Lumped Capacitance Model Research Articles

An Experimental Investigation Of Local Thermo-Fluidic Heat Transfer In A U-Shaped Mini-Channel Sink

This study investigates experimentally a heated U-shaped mini-channel heat sink using Infrared Thermography and Particle Image Velocimetry for a water coolant flow of Reynolds numbers of 280, 650, and 1350 (based on the hydraulic channel diameter). The choice of this cell geometry is based on its role as a simplified unit of a serpentine heat exchanger, which is proved to be one of the most promising for cooling processes. The use of the infrared camera allows the detection of temperature fields on top of the external surface of the cell. Therefore, aiming to derive the temperature distribution on the channel roof, a dedicated transfer function is implemented. Moreover, we employed the lumped capacitance model for thermal analysis on both infrared measurements and thermocouple data. The latter are recorded to capture the cooling process of the aluminium base and water temperature at the end of the outlet tube. As a result, thermal transient rate, cooling magnitude and equilibrium temperature are obtained. These parameters indicate that higher Reynolds numbers correspond to increased thermal transient rates, enhanced cooling effects, and lower equilibrium temperatures. A non-uniform distribution of heat transfer along the channel is reported, with the most efficient cooling area localized close to the first 90-degree corner. These findings are consistent with numerical simulations and previous experimental observations. PIV results reveal the presence of two fluid acceleration zones following both 90-degree corners, which contribute to improve the water cooling ability in their respective regions. Additionally, the formation of two recirculating bubbles is reported at the inner wall from corners vertices, whose intensity is dependent on Reynolds number, pushing the main flow towards the outer channel wall and reducing the local heat transfer. Turbulent kinetic energy distributions are also investigated, pointing out the presence of intense areas that better match with regions of minimum equilibrium temperature than maximum velocity zones. This suggests the presence of local turbulent unsteadiness and three-dimensional phenomena, which contributes significantly to cooling enhancement.

Heat-Transfer Mechanisms in a Solar Cooking Pot with Thermal Energy Storage

This paper presents a detailed analysis of the heat-transfer mechanisms in a solar cooking pot with thermal energy storage using computational fluid dynamics (CFD). The vast majority of studies on solar cookers have been experimentally performed using local temperature measurements with thermocouples. Therefore, the heat-transfer mechanisms can only be studied using lumped capacitance models as the detailed profiles of temperature and heat fluxes inside the cooker are missing. CFD is an alternative modelling technique to obtain this detailed information. In this study, sunflower oil is used as both cooking fluid and energy storage medium. Comparison of the model with the available experimental data shows that the deviation is within the measurement accuracy of the latter. Hence, despite some assumptions, such as axisymmetry and an estimation of the heat transfer parameters to the ambient, the model is able to describe the involved physical processes accurately. It is shown that, initially, the main heat-transfer mechanism is conduction from the cooker’s bottom towards the thermal energy storage (TES). This heats up the oil near the bottom of the TES, creating convective plumes, which significantly enhance the heat transfer. In equilibrium, about 79% of the incoming solar flux goes towards heating up the TES. The heat is further transferred to the pot, where convective plumes also appear much later in time. However, the heat transfer to the pot is much smaller, with an average heat-transfer coefficient of 1.6 Wm−2K−1 compared to 7.5 Wm−2K−1 for the TES. After two hours of charging, the oil reaches a temperature of 397 K in the TES and 396 K in the cooking pot. Moreover, the temperature distribution in the cooker is quasi-uniform. During the charging period, the storage efficiency of the TES is about 29%. With the results in this study, solar cooking pots with TES can be further optimized towards efficiently transmitting the heat form the solar radiation to the food to be cooked.

