conditions, and the BEM is used to solve the direct problem. The CGM minimizes the objective function and calculates the sensitivity coefficients with the complex variable derivation method (CVDM). Comparative results show that the present approach is more accurate, stable, and efficient than the conventional CGM, which is attributed to the calculation of the sensitivity coefficients by CVDM. The effects of the value of thermal contact resistance, thermal conductivity ratio, Biot number, initial guess, measurement error, and the number and position of measurement points on the inversion results are also analyzed. Finally, the effectiveness of this approach is demonstrated through numerical examples, and the inversion results show its stability, efficiency, and accuracy in identifying different and complex distributions of thermal contact resistance. Furthermore, this approach is feasible for nonintrusive measurement, which is very meaningful in practical applications.

A numerical framework for three-dimensional optimization of cooling channels in thermoplastic printed molds

The rapid progress of additive manufacturing (AM) technology in the last few decades has unlocked new potentials for the injection molding industry by enabling the quick and cost-efficient manufacture of molds with complex geometries Despite the wide literature regarding experimental investigations on AM polymer-based soft tools specifically produced to cope with low-volume production of small-sized injected parts, their lifespan remains uncertain, and premature failures are often related to poor thermal performance. This paper is devoted to the numerical study and enhancement of the heat transfer within a thermoplastic 3D printed insert with cooling channels (CCs). Experimental thermal characterization is performed on printed composite samples made of polycarbonate reinforced with carbon fibers, considered as tool material. The simulations are performed on an industrial case, thereby facilitating a comprehensive validation of the proposed framework. Parametric studies show a marked cycle time sensitivity to insert thermal conductivity within the 0.1–1.0 W/(mK) range while demonstrating negligible influence on cycle times for polymer–polymer thermal contact resistance values below 10−3m2K/W. Furthermore, to find a suitable arrangement of the CCs’ layout, we propose here an accurate optimization methodology based on 3D overset meshes in the finite element method context coupled to the augmented Lagrangian particle swarm optimizer. The optimized bent CCs’ configuration enhances part surface temperature uniformity by 42% and reduces its temperature delta by over 6∘C, all while employing 67% of the reference cycle time. The thermal shortcomings of the thermoplastic AM mold, compared to its steel counterpart, are also addressed in this work.

Meta‐analysis of thermal contact resistance in injection molding: A comprehensive literature review and multivariate modeling

AbstractThis article provides the first multivariate analysis of reported thermal contact resistance (TCR) values from different characterization approaches (injection and compression molding) having missing data. The missing data are estimated by principal components analysis (PCA) with alternating least squares (ALS), and then the main effects are modeled using multiple regressions. Three models of increasing complexity are presented, each of which provides reasonable model fidelity relative to the TCR values reported in the literature. The primary cause of differences between reported TCR values as characterized by injection molding and compression molding can be explained by the melting of the polymer to make intimate contact with the metal mold during processing. Typical values of TCR are on the order of 0.0002 m2K/W, corresponding to heat transfer coefficients of 5000 W/(m2K). The analyses suggest that the TCR decreases significantly with increasing processing temperature and pressure but increases most significantly during cooling with the development of an air gap between the polymer and mold. Accordingly, it is strongly recommended that injection molding simulations incorporate modeling of the TCR as a function of the processing states for accurate prediction of the air gap, residual stresses, shrinkage, and warpage.Highlights Multivariate analysis of thermal contact resistance data from the literature. Sparse data handled by principal component analysis and alternating least square. Comparison of injection molding and compression molding measurements. Results suggest thermal contact resistance should be modeled as a function of the processing states.

