Internal Thermal Resistance Research Articles

Reliability Investigation of a Carbon Nanotube Array Thermal Interface Material

As feature density increases within microelectronics, so does the dissipated power density, which puts an increased demand on thermal management. Thermal interface materials (TIMs) are used at the interface between contacting surfaces to reduce the thermal resistance, and is a critical component within many electronics systems. Arrays of carbon nanotubes (CNTs) have gained significant interest for application as TIMs, due to the high thermal conductivity, no internal thermal contact resistances and an excellent conformability. While studies show excellent thermal performance, there has to date been no investigation into the reliability of CNT array TIMs. In this study, CNT array TIMs bonded with polymer to close a Si-Cu interface were subjected to thermal cycling. Thermal interface resistance measurements showed a large degradation of the thermal performance of the interface within the first 100 cycles. More detailed thermal investigation of the interface components showed that the connection between CNTs and catalyst substrate degrades during thermal cycling even in the absence of thermal expansion mismatch, and the nature of this degradation was further analyzed using X-ray photoelectron spectroscopy. This study indicates that the reliability will be an important consideration for further development and commercialization of CNT array TIMs.

Thermal transport at a nanoparticle-water interface: A molecular dynamics and continuum modeling study.

Heat transfer between a silver nanoparticle and surrounding water has been studied using molecular dynamics (MD) simulations. The thermal conductance (Kapitza conductance) at the interface between a nanoparticle and surrounding water has been calculated using four different approaches: transient with/without temperature gradient (internal thermal resistance) in the nanoparticle, steady-state non-equilibrium, and finally equilibrium simulations. The results of steady-state non-equilibrium and equilibrium are in agreement but differ from the transient approach results. MD simulation results also reveal that in the quenching process of a hot silver nanoparticle, heat dissipates into the solvent over a length-scale of ∼2 nm and over a time scale of less than 5 ps. By introducing a continuum solid-like model and considering a heat conduction mechanism in water, it is observed that the results of the temperature distribution for water shells around the nanoparticle agree well with the MD results. It is also found that the local water thermal conductivity around the nanoparticle is greater by about 50% than that of bulk water. These results have important implications for understanding heat transfer mechanisms in nanofluid systems and also for cancer photothermal therapy, wherein an accurate local description of heat transfer in an aqueous environment is crucial.

Calculation Model of Effective Thermal Conductivity of a Spiral-wound Lithium Ion Battery

This paper proposed an analytical model which can calculate the effective thermal conductivity (ETC) of a spiral-wound Lithium-ion battery (Li-ion battery). It bases on a two-dimensional energy balance with both radial and spiral heat transfer, as well as internal thermal contact resistance (TCR) considered simultaneously and studies the influence of winding layers and winding tension on the ETC. Results show that the analytical data are in good agreement with the numerical results. With the winding layers decreased and the winding tension enhanced, the ETC of Li-ion battery increases gradually. The radial temperature in Li-ion battery is also investigated which demonstrates a relatively higher temperature when considering the internal TCR.

Reduction of Internal Loss and Thermal Resistance in Diode Lasers with Coupled Waveguides

The results of studying edge-emitting quantum-well lasers with a layered design having coupled planar waveguides, capable of suppressing the generation of excited transverse modes, are presented. In this case, a low internal loss (0.4 cm–1) is provided, combined with a small depth (~0.9 μm) of the active region, which results in a low thermal resistance of 6.0 (K/W) mm without a submount.

Dynamic simulation and analysis of thermal decomposition of binary particles with composite textures

CaC2 production via oxygen-thermal heating by combustion of coals or chars presents advantages over the conventional electro-thermal process and is increasingly gaining interest for effective use of carbon resources. In this investigation, with a particular focus on the reactor design aspect of the oxygen-thermal process, a one-dimensional unsteady pyrolysis model of bituminous coal-calcium containing composite pellets is established to describe the coupled external and internal heat transfer and decomposition rate steps. It is demonstrated by simulation that calcium hydroxide is a suitable calcium source and preferably used in a pseudo-homogeneous composite form with coal; in decomposition, the endothermic effect of calcium hydroxide is greater than that of the coal, and the endothermic effect of evaporation can be ignored; the relative importance of the involving rate steps is in the order of internal thermal resistance > external thermal resistance> reaction kinetics.