A computational study on air-entrainment and pressure distribution for natural convection cooling of a hybrid IRS device

The infrared suppression (IRS) device is an essential component of a naval warship, which passively cools the hot flue gas issuing out of the engine exhaust so as to suppress the infrared emissions. In this work, the natural convection cooling of the hot funnels of a hybrid-type IRS device has been numerically investigated in a finite volume framework by varying the diameter ratio (DR) and the Rayleigh number (Ra) in the range of 1.025 ≤ DR ≤ 1.5, and 1010≤Ra≤1012, respectively. It is observed that the Nusselt number as well the air entrainment ratio augments with the Rayleigh number. However, we noticed an initial increment in the Nusselt number with DR, and thereafter decreases marginally with a further increase in diameter ratio after attaining a peak. An optimum diameter ratio (DR = 1.1) has been obtained for the maximum heat transfer from the funnel walls. At the entry of the base and third funnel, intense suction pressure is induced, whereas the pressure recovers throughout the remaining portions of the IRS device. The influence of air entrainment on the flow and heat transfer phenomenon has been explained by delineating temperature contours, velocity vectors, and streamlines for different representative cases of the computational study. In addition, we nonlinearly regressed the computational data to propose an empirical correlation for the average Nusselt number. Furthermore, the estimation of cooling time has been done through lumped capacitance model.

EARLY DETECTION AND MANAGEMENT OF THERMAL RUNAWAY IN BATTERIES USING WATER MIST FOR AIR PRECOOLING

In the present study, the use of air, precooled with a water mist for management of thermal runaway of a lithium ion cell is studied. A lumped capacitance model of the battery based on ordinary differential equations representing thermal transport and chemical kinetics of a 18,650 NCA/graphite cell based on Arrhenius electrochemical equations is used to simulate the thermal behavior, and an efficiency factor is used to account for the venting of the cell. An Eulerian approach is used for the evaporation of water mist. Both convective and radiative heat transfer are considered for modeling the heat transfer for the lithium cell. For convective heat transfer, flow across a cylinder is considered for maximizing heat transfer. Additionally, two basic methods of triggering mist precooling based upon the temperature of the battery and solid electrolyte interphase degradation were tested. Based upon the results, a conclusion was drawn that mist precooling triggered using temperature as a parameter can be an effective method to control thermal runaway.

Experimental study on heat generation characteristics of lithium-ion batteries using a forced convection calorimetry method

This paper presents a forced convection calorimetry method, based on the lumped capacitance model, to measure the continuous noise-free heat generation rate of batteries. The method was verified via reference sample calibration. Battery test results indicated that the discharge current, ambient temperature, and cycle aging significantly affect the heat generation characteristics of batteries. A larger discharge current and lower ambient temperature of 20–45 °C caused a greater heat generation rate and faster temperature increase. The average heat generation rate over the discharge period exhibited a quadratic polynomial correlation with the discharge current and a negative quadratic polynomial correlation with the ambient temperature. The cycling process increased the heat generation rate, reflecting battery aging. The cycle charge rate had a significant impact on the battery life. Moreover, the two cells started to display different heat generation characteristics after being cycled by different currents even at a similar state of health, revealing that the cycling process and different cycle rates may aggravate the battery inconsistency.

Theory and Practices of Li-Ion Battery Thermal Management for Electric and Hybrid Electric Vehicles

This article surveys the mathematical principles essential for understanding the thermal management of Li-ion batteries, the current technological state of the art, and the solution. Since the thermal management of electric drive vehicles has environmental, economic, and safety impacts, this review focuses on the efficient methods of battery thermal management (BTM) that were proposed to overcome the major challenges in the electric vehicle industry. The first section examines the perspective of battery-driven vehicles, the principles of Li-ion batteries with a thermal runaway, and their implication for battery safety. The second section discusses mathematical approaches for effective BTM modeling, including the thermal-fluidic network model, lumped capacitance model, spatial resolution lumped capacitance model, equivalent circuit model, impedance-based model, and data-driven model. The third section presents the current state-of-the-art technologies, including air-based, liquid-based, PCM-based, in situ BTM methods, and heat pipe and thermoelectric module-based methods. The conclusion section summarizes the findings from existing research and the possible future directions to achieve and employ better thermal management techniques.

