Heat Transfer Law Research Articles

On the analysis of an ecological regime for energy converters

In the context of Finite Time Thermodynamics, an ecological-like function is built based on the ecological and efficient power energy functions. By means of an optimization analysis of the Curzon–Alhborn heat engine with a Newtonian heat transfer law, a comparative study between our proposal and the maximum power, ecological and efficient power criteria is carried out. With this different approach, contrasted to the other regimes, there is an increase in efficiency, and it results in a decrease in the maximum power output and the dissipation. The analysis is extended to a Müser engine, and an example related with solar energy converters is presented. In addition, a semi-analytical method is used to obtain approximate formulas for certain thermal efficiencies, which are usually obtained numerically and no analytic expressions are given.

Minimizing entransy dissipation for heat transfer processes withq∝Δ(Tn)and heat leakage

Heat transfer process with heat leakage and generalized radiative heat transfer law (HTL) [q∝Δ(Tn)] is investigated. Optimality condition for the minimum entransy dissipation (MED) is derived by applying average optimal control theory. On the basis of the general optimization result, the results for four special cases of Newtonian [q∝Δ(T)], linear phenomenological [q∝Δ(T−1)], radiative [q∝Δ(T4)], and mixed [q∝Δ(T4) with q∝Δ(T)] HTLs are further obtained. Optimal paths are compared with the common strategies of constant heat flux rate and constant hot fluid temperature operation. Numerical examples are presented, and influences of heat transferred amount and heat leakage on optimization performances are analyzed.

Thermal Brownian refrigerator with external and internal irreversibilities

In this paper, a new model of irreversible thermal Brownian refrigerators considering external and internal irreversibilities is established by using finite time thermodynamics. The analytical formulas of cooling load and coefficient of performance (COP) are derived with Newtonian heat transfer law. The operating temperatures of the refrigerator are obtained by solving equations, and the basic performance characteristics and valid working areas are studied. The optimal performance is achieved by optimizing the design parameters and the heat transfer process. The effects of key parameters, temperature ratio and irreversible factors on optimal performance are investigated. The new model performance is compared with that of previous models. Results show that the new model provides a unified description for thermal Brownian refrigerators. The cooling load and COP exist maximal values about thermal conductance ratio between the two heat exchangers. When the thermal conductance ratio and other design parameters are optimal, the corresponding operating temperatures of the thermal Brownian refrigerator reach the optimal values. The results are universal, and it contains the results of previous models with different irreversible factors.

Study of the convection heat transfer law and temperature prediction of the duct in high-temperature tunnels

During the construction of tunnels subjected to high temperatures (here called high-temperature tunnels), ventilation cooling is an essential requirement. A high-temperature section of a construction tunnel on the Sichuan-Tibet Railway was used as a test case to study the heat exchange on both sides of the ventilation duct during active cooling. We used theoretical analysis and numerical simulation to establish a model for calculating the temperatures associated with the ventilation duct, and studied the influence of different factors on the convection heat exchange on the inside and outside the duct during the ventilation cooling process. According to simulation and field measurement results, the airflow temperature inside the duct rose with the distance from the inlet, and the temperature near the duct's wall was higher than the temperature in the center. After analyzing different influencing factors, it was found that duct material and thickness have little effect on the convection heat transfer inside the duct. But the convection heat transfer intensity would rise when the temperature difference between the inside and the outside of the duct increased, and the heat flux ( q ) through the wall increased by 1.5 W/m 2 . The average air temperature trend of the ventilation duct section was stable as the ventilation distance increased. It increased linearly as ventilation distance increased. While the effect of ventilation cooling gradually declined, and the overall temperature of the air of the tunnel rose when the ventilation distance increased. As a result, heat exchange along the duct should be fully considered in the design and application of the ventilation cooling process to ensure that the airflow temperature reaching the excavation face at the head of the tunnel meets the operational requirements.

Mathematical Modeling of the Protective Effect of Ethyl Silicate Gel Coating on Textile Materials under Conditions of Constant or Dynamic Thermal Exposure

The influence of the process of fire-retardant coating on textiles on the degree of fire protection of cotton and blended fabrics is investigated. Physical-chemical properties of impregnated samples of textile materials depending on the composition of ethyl silicate hydrolysates, concentration and content of diammonium hydrogen phosphate on fire resistance of impregnated samples, time of onset destruction and area of charring of samples after fire tests are analyzed. The obtained experimental data showed the need to build a mathematical model of the protective action of the gel coating based on the laws of heat and mass transfer, which under conditions of maximum simplicity and minimal artificiality takes into account the main processes from the external heat flow processes of heat transfer, thermal decomposition, evaporation and removal of mass, as well as to develop algorithms and software for computer modeling of the protective action of such a coating in conditions of constant or dynamic thermal exposure. A mathematical model of fire-retardant action of organosilicon coating on cellulose-containing fiber of fabric threads has been developed. It provides predictive estimates of fire safety parameters of textile materials, based on the level of thermal impact on the surface of the protected material.