Explicit Multipole Formulas for Calculating Thermal Resistance of Single U-Tube Ground Heat Exchangers

Borehole thermal resistance is both an important design parameter and a key performance characteristic of a ground heat exchanger. Another quantity that is particularly important for ground heat exchangers is the internal thermal resistance between the heat exchanger pipes. Both these resistances can be calculated to a high degree of accuracy by means of the well-known multipole method. However, the multipole method has a fairly intricate mathematical algorithm and is thus not trivial to implement. Consequently, there is considerable interest in developing explicit formulas for calculating borehole resistances. This paper presents derivation and solutions of newly derived second-order and higher-order multipole formulas for calculating borehole thermal resistance and total internal thermal resistance of single U-tube ground heat exchangers. A new and simple form of the first-order multipole formula is also presented. The accuracy of the presented formulas is established by comparing them to the original multipole method. The superiority of the new higher-order multipole formulas over the existing formulas is also demonstrated.

EVAPORATION CHARACTERISTICS OF A CONFINED NANOFLUID BRIDGE BETWEEN TWO HEATED PARALLEL PLATES

This paper focusses on understanding the thermophysics and contact line dynamics of evaporating liquid bridges of pure water and nanofluids (0.1% and 0.5% v/v of CuO nanoparticles of average particle size < 50 nm), confined between two heated parallel glass substrates, maintained at a fixed distance, under near constant temperature boundary conditions (60°C and 80°C, respectively). Externally controlled, thin film indium-tin oxide (ITO) coated heaters were fabricated on the glass substrate to maintain the thermal boundary condition. High-resolution images of the liquid bridges were obtained during the evaporation process and later digitally analyzed to find the temporal evolution of relevant geometrical parameters. Subsequently, different thermal resistances involved were estimated, leading to the overall heat transfer coefficient. The order of magnitude of the interfacial resistance was found negligible as compared to the internal thermal resistance of the liquid bridge. Nanofluids evidently showed enhanced diffusional conductivity, and hence increased overall heat transfer coefficient, with a unique contact line motion, involving stick-slip behavior. Strong pinning effect at the contact line was observed during nanofluid evaporation, as a result of deposition of the particles, due to which the life span of nanofluid liquid bridge was much shorter than that of pure water. The rate of evaporation was dependent on the nanoparticle loading.

A method for the outdoor thermal characterisation of high-concentrator photovoltaic modules alternative to the IEC 62670-3 standard

The IEC 62670-3 standard recommends the open-circuit voltage method to calculate the cell temperature inside high-concentrator photovoltaic (HCPV) modules. This method requires knowledge of the temperature coefficient of open-circuit voltage (β), and the same standard provides a procedure to get this parameter. In this paper, an alternative method for the thermal characterisation of HCPV modules is proposed. As an advantage, it allows obtaining both the β parameter and the internal thermal resistance (ρ) of the device from outdoor measurements. No internal sensor for measuring the cell temperature is required as in the case of the IEC 62670-3 standard. Knowing the ρ parameter allows a more accurate characterisation of the cell temperature. The proposed procedure is applied to a real HCPV module. An outdoor experimental campaign of two months in Jaén (Southern Spain) was carried out. The β value was underestimated in a 0.50% and the ρ value was overestimated in a 4.18%. When applying the estimated parameters for the prediction of the cell temperature, the open-circuit voltage method gave a root mean square error (RMSE) of 1.41 °C, while the internal thermal resistance method gave a RMSE of 0.62 °C.

Online Calculation of the Increase in Thermal Resistance Caused by Solder Fatigue for IGBT Modules

This paper addresses the catastrophic failure of power converter systems caused by the aging of the insulated-gate bipolar transistor (IGBT) module. Monitoring the aging state of IGBT in real time enables the defective module to be found and be replaced timely. Solder fatigue increasing the internal thermal resistance of the module has been identified as one of the main root causes of IGBT module aging. In this paper, a novel event-driven solder fatigue monitoring mechanism is proposed. The proposed method consists of two models which are a dynamic solder aging monitoring model and an event-driven online calculation model of the increase in thermal resistance. The dynamic solder aging monitoring model detects solder fatigue in real time by the variations of case temperatures with thermal sensors on the bottom surface of the baseplate. The event-driven online calculation model estimates the increase in thermal resistance at the occurrence of the solder aging event by the junction temperature from thermosensitive electrical parameters, which are not affected by the solder fatigue. With the cooperation of two models, the aging level of the IGBT module caused by solder fatigue is evaluated. Simulation and experimental results are provided to verify the effectiveness of the proposed method.

