An experimentally validated thermo-mechanical model for the prediction of thermal contact conductance

A predictive model for estimating thermal contact conductance between two nominally flat metallic rough surfaces has been developed and experimentally validated. The predictive model consists of two complementary parts, the first of which is a surface deformation analysis to calculate the actual area of contact for each contact spot, while the second accounts for the effects of constriction resistance and gas gap conductance between the contacting surfaces. A surface characterization technique is developed which generates an equivalent 3-D surface profile from multiple 2-D profiles and determines the unique wavelengths of importance for the surface deformation and constriction resistance models. For given surface profiles and material properties of two contacting surfaces, and a specified contact pressure, the surface characterization technique filters out non-essential wavelengths on the surface, after which the surface deformation analysis calculates the deformation and contact area of each contacting asperity by considering three different modes of deformation, namely, elastic, elastic–plastic, and plastic. The constriction resistance model is then used to calculate the constriction resistance for each contacting asperity based on the area of contact and radius of curvature of the asperity. The constriction resistance values for all the contacting asperities are then used to calculate the total thermal contact conductance. An experimental facility has also been constructed to measure thermal contact conductance of interfaces to verify the results of the predictive model. Good agreement has been found between the model predictions and experimental measurements, validating the modeling approach.     

Gap conductance in contact heat transfer

At low contact pressures, conduction across the gas gap is the predominant mode of heat transfer in a joint. Experimental results are presented for the solid spot and the gap conductance for a range of surface finishes and several interstitial gases and gas mixtures. The mean separation distance is then estimated as the difference between the effectiive gap thickness and the temperature jump distance. It is seen that a simple relation exists between the mean separation distance and surface roughness for all the gases and gas mixtures. This correlation satisfies 85% of data points to within ±4%.     

Transient characteristics of thermal contact conductance between isotropic rough surfaces of metals

Transient measurements of thermal contact conductance are made on the interface between isotropic rough surfaces of metals in air. We present an analytical solution for temperature distribution of the one‐dimensional symmetric system with the condition of time‐dependent temperatures at two points in each body, and thereby interface temperature drops and heat fluxes can be obtained without the condition of heat‐flux continuity at the interface. Contacting surfaces of rod samples (Naval brass, JIS?SK5 carbon tool steel, and JIS?SUS 304 stainless steel) of 25‐mm diameter are uniformly polished using an emery 320 paper. Transient characteristics of both temperatures and heat fluxes at the interface are experimentally determined using the analytical solution. It is revealed through the transient experiment that the thermal contact conductances are not constant at the early stage, but rapidly increase from zero and that the discontinuity of interface heat‐flux is observed by about 20 percent for all metal pairs. For the contact between dissimilar metals, the dependence of thermal contact conductance on the direction of heat flow is not distinguishable. © 2001 Scripta Technica, Heat Trans Asian Res, 30(4): 341–356, 2001     

Numerical study of PEMFC heat and mass transfer characteristics based on roughness interface thermal resistance model

The thermal contact resistance (TCR) is the main component of proton exchange membrane fuel cell (PEMFC) thermal resistance due to the existence of surface roughness between the components of PEMFC, and the influence of TCR is often ignored in traditional three dimensional PEMFC simulations. In this paper, the heat and mass transfer characteristics including polarization curve, power density curve, temperature distribution, membrane water content distribution, membrane current density are studied under different component surface roughness conditions, and finally the effect of each TCR on the PEMFC performance is studied. It is found that under the same operating conditions, the TCR makes the radial heat transfer of the PEMFC decrease, and the temperature of the membrane electrode and the temperature difference of each component of the PEMFC is higher than that of the model without TCR. When the surface roughness of components in the PEMFC equals 1 μm, 2 μm, 3 μm, the cell current density decreases by 6.56%, 12.46% and 17.17% respectively when the output cell voltage equals 0.3 V, and the cell power density decreases by 3.64%, 7.54%, 13.14% respectively when the cell current density equals 1.2 A·cm^?2. When the TCR between the CL and PEM equals 0.003 K·m²·W^?1, 0.005 K·m²·W^?1, 0.01 K·m²·W^?1, the cell current density is increased by 2.30%, 3.65%, 6.74% respectively under the condition that the output cell voltage equals 0.3 V, and the cell power density is increased by 1.24%, 1.85%, 3.10% respectively when the cell current density equals 1.2 A·cm^?2. The results show that the numerical simulation of PEMFC cannot ignore the effect of TCR.     