Quantifying the temperature of heated microdevices using scanning thermal probes

Quantifying the temperature of microdevices is critical for probing nanoscale energy transport. Such quantification is often accomplished by integrating resistance thermometers into microdevices. However, such thermometers frequently become structurally unstable and fail due to thermal stresses at elevated temperatures. Here, we show that custom-fabricated scanning thermal probes (STPs) with a sharp tip and an integrated heater/thermometer can accurately measure the temperature of microdevices held at elevated temperatures. This measurement is accomplished by introducing a modulated heat input to the STP after contacting the microdevice with the STP's tip and characterizing the DC and AC components of the STP's temperature. From these measured temperature components, the tip-to-sample thermal resistance and the microdevice surface temperature are deduced simultaneously via a simple lumped-capacitance model. The advances presented here can greatly facilitate temperature measurements of a variety of heated microdevices.

Observer Design for Estimation of Nonobservable States in Buildings

Efficient temperature control requires more than air temperature measurements. Relevant variables, such as wall, ceiling, and other construction temperature evolution are usually unmeasured. Estimation of such quantities is often difficult because they are not observable with respect to available data. Their availability however would allow efficient control design. In this paper, we propose a method for designing state observers that efficiently estimate not only observable but also nonobservable (but detectable) state variables. Our method uses contraction semigroup, to obtain observer with a monotonic error reduction. Proposed approach gives twice as fast estimation as pure simulation and avoids transitional error standard observer would have. Problem of state estimation in building control applications is an important one. Attractiveness of obtaining values of physically unmeasurable variables is easily visible, as it would allow more efficient methods of temperature control. In this paper, authors discuss the problem of such estimation using a lumped capacitance model. This type of model is usually only detectable but not observable. Methods of observer tuning for such systems are not discussed properly in the literature and require special consideration. In this paper, three approaches for estimation are compared: pure model, eigenvalue shifting, and contraction semigroup observer. Results are illustrated with numerical experiments.

Analysis and application of a lumped-capacitance model for urban building energy modelling

Buildings are one of the major responsible of energy consumption and carbon emissions worldwide. Due to the continuous growth of cities, researchers moved their focus from single buildings to urban scale analyses.The present work aims at demonstrating the reliability of a lumped-capacitance model in the evaluation of heating and cooling demand at urban level. The model presented extends a previous one with different modules for solar radiation pre-processing, HVAC systems and photovoltaic production estimation. A case-study district of 13 buildings in Padua (Italy) has been analysed, considering detailed single buildings simulations with EnergyPlus as benchmark.Results show that the model leads to good accuracy in the evaluation of the district energy demand for both space heating and cooling. The major sources of error are geometrical simplifications, shadowing and thermal zoning effects, thus showing the importance of high-quality input data in urban modelling. However, results highlight how simple corrections may enhance the accuracy when detailed geometrical information is not available. Finally, the model has been used to assess the cost and energy saving potential of several building retrofit measures and PV installations on the considered district, providing an important indication in the investment priority for decision makers.

An experimental investigation on the transient heat transfer characteristics using air/water droplets two-phase flow

The present study focused on evaluating the heat transfer behavior and predicting the surface resulting status during air/water droplets two-phase flow. Transient heat transfer based on the lumped capacitance model (LCM) was investigated experimentally under a range of water droplets concentration, surface temperature, and varying Re number. Compared with a single-phase air cooling, the transient surface temperature decreased with the increase in water droplets concentration and Re number. At the same cooling time, the surface temperature decreases about 13.5%, 47%, and 53.2% for (j = 46.79 – 111.68 kg/m2 hr). It was also noticed that the heat transfer coefficient increased with the increase in water droplets concentration and reach its maximum value at (j = 111.68 kg/m2 hr). Based on the analysis of the experimental results, the heat transfer mechanism due to the impacting of water droplets on the sphere surface was classified into three important physical regimes. Clear convection heat transfer regime corresponds to the dry region (region I); Convection and evaporation regimes correspond to the dry-out and wet regions (region II and III).