Thermal contact resistance measurement between two intersecting PAN type carbon fibers using the T-type 3ω method

The prediction of the effective thermal conductivity of composites filled with carbon fibers requires the knowledge of the microstructure, the relative amount and thermal properties of filler and matrix materials, the orientation of non-isometric filler phases and the thermal contact resistances between fibers and matrix and also between fibers. However, information at small scale are often missing especially thermal contact resistances. The present work describes the measurement of the thermal contact resistance (TCR) between two crossed carbon fibers which is performed by an adaptation of the T-type 3ω method for thermal conductivity measurement of wires. The first carbon fiber is connected to two copper blocks supplied by a modulated electrical current providing a volumetric heating. The second fiber fixed on a U-shape holder is delicately implemented over the first one. After performing a secondary vacuum, the 3ω voltage V3ω of the first fiber is recorded as function of the frequency of the modulated current. Knowing the applied force, the contact area between the two carbon fibers is calculated from bending and deformations then a 3D numerical model describing heat transfer in two crossed carbon fibers is used to estimate the TCR at their intersection. In addition, a detailed sensitivity analysis of the unknown parameter TCR is performed allowing to find optimal operating conditions especially the frequency range. Measurements are performed with PAN type carbon fibers (FT300B) picked up from the same bundle. Different TCR estimations were performed by fitting numerical and computed V3ω voltage as function of frequency. Finally, values of TCR between crossed carbon fibers were found equal (10.4 ± 10.1) 105 kW−1 which provides an order of magnitude for such phenomenon.

Experimental Analysis of Heat Transfer at the Interface between Die Casting Molds and Additively Manufactured Cooling Inserts

The rate of heat transfer to the mold during solidification determines the cooling rate of castings, which significantly impacts their characteristics. The use of an insert produced by additive manufacturing in the mold, with appropriately designed cooling channels, enables adequate cooling control of the entire piece. This article investigates the heat transfer properties at the interface between two types of steel used for die casting molds (steel A) and additively manufactured cooling inserts (steel B). The study analyzed the impact of coolant water flow rate channel (215, 300, and 425 mL/min.) and contact pressure between the two types of steel (0, 15, and 30 bar) on the thermal behavior of the mold/insert assembly in both transient and steady states. The time constants of the system associated with the coolant flow rate transitions from 215 to 300 mL/min and from 215 to 425 mL/min were determined during the transient mode. The findings indicated that increasing the proximity of the cooling channel to the interface, coolant flow rate, and contact pressure resulted in a faster cooling response in the transient state. For the tested conditions, the determination of thermal contact resistance (TCR) was carried out in the steady state. The TCR values were affected by the contact pressure between the two steel pieces, showing, with an increase of 30 bar, a decrease of 21% and 33% for cooling channels located at 6.5 and 9.5 mm from the interface, respectively. Within the tested range, the TCR values were not significantly affected by variations in cooling flow rates. Lower TCR values were observed when the cooling channel was positioned closer to the interface (~ 28%). The study provides valuable insights into the factors affecting thermal contact resistance and process parameters. It can aid in optimizing cooling insert design for casting molds, namely by numerical analysis.

Research on thermal contact resistance between C/C and resin thermal protection materials for solid rocket motor nozzles considering real surface roughness

C/C composite and resin materials have been applied in rocket motor nozzles. This study aims to investigate the thermal contact resistance (TCR) between C/C composite and resin materials. Contact surfaces are scanned by surface morphological-measuring instrument. The TCR values are solved numerically. With the steady-state heat flux method, the TCR values are experimentally measured at different temperatures and pressures. The study results show that the TCR value between C/C composite and resin materials varies in the range of 1.8245 × 10–3 ∼7.5851 × 10–3 K·m2·W-1 at different pressures and temperatures. The average TCR error between numerical analysis and test results is 8%, which indicates a high accuracy. The developed TCR numerical prediction model can provide a reference for thermal-structural design and analysis of nozzles.