Validation of borehole heat exchanger models against multi-flow rate thermal response tests

A recently developed vertical borehole ground heat exchanger model that accounts for transit time effects and time-varying short-circuiting heat transfer has been validated against two multi-flow-rate thermal response tests (MFR-TRT). The MFR-TRT, when performed with a wide range of flow rates, results in significant changes in the borehole thermal resistance, the borehole internal thermal resistance, and the short-circuiting heat transfer between the two legs of a single U-tube. The model accounts for short-circuiting by an analytically computed weighting factor that is used to determine the mean fluid temperature. The weighting factor portion of the model can be readily utilized in other ground heat exchanger models that currently rely on a simple mean fluid temperature. Use of the weighting factor is shown to give significantly better estimations of entering and exiting fluid temperature than using the simple mean fluid temperature. The new model is also compared to an alternative approach − using an effective borehole thermal resistance. While both the effective borehole thermal resistance model and the weighting factor give quite good results a few hours after a step change in flow rate, the weighting factor model gives much better results in the first few hours after a step change in flow rate.

Influence of spiral pitch on the thermal behaviors of energy piles with spiral-tube heat exchanger

Energy pile is a cost-effective solution for ground-coupled heat pump systems to take the place of borehole ground heat exchanger partly. This paper focuses on the influence of spiral pitch on the transient thermal behaviors of an energy pile with spiral-tube heat exchanger. A transient 3D numerical model was established and solved by using the finite element method. The thermal resistances and the heat transfer rates were obtained and analyzed for the energy piles with four kinds of spiral pitch. The proposed g-functions of circulated fluid temperature were used to study fluid temperature and coefficient of performance based on the superposition method. As spiral pitch decreases, the change in both fluid temperature and internal thermal resistance diminishes but the change is narrowed down, although the total rate of the heat transfer on pile surfaces is almost same for all piles. For both heating and cooling, the difference between the extreme fluid temperatures diminishes and the mean coefficient of performance increases as spiral pitch decreases. The energy pile with a small spiral pitch is energy-efficient and has a better applicability. The increase of spiral pitch (SP=0.25–2.0) leads to a reduction of the mean coefficients of performance (0.77–16.49%) according to the influential factors.

Equivalent Electrical Circuits of Thermoelectric Generators under Different Operating Conditions

Energy harvesting has become a promising and alternative solution to conventional energy generation patterns to overcome the problem of supplying autonomous electrical systems. More particularly, thermal energy harvesting technologies have drawn a major interest in both research and industry. Thermoelectric Generators (TEGs) can be used in two different operating conditions, under constant temperature gradient or constant heat flow. The commonly used TEG electrical model, based on a voltage source in series with an electrical resistance, shows its limitations especially under constant heat flow conditions. Here, the analytical electrical modeling, taking into consideration the internal and contact thermal resistances of a TEG under constant temperature gradient and constant heat flow conditions, is first given. To give further insight into the electrical behavior of a TEG module in different operating conditions, we propose a new and original way of emulating the above analytical expressions with usual electronics components (voltage source, resistors, diode), whose values are determined with the TEG’s parameters. Note that such a TEG emulation is particularly suited when designing the electronic circuitry commonly associated to the TEG, to realize both Maximum Power Point Tracking and output voltage regulation. First, the proposed equivalent electrical circuits are validated through simulation with a SPICE environment in static operating conditions using only one value of either temperature gradient or heat flow. Then, they are also analyzed in dynamic operating conditions where both temperature gradient and heat flow are considered as time-varying functions.

Evaluation of low-pressure flooded evaporator performance for adsorption chillers

In an adsorption chiller, the refrigerant (water) operating pressure is low (0.5–5 kPa) and the cooling power generation of a flooded evaporator is affected by the height of water column. To resolve this issue, we experimentally investigate the performance of a flooded evaporator as a function of water height. The results show an optimum water height equal to 80% of the tube diameter leading to achieve the highest cooling power. Under this condition, the internal and external thermal resistances on the inside and outside of the evaporator tubes account for up to 73% of the overall thermal resistance. To reduce the internal thermal resistance, twisted and Z-type turbulent flow generators are incorporated into the evaporator tubes. The evaporator cooling power shows an increase by 12% and 58% when twisted tape and Z-type turbulators are used at a cost of an increase in the internal pressure drop by 2.5 and 14.5 times, respectively. The twisted tape and Z-type turbulators improve the average specific cooling power of the adsorption chiller by 9% and 47%, respectively. To reduce the external thermal resistance, the outside surface of the evaporator tubes is coated with porous copper. The coated evaporator increases the overall heat transfer coefficient by 1.4 times and improves the specific cooling power of the adsorption chiller by 48% compared to the uncoated tubes.