Estimating the thermal contact conductance of metals by ultrasonic waves

Experiments and numerical simulations were performed to study heat transfer through a contact interface between two metallic solids in order to clarify the effects of roughness and waviness of the contact surface on the mean thermal contact conductance h_m. In the experiments, the characteristics of an ultrasonic transmission were also investigated so as to obtain a relation between h_m and the transmitted sound energy ratio, with and without attenuation, at the contact interface E_r. Ten pairs of brass specimens were tested in an atmospheric environment at room temperature. Each specimen was a cylindrical block 40 mm in diameter and 45 mm long. The contact surface was finished by polishing, grinding, milling, or turning. Mean nominal contact pressures p_m from 0.08 to 1.67 MPa were applied to the test columns. Our analysis takes account of the radial distribution of thermal contact conductance, using numerical solutions of the two-dimensional cylindrical heat conduction equation to simulate the heat transfer experiments. From the simulations, the effects of roughness and waviness on the temperature fields around the contact surfaces and on h_m were clarified. Finally, for flat rough surfaces, an empirical correlation expression between h_m and E_r is proposed. Using this expression, h_m can be predicted to within about ±50%. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(2): 130–141, 1998     

Effect of electroplating on the thermal conductance of fin–tube interface

This paper presents the experimental results of thermal contact conductance, heat transfer and interfacial temperature drop of finned tube heat exchanger test specimens. The results were based on the measured temperatures at several locations on the test specimen so that the thermal contact conductance could be directly determined. Each test specimen was assembled by mechanically expanding seven tubes into a single fin. The geometry of the specimens was based on a commonly used model of heat exchangers. The specimens included one bare tube (non-coated) specimen and four electroplated tube specimens. The plating metals were zinc, tin, silver and gold. The thickness of the plating in each case was 5 μm.Experiments have been conducted in both vacuum and nitrogen. Maximum enhancement was obtained when the tube was coated with tin. This indicates that, although the thermal conductivity is important, the softness of the plating material also plays an important role in enhancing the thermal conductance of the interface. The presence of an interstitial gas such as nitrogen is beneficial for the heat transfer and the thermal contact conductance. It is also noted that the interfacial temperature drop alone does not fully reflect the efficiency of the heat exchanger.     

Thermal contact conductance: effect of overloading and load cycling

An experimental investigation is carried out to study the effects on joint conductance of progressive loading and unloading, cyclic loading and overloading to a predetermined value. The test pair used is AISI 304 stainless steel, bead blasted to an effective rms surface roughness of 7.55 μm and a slope of 0.36 rad. In all cases a hysteresis loop is seen to exist for the loading unloading cycle and is seen to decrease with increasing number of cycles. The conductance values eventually appear to settle down to values higher than those obtained during first loading. Enhancement of contact conductance by cyclic loading is found to be rather small. On the other hand overloading the test pairs to a predetermined contact pressure is found to be promising.     

Ultra-fast pulse-laser heating on a two-layered semi-infinite material with interfacial contact conductance

The temperature distribution of a two-layered material in a semi-infinite domain subjected to ultra-fast pulse-laser heating at the front surface is solved in this study. The interfacial contact conductance existing at the interface is included in the analysis. The dual-phase-lag (DPL) model is applied to examine the lagging behavior of the two-layer material. The effects of interfacial contact conductance and the thickness of the surface layer on the temperature solution of the material are also investigated.     

Modelling of thermal contact resistance within the framework of the thermal lattice Boltzmann method

A novel numerical approach, termed the partial bounce back scheme, is introduced within the framework of the thermal lattice Boltzmann method to account for thermal contact resistance between contacting surfaces. The correlation between thermal contact resistance and the partial bounce back parameter is established. A special case of the scheme leads to a new approach that can be directly applied for the treatment of adiabatic thermal boundary conditions in the thermal lattice Boltzmann method. Numerical examples are provided to validate and demonstrate the accuracy and effectiveness of the proposed methodology.     