Comparative study on steady and unsteady heat transfer analysis of a spherical element using air/water mist two-phase flow

In this study, two approaches to investigating the process cooling of a heated sphere were performed using air as well as air/water mist two-phase flow. Steady-state and unsteady heat transfer analysis were compared in the terms of the aver-age surface temperature and heat transfer rate between the sphere surfaces and the cooling fluid. When the Bi < 0.1, the temperature variation inside sphere can be neglected and the wildly known lumped capacitance model can be applied to estimate the heat transfer coefficient by measuring the sphere surface temperature. The effect of the different factors such as the inlet Reynolds numbers, surface temperature and water mist rate on heat transfer characteristics are examined. The experimental results showed that the presence of water mist leads to a significant increase in heat transfer rate over the use of air coolant alone. Also, the un-steady thermal behaviors of the water mist impingement on the heated surface and dynamic-state of cooling process changing over the sphere surface were analyzed experimentally based on the unsteady surface temperature measurements. The experimental results of the unsteady heat transfer were compared to the results obtained from steady-state estimation under the corresponding surface temperature of the sphere. Moreover, the new proposed empirical correlation for the Nusselt number based on the present experimental data are given for practical uses. Results reasonably agree well within ?3.8%.

A review study on the modeling of high-temperature solar thermal collector systems

Concentrated solar power technologies are gaining more attention in the last two decades in order to replace the conventional power technologies and reduce their environmental impact. Among the developed concentrating technologies, parabolic trough solar collector and solar tower are the most mature and dominant technologies. As part of the continuous development of these technologies, significant efforts have been deployed to predict and improve their performance, and therefore reduce their cost and make them more competitive. In this context, numerous analytical and numerical studies have been developed and presented in the literature. This review aims to summarize the state-of-the-art modeling approaches used to simulate, predict and evaluate the optical, thermal and dynamic performance of high-temperature solar thermal collectors. The review includes the different analytical and ray tracing models used to determine the non-uniform flux on the receiver aperture. Energy balance models are also presented as simple and easy computational models suitable to predict the thermal performance at a reasonable time and computational cost, whereas Computational Fluid Dynamic models are more convenient to study the details of the coupled fluid flow and heat transfer in the internal and external flow. The review also includes dynamic models such as the lumped capacitance models which are used to simulate the dynamic characteristics of the heat transfer fluid and interaction with the solar receiver under transient conditions. The dynamic behavior of the whole solar plant using different codes is examined. Furthermore, different features and capabilities of those approaches are also analyzed and compared. Finally, the use of numerical modeling in the development of new designs and assessment of the use of nanofluids is discussed. In summary, this work presents a comprehensive review of the existing numerical models and could serve as a guideline to develop new models for future trends in concentrating solar technologies.

Heat storage and release behavior in a thin vessel heat storage unit using salt hydrate latent heat storage material

Recently, there has been considerable interest in heat storage materials. Among them, sodium acetate trihydrate (melting point: 58 °C; latent heat: 264 kg/kg) is a suitable latent heat storage material for recovering and using exhaust heat in a temperature range lower than 100 °C, which is discharged in homes and factories. The purpose of this study was to investigate the heat storage and release behavior of sodium acetate trihydrate in a thin-vessel heat storage unit (160 mm × 130 mm × 4.8 mm) made of glass and polycarbonate. The sodium acetate trihydrate in the unit was heated or cooled by flowing water in water channels (width: 1 mm) disposed on both sides of the heat storage unit. From the experimental results, performance deterioration was evident in the heat storage and release process of sodium acetate trihydrate due to phase separation during heat storage and supercooling during heat release. Therefore, a thickener and a nucleating agent were added to sodium acetate trihydrate to suppress phase separation and supercooling effects. The results revealed that the thickener and nucleating agent were unevenly distributed in the case of repeated heat storage and release. The heat transfer numerical simulation adopting the lumped capacitance model was confirmed to be useful for investigating the melting behavior of sodium acetate trihydrate.