Transient spray cooling: Similarity of dynamic heat flux for different cryogens, nozzles and substrates

Spray cooling is widely used in industries. Understanding of the complex surface heat transfer characteristics is essential to enhance cooling efficiency. In the present study, surface heat transfer of transient spray cooling with different cryogens, nozzles, and substrates were investigated. Minimum surface temperature reached −46.1°C, −55.9°C, and −57.9°C and maximum surface heat flux values were 294.9, 364.1, and 377.4kW/m2 for R134a, R407C, and R404A, respectively, on an epoxy resin block. Results proved that R404A has the best cooling capacity. Compared with that of the straight nozzle, qmax of the expansion-chamber nozzle increased from 266.9, 364.1, and 403.9kW/m2 to 339.3, 442.8, and 445.1kW/m2 or 16.6%, 18.6%, and 16.7% for R134a, R407C, and R404A, respectively. Transient cooling could be divided into two stages, namely, fast boiling cooling and film evaporation cooling. The similarity of dynamic heat flux with different cryogens, nozzles, and substrates was observed, and the dimensionless correlation was proposed by the spray Biot number, which is defined as the ratio between the internal thermal resistance of the substrate and the surface convective heat transfer resistance. The dimensionless Reynolds number Rel and Fourier number Fol were proposed to represent the maximum heat flux (qmax) and the corresponding time (tmax), respectively. By coupling the Jakob number with Rel and the droplet Weber number (We), dimensionless correlations of maximum heat flux and the corresponding time were proposed, through which it is indicated that We number was the key factor in spray cooling.

A numerical and experimental study on fast pyrolysis of single woody biomass particles

A one-dimensional unsteady-state heat transfer model coupled with time dependent mass loss equation of wood particles exposed to drying and pyrolysis conditions was developed. The kinetic parameters were determined experimentally and the regime and characteristics of the conversion were evaluated in terms of the particle size and reactor temperature. The order of mass loss exponent varied from n=1 at temperatures lower than 350°C to n=0.5 at temperatures higher that 350°C. The analysis of conversion time, the time when particles lost 90% of their mass, showed that thermal treatment of particles larger than 0.5mm were controlled by internal thermal resistances. The valid range of particle size to use the simplified lumped model depends on the fluid temperature around the particles. The critical particle size was 0.6–0.7mm for the fluid temperature of 500°C and 0.9–1.0mm for the fluid temperature of 100°C.

Accuracy of borehole thermal resistance calculation methods for grouted single U-tube ground heat exchangers

The borehole thermal resistance – that is, the thermal resistance between the fluid in the U-tube and the borehole wall – is both a key performance characteristic of a closed-loop borehole ground heat exchanger and an important design parameter. Lower borehole thermal resistance leads to better system performance and/or lower total borehole length and possibly lower installation costs. Borehole thermal resistance may be determined using in situ thermal response testing, but for design purposes, it is important to be able to predict the borehole thermal resistance prior to installation. Due to the complexity of calculating it, numerous simplified methods have been proposed. This paper reviews published methods for calculating borehole thermal resistance for grouted boreholes with single U-tubes and compares their results against a rigorous analytical method.Another quantity that is particularly important for deep boreholes is the internal thermal resistance – that is, the thermal resistance between the upward-flowing and downward-flowing fluid paths in the borehole. Short-circuiting between the two legs has the effect of reducing the total heat transfer and can be quantified as an adjustment to the borehole thermal resistance, resulting in an effective borehole thermal resistance. A few simplified methods for calculating internal thermal resistance are compared against a rigorous analytical method.The simplified methods for calculating both borehole thermal resistance and internal thermal resistance are compared in parametric studies spanning the range of borehole diameters, pipe spacing, ground thermal conductivities and grout thermal conductivities found in practice. Many of the simplified methods work well with some combinations of parameters and poorly with others. The first-order multipole expressions are closed-form algebraic expressions that give results within 2% (for borehole thermal resistance) and 6% (for internal thermal resistance) over the entire range of parameters. This represents significantly better accuracy than any of the other simplified methods and, therefore, the first-order multipole algorithm is recommended for single U-tube applications when the tubes are symmetrically placed.