Dimensionless analysis of thermal contact resistance impact on heat transfer performance of rectangular fins applied in nuclear plant

This work aims to investigate the effects of welded Thermal Contact Resistance (TCR) on heat transfer for rectangular fins applied in passive nuclear plant. The dimensionless equations are established to describe fin efficiency and overall surface efficiency when subjected to TCR. An experimental set-up using a hot box are developed， and 18 experiments of fins with bilateral fillet welding (BFW) and unilateral penetration welding (UPW) are performed to obtain the range of TCR. Results show that the TCR values are about 0.006 and 0.002 (m2 K)/W for BFW and UPW, respectively. Dimensionless fin efficiency ηf' and overall surface efficiency η0' are governed by several dimensionless parameters that group thermal resistance, important material properties, and geometric parameters of the fin or substrate. TCR has a remarkable effect in the range of 10−4<Bi < 10−2, and the adverse effect of TCR on ηf' and η0' can be weakened by changing the geometric dimensions or material properties in a certain range.

Thermal Contact Resistance between Mold Steel and Additively Manufactured Insert for Designing Conformal Channels: An Experimental Study

The focus of this research is on thermal contact resistance between a mold and its insert, specifically inserts made by additive manufacturing (AM). Using a thermal steady-state system and varying contact pressures (0, 50, 75, and 100 bars), we present experimental results of the thermal contact resistance at the contact interface between steel A (1.2344), obtained from an extruded rod, and steel B (1.2709), produced by laser powder bed fusion. Thermal tests were performed for unbonded and bonded configurations. Results showed that increasing the contact pressure allows the system equilibrium to be reached at lower temperatures. Furthermore, thermal tests showed that in the transition zone of the bonded configuration, a well-defined resistance is not formed between the two steel samples as it occurs in the unbonded configuration. For the unbonded configuration, the thermal contact resistance values decrease with increasing applied contact pressure, improving the system’s heat transfer.

An equivalent temperature model of 3-D steady heat conduction analysis for a fiber metal laminated plate coated with a thermal barrier

In this paper, an equivalent temperature model of 3-D steady heat conduction analysis for a fiber metal laminated plate coated with a thermal barrier is presented. The separate variable method and equivalent temperature method are applied comprehensively to solve the temperature field at the interface between the thermal barrier and top aluminum 2024-T3 layer for the fiber metal laminated structure firstly, and values of other layers? temperature and thermal contact resistance are obtained based on balance principle of heat flux between respective adjacent top and bottom layers subsequently. The aim of this research is to understand the influences of kinds of fiber species, numbers of fiber metal laminated, thickness ratio between total coated figer metal laminated structure and thermal barrier as well as temperature distributed function on the values of thermal contact resistance between respective adjacent layers and temperature distribution from top to bottom surfaces for the coated figer metal laminated structure. Especially, the ratio of thermal contact resistance between maximum and minimum values are about five times no matter considering one or two kinds of fiber species. Besides the present results (mainly geometrical and physical parameters? effect) could guide engineers designing the coated figer metal laminated structures to adapt to high temperature environment especially aerospace temperature environment.

Evaluation of Thermal Contact Resistance Between Two Solid Surfaces Using Photoacoustic Technique

Thermal contact resistance is one of the factors that complicates heat transfer between the interfaces of different components. Because heat transfer is influenced by several factors, it is difficult to estimate all the influencing factors for practical applications. In this study, the thermal contact resistance between two solid surfaces was evaluated using the photoacoustic (PA) technique. The samples consisted of a metal foil and metal cylinders, which had various surface roughnesses at the contact faces measured at the same contact pressure. A one-dimensional analytical solution of the phase lag of the PA signal showed a similar trend with the experimental results. However, there were some quantitative differences between the two groups. By comparing the numerical calculation results for the developed heat conduction model of a cylindrical coordinate system with the experimental results, we found that the in-plane distribution of thermal contact resistance at the contact face contributed to the deviation between the experimental results and the numerical results. The thermal contact resistance was evaluated by considering the in-plane distribution of the thermal contact resistance, and reasonable values of thermal contact resistance were obtained.