On the comparison between computational fluid dynamics (CFD) and lumped capacitance modeling for the simulation of transient heat transfer in solar dryers

In this paper transient heat transfer in a solar food drier is modeled by using both computational fluid dynamics (CFD) and lumped capacitance modeling techniques. The CFD model is used to simulate the air flow and transient heat transfer within the dryer. A lumped capacitance model, developed from energy exchanges between various components of the drying chamber, is extensively compared with the results of the CFD model. The two models predict both a 40 °C rise in steady-state temperature within the drying chamber. Before reaching this temperature, there is about 8 °C RMS deviation between the transient temperature prediction of the two models. This deviation is mainly caused by the heat transfer coefficient around the food rack shelfs. Fitting these coefficients give rise to a minimal RMS deviation between the two models of 1.8 °C and 0.9 °C on the lower and upper rack shelfs respectively. The transient heat transfer phenomenon from CFD modeling also showed that the spatial distribution of temperature after 30 min is uniform thus validating the very assumption of lumped capacitance modeling. This demonstrates that the lumped capacitance model can supplant the computationally demanding CFD modeling technique in predicting transient heat transfer phenomenon in solar food dryers.

Common-Mode Noise Modeling and Reduction for 1-MHz eGaN Multioutput DC–DC Converters

Enhancement-mode gallium nitride (eGaN) high-electron-mobility transistors (HEMTs) are promising to increase the switching frequency into multimegahertz for the high power density. However, it is a serious challenge to identify the equivalent lumped capacitances of megahertz multiwinding planar transformers for common-mode (CM) noise analysis to optimize the electromagnetic interference filters. The couple turn with its one-capacitor model is proposed to quantify the total CM noise current via the high-frequency transformer. With the modeled total CM noise current, the equivalent lumped interwinding capacitance model of the transformer can be derived conveniently and accurately. A complete CM noise path model is built for a GaN-based active clamp forward with a self-driven synchronous rectification multioutput converter. Then, a CM noise cancelation capacitance is applied and optimized to generate a reverse extraction current to cancel the CM noise current. Compared with other methods, the proposed modeling technique can build the equivalent lumped interwinding capacitance model of the multiwinding planar transformer in the printed circuit board layout stage before it is fabricated physically. The proposed model is verified by the experimental results with a 1-MHz GaN prototype with 100-V input, 5-V/6-A, and ±12-V/ 0.83-A outputs. The CM noise spectrum is well predicted. The CM noise is reduced by around 15 dB (a reduction of 12.6%) below 9 MHz.

Evaluation of convective heat transfer coefficient and specific heat capacity of a lithium-ion battery using infrared camera and lumped capacitance method

The electrochemical performance of lithium-ion batteries is highly temperature dependent. An accurate determination of battery thermal parameters is crucial for research including cell thermal analysis, safety design, and multiphysics simulations. This work explores the possibility to use a lumped capacitance model based experimental approach to measure the battery convective heat transfer coefficient and specific heat capacity. In this approach, the transient temperature of the battery and its can (by removing the jellyroll) is measured with an infrared radiation camera. When the Biot number of the battery Bi ≪1, the lumped capacitance model can be used to determine cell specific heat capacity through the measured battery surface temperature, where the convective heat transfer coefficients of both the can and the battery are the same and the specific heat capacity of the can is known. As an example, the specific heat capacity of LG G5 smartphone batteries is measured to demonstrate the proposed approach. The specimens are tested under both natural and forced convection conditions. The measured cell specific heat capacity is very consistent between these two convection conditions.

Effects of Transient Heat Transfer on Compressor Stability

The effects of heat transfer between the compressor structure and the primary gas path flow on compressor stability are investigated during hot engine re-acceleration transients. A mean line analysis of an advanced, high-pressure ratio compressor is extended to include the effects of heat transfer on both stage matching and blade row flow angle deviation. A lumped capacitance model is used to compute the heat transfer of the compressor blades, hub, and casing to the primary gas path. The inputs to the compressor model with heat transfer are based on a combination of full engine data, compressor test rig measurements, and detailed heat transfer computations. Nonadiabatic transient calculations show a 8.0 point reduction in stall margin from the adiabatic case, with heat transfer predominantly altering the transient stall line. 3.4 points of the total stall margin reduction are attributed to the effect of heat transfer on blade row deviation, with the remainder attributed to stage rematching. Heat transfer increases loading in the front stages and destabilizes the front block. Sensitivity studies show a strong dependence of stall margin to heat transfer magnitude and flow angle deviation at low speed, due to the effects of compressibility. Computations for the same transient using current cycle models with bulk heat transfer effects only capture 1.2 points of the 8.0 point stall margin reduction. Based on this new capability, opportunities exist early in the design process to address potential stability issues due to transient heat transfer.