A Novel Identification Method of Thermal Resistances of Thermoelectric Modules Combining Electrical Characterization Under Constant Temperature and Heat Flow Conditions

The efficiency of a Thermoelectric Module (TEM) is not only influenced by the material properties, but also by the heat losses due to the internal and contact thermal resistances. In the literature, the material properties are mostly discussed, mainly to increase the well-known thermoelectric figure of merit ZT. Nevertheless, when a TEM is considered, the separate characterization of the materials of the p and n elements is not enough to have a suitable TEM electrical model and evaluate more precisely its efficiency. Only a few recent papers deal with thermal resistances and their influence on the TEM efficiency; mostly, the minimization of these resistances is recommended, without giving a way to determine their values. The aim of the present paper is to identify the internal and contact thermal resistances of a TEM by electrical characterization. Depending on the applications, the TEM can be used either under constant temperature gradient or constant heat flow conditions. The proposed identification approach is based on the theoretical electrical modeling of the TEM, in both conditions. It is simple to implement, because it is based only on open circuit test conditions. A single electrical measurement under both conditions (constant-temperature and constant-heat) is needed. Based on the theoretical electrical models, one can identify the internal and thermal resistances.

Experimental study on the anti-jacking-up performance of a screw pile for photovoltaic stents in a seasonal frozen region

The soils in seasonal frozen regions freeze and thaw frequently, causing severe frost heave and thaw settlement problems, which bring challenges to piles of photovoltaic stents. In this paper, laboratory tests are conducted with different types of screw piles under freezing conditions, with also using smooth piles for contrast. The aim is to simulate the freezing process of screw piles according to practical working conditions based on the similarity principle. Internal thermal resistance is ignored. The change laws of temperature, displacement, as well as the influence factors of types of screw piles are analyzed. The results indicate that: with a freezing depth of 30 cm, which is half of the pile length, large-double-bladed screw piles perform the best in antijacking-up, while all-bladed screw piles perform the worst, independent of the types of soil samples tested. The fitting relationship between jacking-up displacement and freezing depth is also proposed for each type of pile. Results obtained can provide an important reference to site construction in seasonal frozen regions.

Analysis of internal and external thermal resistances of heat pipes including fins using a three-dimensional numerical simulation

A complete thermal network analysis for a cylindrical heat pipe is presented and the dominant thermal resistances are identified. The proposed numerical model was developed to simulate heat pipe operation and has been verified for both low and high applications including heat sources and sinks as a single-domain conjugate problem. Steady-state and transient solution methods were performed for a three-dimensional heat pipe with a compressible vapor core and a wick governed by pure conduction. The numerical model accounts for the full external coolant domain, with and without external fins on the condenser, to investigate their influence on the thermal resistance network. The numerical results indicate that the overall heat pipe thermal resistances can be predicted with as little as 1%–28% variation from empirical correlations, based on the choice of heat pipe dimensions, materials and operating conditions. It was found that the vapor core thermal resistance can become significant as the operating temperature increases, however, the largest thermal resistances are those corresponding to the external heat transfer fluids.

Method and Apparatus for Determining Operational Parameters of Thermoelectric Modules

The main aim of this work was to construct and test an apparatus for characterization of high temperature thermoelectric modules to be used in thermoelectric generator (TEGs) applications. The idea of this apparatus is based on very precise measurements of heat fluxes passing through the thermoelectric (TE) module, at both its hot and cold sides. The electrical properties of the module, under different temperature and load conditions, were used to estimate efficiency of energy conversion based on electrical and thermal energy conservation analysis. The temperature of the cold side, Tc, was stabilized by a precise circulating thermostat (≤0.1°C) in a temperature range from 5°C to 90°C. The amount of heat absorbed by a coolant flowing through the heat sink was measured by the calibrated and certified heat flow meter with an accuracy better than 1%. The temperature of the hot side, Th, was forced to assumed temperature (Tmax = 450°C) by an electric heater with known power (Ph = 0–600 W) with ample thermal insulation. The electrical power was used in calculations. The TE module, heaters and cooling plate were placed in an adiabatic vacuum chamber. The load characteristics of the module were evaluated using an electronically controlled current source as a load. The apparatus may be used to determine the essential parameters of TE modules (open circuit voltage, Uoc, short circuit current, Isc, internal electrical resistance, Rint, thermal resistance, Rth, power density, and efficiency, η, as a function of Tc and Th). Several commercially available TE modules based on Bi2Te3 and Sb2Te3 alloys were tested. The measurements confirmed that the constructed apparatus was highly accurate, stable and yielded reproducible results; therefore, it is a reliable tool for the development of thermoelectric generators.