Investigation of thermal performance of solar air heater having roughness elements as a combination of inclined and transverse ribs on the absorber plate

An experimental investigation has been carried out to study the heat transfer and friction characteristics by using a combination of inclined as well as transverse ribs on the absorber plate of a solar air heater. The experimental investigation encompassed the Reynolds number (Re) ranges from 2000 to 14 000, relative roughness pitch (p/e) 3–8 and relative roughness height (e/D_h) 0.030. The effect of these parameters on the heat transfer coefficient and friction factor has been discussed in the present paper and correlations for Nusselt number and friction factor has been developed within the reasonable limits. A procedure to compute the thermal efficiency based on heat transfer processes in the system is also given and the effect of these parameters on thermal efficiency has been discussed.     

CFD modeling of thermal contact resistance between solid contacting surfaces

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 (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.     

Thermal contact resistance at low contact pressure: Effect of elastic deformation

Existing models over-predict the thermal contact resistance of conforming rough joints at low contact pressures. However, the applicable pressure range in some applications such as microelectronics cooling is low. A new model is developed which is more suitable for low pressures. The effect of elastic deformations beneath the plastically deformed microcontacts is determined by superimposing normal deformations due to self and neighboring contact spots in an elastic half-space. A parametric study reveals that the elastic deformation effect is an important phenomenon at low contact pressures. The model is compared with data and good agreement is observed at low contact pressures.     

Effect of surface roughness of composite bipolar plates on the contact resistance of a proton exchange membrane fuel cell

Polymer electrolyte membrane fuel cell performance strongly depends on properties of the fuel cell stack bipolar plates. Composite bipolar plates, though low cost and convenient in manufacturing, raise a major concern due to their high interfacial contact resistance caused by the mechanical treatment used to remove the polymer-rich layer on the surface. It is observed that most of this contact resistance is governed by electrical properties of the interface layer between the contacting surfaces. Measurements of contact resistance of mechanically polished composite bipolar plate/gas diffusion layer interface reveal a substantial influence of surface topography on the contact resistance, which varies significantly depending on the substrate surface treatment and roughness of composite bipolar plates.     

Inverse heat transfer problem of thermal contact conductance estimation in periodically contacting surfaces

The problems involving periodic contacting surfaces have different practical applications. An inverse heat conduction problem for estimating the periodic Thermal Contact Conductance (TCC) between one-dimensional, constant property contacting solids has been investigated with conjugate gradient method (CGM) of function estimation. This method converges very rapidly and is not so sensitive to the measurement errors. The advantage of the present method is that no a priori information is needed on the variation of the unknown quantities, since the solution automatically determines the functional form over the specified domain. A simple, straight forward technique is utilized to solve the direct, sensitivity and adjoint problems, in order to overcome the difficulties associated with numerical methods. Two general classes of results, the results obtained by applying inexact simulated measured data and the results obtained by using data taken from an actual experiment are presented. In addition, extrapolation method is applied to obtain actual results. Generally, the present method effectively improves the exact TCC when exact and inexact simulated measurements input to the analysis. Furthermore, the results obtained with CGM and the extrapolation results are in agreement and the little deviations can be negligible.     

Optical measurement of thermal contact conductance between thin,waferlike solid samples by using laser AC heating and reflectance thermometry: Reconsideration of the loading method for the samples

A noncontact optical technique for measuring the thermal contact conductance between two thin, waferlike solid samples was developed. In this technique, one solid surface is heated with a modulated laser beam; the corresponding temperature modulation of the other solid surface across their interface is monitored by using the reflectance of a probe laser beam. Each sample can become slightly bent if its edge is compressed by the sample holder, so the contact pressure between the samples (in the range of 0.8 to 10 MPa) was calculated by elastic and plastic numerical analyses. By using the calculated contact pressure, the correlation between contact pressure and thermal contact conductance could be determined more accurately. Also, the appropriate thickness of the glass plates used to fix the samples was derived by calculating the thickness where the local contact pressure is almost the same as the averaged pressure. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(6): 498–512, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10049     

Effect of nonuniformity of the contact pressure distribution on the electrical contact resistance in proton exchange membrane fuel cells

Electrical contact resistance (ECR) is one of the most important factors affecting the ohmic loss in proton exchange membrane (PEM) fuel cells. Dominated by the contact pressure at the interface of two neighboring components, the ECR can be reduced by increasing the clamping force applied on fuel cell stack. However, too large a clamping force will result in excessive resistance to the transport of reactants in the gas diffusion layer (GDL) and even damage to the fuel cell components. Therefore, for a given clamping force, the minimum ECR is expected by making the pressure distribution as uniform as possible. This paper investigates two questions: (a) how to evaluate the distribution of non-uniform pressure based on the ECR, and (b) in what situation will a uniform pressure distribution reduce the ECR obviously, i.e., the sensitivity of the contact resistance to the pressure distribution.     