4D simulation of quench behavior in quasi-isotropic superconducting cable of stacked REBCO tapes considering thermal contact resistance

The quench characteristic is a critical issue for the application of superconducting cable. In order to study the process of the quench behavior in the cable accurately, a four-dimensional (4D) quench model for quasi-isotropic superconducting cable was developed and presented, in this paper. We first consider that the materials of the cable are in perfect thermal contact with the neighboring ones, and the radial temperature field and current redistribution at different time and different axial distances during the quench process are obtained. Then, thermal contact resistance (TCR) is considered. In addition, the minimum quench energy (MQE) and the quench propagation velocity (QPV) in axial direction of the two cases are investigated and compared. The results show that the maximum temperature of the heating area (Tmax) is higher and QPVs are greater than the case without considering TCR. In addition, there is temperature gradient in the cross section of the cable. Finally we evaluate the sensitivity of thermal stability for the quasi-isotropic cable on the different values of TCR and positions where TCR is inserted. It is concluded that TCR among REBCO tapes has little effect on MQE and QPV of quasi-isotropic superconducting cable. The results are useful for the application of the quasi-isotropic superconducting cable immersed in liquid nitrogen, and this numerical model can also be used for simulating the quench process of other superconducting cables or conductors.

Thermal and Aerodynamic Researches of Staggered Bundles for Choice of an Effective Spacing of Round-Finned Tubes

The results of an experimental study of local modeling of convective heat transfer and aerodynamic resistance of staggered six-row bundles of bimetallic tubes with spiral knurled aluminum fins under transverse air flow in the range of its velocity alteration in a compressed bundle section of 1.9−11.0 m/s are presented. The velocity range covers the possible modes of operation of industrial air coolers (AVO). The fins with a diameter of approximately 57 mm are rolled on a steel supporting tube with an outer diameter of 25 mm. Tube finning ratio j = 19.26. Such tubes are widely used in the heat exchange sections of AVO of natural gas, in particular, at “Gribanovskii Engineering Plant” JSC (Russia). To measure the reduced heat transfer coefficients, an electric calorimeter had been developed by the authors with a power input of 600−1300 W. The temperature of the wall surface at the base of the fins did not exceed the range of 77–92 °C. The transverse tube spacing in bundles S1was 64.0 or 68.0 mm, while the longitudinal spacing S2 was 54.4 or 50.0 mm. The heat transfer of each transverse row of six-row bundles was measured, as well as the average heat transfer and aerodynamic drag, which are summarized by the similarity equation of a power type. The heat transfer rate of the last transverse row in the direction of air movement is 0–5 % lower than the heat transfer rate of the stabilized rows, and here new features of heat transfer variations in the insufficiently studied area of spacing changes S1 and S2 have been found. The thermal contact resistance (TCR) was measured in the range of the average temperature of the contact surfaces tк = (79–95) оС, and no dependence of the value of TCR on tк for the specified interval was found. The numerical average value of TCR was Rк = 2,13 × 10–4 m2×K/W, which is typical for reliable mechanical connection of the finned aluminum shell with the supporting steel tube made of carbon steel. The results of variant thermal and aerodynamic calculations with the use of the obtained data established the technical and economic feasibility of placing tubes at the vertices of an isosceles triangle with spacing S1 = 68–69 mm and S2 = 55 mm with failure to use the location of the tubes along an equilateral triangle with S1 = S2' = 64 mm (where S2' – is diagonal spacing). With Q = idem and other conditions being equal, the number of tubes on AVO decreases by 5.7 % with a decrease in power consumption to 4.0 %.

Modeling the Evolution of Residual Stresses in Thermally Sprayed YSZ Coating on Stainless Steel Substrate

This study is based on Eulerian method to model residual stresses for yttrium-stabilized zirconia coating applied to stainless steel substrate. A commercially available finite element software ABAQUS/Explicit is used to conduct this study. Single and multiple-particle impact analyses were carried out, and the residual stress data have been reported. The analysis is performed for two different values of thermal contact resistance and the through-thickness residual stress profiles obtained within the coating for single particle are tensile, while the substrate has a mixture of tensile and compressive residual stresses. For multiple impact model, the residual stress data have been presented for substrate with and without cooling. The residual stresses within the coating without substrate cooling are mostly tensile while the substrate is compressive. The residual stresses within the coating with substrate cooling are mostly tensile with compressive stresses on the top of the coating, while the substrate consists of compressive stresses. The obtained residual stresses are compared with experimental and analytical data.