FracTional Lumped Capacitance

Abstract A new lumped capacitance model that employs fractional order operators is proposed for use on transient heat conduction problems. Details and implications of the fractional lumped capacitance model’s development and application are discussed. The model is shown to agree with observed heating and cooling temperature profiles of laser aiming paper being heated by a laser under various conditions.

An experimental and computational approach to thermoelectric-based conditioned mattresses

This paper sets out to describe the design, construction and testing of a thermoelectric-based conditioned mattress intended to reduce the human-mattress interface temperature, in order to increase the user’s sleep quality and thermal comfort in warm locations of Spain. A prototype is constructed and tested, which includes a mattress and a thermoelectric system that cools the inner air and governs the human-mattress interface temperature. This temperature results 2.1 °C lower than that of the room ambient, for 90 W of supplied electric power to the thermoelectric modules, with a coefficient of performance of 0.34. Under this scenario, the comfort perceived by the user is expected to improve compared to that provided by a no-conditioned mattress. The prototype is modified so that the inner air is pumped directly to the human body. With this improvement, the relevant temperature is now that of the inner air, which results 3.4 °C lower than the room ambient temperature, thus expected to increase even more the comfort perceived by the user, with 0.58 of coefficient of performance. In order to simulate both the transient and steady state of the global system, a lumped-capacitance model is devised specifically for this application. The validation process is conducted comparing simulated and experimental values of electric current, temperature difference between ends of the modules, temperature difference between the inner air and the ambient, and coefficient of performance. In steady state, the theoretical model predicts the experimental results with deviations below ±9%. Computational results indicate that the inner air temperature increases by only 1 °C, when air humidity increases from zero to 100%. Under the 100%-humidity scenario, the inner air temperature is still 2.4 °C lower than the room ambient temperature, reducing slightly the coefficient of performance to 0.47.

The Lumped Capacitance Model for Unsteady Heat Conduction in Regular Solid Bodies With Natural Convection to Nearby Fluids Engages the Nonlinear Bernoulli Equation

For the analysis of unsteady heat conduction in solid bodies comprising heat exchange by forced convection to nearby fluids, the two feasible models are (1) the differential or distributed model and (2) the lumped capacitance model. In the latter model, the suited lumped heat equation is linear, separable, and solvable in exact, analytic form. The linear lumped heat equation is constrained by the lumped Biot number criterion Bil=h¯(V/S)/ks < 0.1, where the mean convective coefficient h¯ is affected by the imposed fluid velocity. Conversely, when the heat exchange happens by natural convection, the pertinent lumped heat equation turns nonlinear because the mean convective coefficient h¯ depends on the instantaneous mean temperature in the solid body. Undoubtedly, the nonlinear lumped heat equation must be solved with a numerical procedure, such as the classical Runge–Kutta method. Also, due to the variable mean convective coefficient h¯ (T), the lumped Biot number criterion Bil=h¯(V/S)/ks < 0.1 needs to be adjusted to Bil,max=h¯max(V/S)/ks < 0.1. Here, h¯max in natural convection cooling stands for the maximum mean convective coefficient at the initial temperature Tin and the initial time t = 0. Fortunately, by way of a temperature transformation, the nonlinear lumped heat equation can be homogenized and later channeled through a nonlinear Bernoulli equation, which admits an exact, analytic solution. This simple route paves the way to an exact, analytic mean temperature distribution T(t) applicable to a class of regular solid bodies: vertical plate, vertical cylinder, horizontal cylinder, and sphere; all solid bodies constricted by the modified lumped Biot number criterion Bil,max<0.1.