Simulation of thermal stresses in anode-supported solid oxide fuel cell stacks. Part II: Loss of gas-tightness, electrical contact and thermal buckling

Structural stability issues in planar solid oxide fuel cells arise from the mismatch between the coefficients of thermal expansion of the components. The stress state at operating temperature is the superposition of several contributions, which differ depending on the component. First, the cells accumulate residual stresses due to the sintering phase during the manufacturing process. Further, the load applied during assembly of the stack to ensure electric contact and flatten the cells prevents a completely stress-free expansion of each component during the heat-up. Finally, thermal gradients cause additional stresses in operation.The temperature profile generated by a thermo-electrochemical model implemented in an equation-oriented process modelling tool (gPROMS) was imported into finite-element software (ABAQUS) to calculate the distribution of stress and contact pressure on all components of a standard solid oxide fuel cell repeat unit.The different layers of the cell in exception of the cathode, i.e. anode, electrolyte and compensating layer were considered in the analysis to account for the cell curvature. Both steady-state and dynamic simulations were performed, with an emphasis on the cycling of the electrical load. The study includes two different types of cell, operation under both thermal partial oxidation and internal steam-methane reforming and two different initial thicknesses of the air and fuel compressive sealing gaskets.The results generated by the models are presented in two papers: Part I focuses on cell cracking. In the present paper, Part II, the occurrences of loss of gas-tightness in the compressive gaskets and/or electrical contact in the gas diffusion layer were identified. In addition, the dependence on temperature of both coefficients of thermal expansion and Young's modulus of the metallic interconnect (MIC) were implemented in the finite-element model to compute the plastic deformation, while the possibilities of thermal buckling were analysed in a dedicated and separate model.The value of the minimum stable thickness of the MIC is large, even though significantly affected by the operating conditions. This phenomenon prevents any unconsidered decrease of the thickness to reduce the thermal inertia of the stack. Thermal gradients and the shape of the temperature profile during operation induce significant decreases of the contact pressure on the gaskets near the fuel manifold, at the inlet or outlet, depending on the flow configuration. On the contrary, the electrical contact was ensured independently of the operating point and history, even though plastic strain developed in the gas diffusion layer.     

Experimental investigation of thermal contact conductance at low temperature based on fractal description

An experimental investigation of thermal contact conductance was conducted with pressed pairs of aluminum alloy 5052 and stainless steel 304 over the low temperature range from 155 to 210 K, with nominal contact pressure from 1 to 7 MPa. The contact surfaces were prepared through bead blasting and characterized with the fractal dimension D and the parameter G of the Weierstrass–Mandelbrot function. The range of fractal dimension is 1.59–1.86 for aluminum and 1.56–1.92 for stainless steel. And the parameter G is in the magnitude of 10⁻⁷ m. From the measured results, thermal contact conductance over this temperature range (155–210 K) is less than that near or above room temperature (T > 300 K). The load sensitivity at low temperature is less than that at room temperature. The smaller fractal dimension D characterizes the rougher surface when G is on the same magnitude and results in the smaller value of the contact conductance and insensitivity to the contact pressure.     

Estimation of thermal contact resistance and temperature distributions in the pad/disc tribosystem

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent thermal contact resistance for the tribosystem consisting of a semi-infinite foundation (disc) and a plane-parallel strip (pad) sliding over its surface, from the knowledge of temperature measurements taken within the foundation. Subsequently, the temperature distributions in the medium can be determined as well. The temperature data obtained from the direct problem are used to simulate the temperature measurements, and the effect of the measurement errors upon the precision of the estimated results is also considered. Results show that an excellent estimation on the time-dependent thermal contact resistance can be obtained for the test case considered in this study. The current methodology can be applied to the prediction of thermal contact resistance in engineering problems involving sliding-contact elements.