Experimental investigation on thermal contact resistance of alumina fibrous insulation material with Ti-6Al-4V alloy at high temperature and its effective thermal conductivity

Heat transfer through thermal insulation material is an important process in the design and performance evaluation of an insulation system, which is a key component of space vehicles. Accurate information on heat transfer analysis requires determination of thermal contact resistance (TCR) between the insulation material and the super-alloy plate. In this study, test equipment was designed to measure the TCR as well as the effective thermal conductivity of low thermal conductivity fibrous insulation material at high temperatures and in atmospheric pressure conditions. Two heat-flux meters were used to measure the heat flux from the bottom (high temperature) to the top (low temperature) of a fibrous sample in the test column. The two-thickness method was used to obtain the TCR and the effective thermal conductivity. An uncertainty analysis was also evaluated, which proved that the most important factor in the TCR measurement was the heat flux calculation. The result reveals that the TCR values become high at small contact pressures. The TCR decreased with an increase in the compressive load and significantly contributed to the total thermal resistance of the fibrous sample, approximately 42% and 35% when the average temperature of the sample was 190 °C and 290 °C, respectively. The effective thermal conductivity of the fibrous sample decreased slightly with an increase in the average temperature due to the presence of the carbonization of the binder resin. The numerical method validated the experimental results well. In addition, the micrograph images of the contact surface were investigated.

Transient responses of sandwich structure based on the generalized thermoelastic diffusion theory with memory-dependent derivative

The present work is devoted to investigating the transient responses of a sandwich structure based on the generalized thermoelastic diffusion theory with memory-dependent derivative. Both the left and the right bounding surfaces are subjected to a thermal shock and a chemical potential shock simultaneously. It is assumed that the values of thermal contact resistance and diffusional contact impedance at the interface are zero with ideal adhesion. The coupled governing equations containing time delay factors and kernel functions, which can be chosen freely according to specific problems, are solved by the Laplace transform together with its numerical inversion. The influences of the material characteristic parameters at the interface on the structural responses are emphatically discussed, and the non-dimensional temperature, chemical potential, displacement, stress as well as concentration at different values of time delay factors and kernel functions are obtained and illustrated graphically. The results show that: the changes of the time delay factors, kernel functions, and material characteristic parameters have the varying degrees of influences on the considered variables. Based on the above conclusions, the sandwich structure working under the thermoelastic diffusion coupling condition can be designed reasonably.

CFD modeling of thermal contact resistance between solid contacting surfaces

ABSTRACTHeat transfer has considerable applications in different industries such as designing of heat exchanger, nuclear reactor cooling, control system for spacecraft, and designing of microelectronics cooling. As the surfaces of two metals contact each other, this issue becomes so crucial. Thermal contact resistance (TCR) is one of the key physical parameters in heat transfer of mentioned surfaces. Measuring the experimental value of TCR in laboratory is highly expensive and difficult. As an alternative, numerical modeling methods could be engaged. In this study, inverse problem method solution is utilized as a proper method for estimation of TCR value. In this order, three different configurations (flat-flat, flat-cylinder, and cylinder-cylinder) were utilized in two steady and unsteady state conditions to predict the value of TCR. A comparison between the measured values and obtained values from the simulation show the errors for flat-flat, flat-cylinder, and cylinder-cylinder configuration after 10 min from starting the experiment are 4.6074%, 0.1662%, and 0.5622%, respectively. And in steady-state condition, the corresponding errors are 6.06e-3%, 1.506%, and 0.846%, respectively. In conclusion, the final results establish the fact that the inverse problem method solution can predict TCR values between contacting surfaces.

Вимірювання теплопровідності листових матеріалів з урахуванням контактних теплових опорів

Розглянуто питання впливу контактних теплових опорів (КТО) на точність вимірювання теплопровідності матеріалів. Наведено конструкцію пристрою для визначення значень КТО. В основі пристрою є пакет із двох пар плоских зразків, розміщених у різній послідовності між джерелом тепла і приймачами тепла однакової температури. Один із зразків у всіх парах має одну і ту саму товщину, другий зразок у двох парах пакета відрізняється за товщиною вдвічі. Реєструють тепловий потік через пакети, різницю температур між серединними зразками пакетів та перепад температур на тонкому зразку і за отриманими даними розраховують шукану величину. Подано результати експериментального визначення КТО між різними матеріалами. Показано, що знехтувати впливом КТО на результат вимірювання у визначенні коефіцієнта теплопровідності різних матеріалів (особливо високотеплопровідних) не можна, оскільки він співвимірний з тепловими опорами досліджуваних зразків. Для виключення цього впливу на результат вимірювання теплопровідності розроблено вимірювальний перетворювач для вимірювання теплопровідності листових матеріалів на основі мостової теплової вимірювальної схеми. Наведено схему з'єднання теплових опорів і КТО, розподілу теплових потоків і температур у зрівноваженій мостовій тепловій вимірювальній схемі та принципову схему вимірювального перетворювача теплопровідності листових матеріалів.

Numerical investigation of thermal contact conductance between linear and curvilinear contacts

Heat transfer has considerable applications in different industries such as designing of heat exchanger, nuclear reactor cooling, control system for spacecraft and designing of microelectronics cooling. As the surfaces of two metals contact each other, this issue becomes so crucial. Thermal contact resistance is one of the key physical parameters in heat transfer of mentioned surfaces. Measuring the experimental value of thermal contact resistance in laboratory is highly expensive and difficult. As an alternative, numerical modeling methods could be engaged. In this study, Inverse problem method solution is utilized as a proper method for estimation of thermal contact resistance value. In this order, three different configurations (flat-flat, flat-cylinder, and cylinder-cylinder) were utilized in two steady and unsteady state conditions to predict the value of thermal contact resistance. In conclusion, the final results establish the fact that the inverse problem method solution can predict thermal contact resistance values between contacting surfaces.

Study on Thermal Contact Resistance Estimation in Planar Medium

Thermal contact resistance(TCR) is one of the important parameters in heat transfer problems of engineering, and it is necessary to estimate the value of TCR effectively in many engineering fields. Considering the limitation of current estimation methods of TCR such as only focusing on one-dimensional thermal conduction, getting a single value of TCR merely, and the temperature measuring points only being placed in temperature gradient direction of mediums, boundary element method(BEM) and conjugate gradient method are combined to estimate the TCR in planar mediums. The value of TCR in relation to the position of contact interface line is estimated with this method, and the positions of temperature measuring points can be selected randomly because of the characteristic of BEM that there is no necessity to discrete the inner area and it is sufficient to discrete the boundary. The analysis of calculation examples base on heat transfer model of planar medium demonstrates that:this method can estimate the TCR effectively, but the ill-posedness is also existed in this method which is one of the inverse problems, and the calculation error of TCR is increased with the distance from temperature measuring points to contact interface, the estimation precision and stability can be improved after optimization with least square method.

Influence of Thermal Contact Resistance of Aluminum Foams in Forced Convection: Experimental Analysis

In this paper, the heat transfer performances of aluminum metal foams, placed on horizontal plane surface, was evaluated in forced convection conditions. Three different types of contacts between the sample and the heated base plate have been investigated: simple contact, brazed contact and grease paste contact. First, in order to perform the study, an ad hoc experimental set-up was built. Second, the value of thermal contact resistance was estimated. The results show that both the use of a conductive paste and the brazing contact, realized by means of a copper electro-deposition, allows a great reduction of the global thermal resistance, increasing de facto the global heat transfer coefficient of almost 80%, compared to the simple contact case. Finally, it was shown that, while the contribution of thermal resistance is negligible for the cases of brazed and grease paste contact, it is significantly high for the case of simple contact.