Thermal Analysis of Coupled Resonant Coils for an Electric Vehicle Wireless Charging System

Electric vehicles use wireless energy transmission to obtain energy, which can effectively avoid the shortcomings of traditional methods. As the carrier of radio energy transmission and reception, the high temperature of the coil triggers the degradation of wireless transmission performance and the aging of the coil, which may cause fire and other safety problems in serious cases. This paper studied the temperature distribution of the magnetically coupled coil model for electric vehicles. Based on the study of the basic law of heat transfer, the coil model was established using ANSYS software, and the boundary conditions and relevant parameters were set. After many simulation experiments and comparisons, it was finally determined that the transmitting coil and the receiving coil were the same sizes, the inner diameter of the coil was 100 mm, the outer diameter of the coil was 181 mm, and the coupling distance between the transmitting coil and the receiving coil was set to 60 mm. Coil models were simulated and analyzed using different materials. The simulation results show that after 30 min of system operation, the material chosen from the temperature range may have been gold, silver, copper, or aluminum, but from the comprehensive consideration of cost and performance, the material of the coil in the model was finally set to copper. Copper was the best material; its temperature maximum was 74.952 °C and lower than the safety value of 80 °C. It is hoped that this study will provide a reference for wireless charging coil design.

Shape optimization of a thermal insulation problem

We study a shape optimization problem involving a solid Ksubset {mathbb {R}}^n that is maintained at constant temperature and is enveloped by a layer of insulating material Omega which obeys a generalized boundary heat transfer law. We minimize the energy of such configurations among all (K,Omega ) with prescribed measure for K and Omega , and no topological or geometrical constraints. In the convection case (corresponding to Robin boundary conditions on partial Omega ) we obtain a full description of minimizers, while for general heat transfer conditions, we prove the existence and regularity of solutions and give a partial description of minimizers.

Optimal Configuration of Finite Source Heat Engine Cycle for Maximum Output Work with Complex Heat Transfer Law

Abstract A finite source heat engine’s optimal configuration is studied. The model includes thermal resistance, heat leakage, a complex heat transfer law, and a heat source with variable temperature. The optimization objective is that the output work is the largest. The influences of factors such as the heat transfer law and heat leakage are analyzed. The results of this paper are universal and inclusive, and provide certain theoretical support for the performance improvement of actual heat engines.

Thermal Field and Stress Analysis of Induction Motor with Stator Inter-Turn Fault

Inter-turn fault (ITF), a typical motor fault, results in significant variations in the thermal characteristics of a motor. For fault, temperature rise (TR) experiments and thermal field-stress field simulations of an induction motor are carried out to reveal the fault characteristics related to ITF. First, based on the actual structure and the cooling type of the motor, a whole-domain simulation model of the fault thermal field was established. The reasonable equivalence of the motor and the calculation of the heat transfer boundaries were conducted during the modeling process. Then, the three-dimensional transient thermal field under a rated load before and after the fault was obtained, and the accuracy of the simulation could be validated through the comparison of the measured TR at several temperature-measuring points. The heat-transfer law and the notable thermal characteristics of the fault can be presented by analyzing the simulated and measured temperature data. In addition, a fault feature is proposed to provide a reference for diagnosis using the temperature difference of winding at different positions at different moments. Finally, the rotor thermal stress distribution of the normal and faulty motor is obtained by thermal-stress-coupled calculation, which can be used to evaluate the possibility of rotor fault caused by ITF.

Efficient system-level simulations of thermal wind sensors considering environmental factors

For the development of micro-electro-mechanical system (MEMS) technology during the past several years, MEMS design has requirements of high precision, high efficiency, iterative design, joint design of structure and circuit and so on. With the improvement of thermal wind sensor performance requirements and the complexity of the application environment, it is becoming increasingly difficult to ignore the impact of environmental factors. However, there is no system-level model considering the influence of environmental factors adequately in macro model. To solve these problems, a 2D thermal wind sensor macro model considering environmental factors is proposed. In order to build a macro model which can reflect the output of sensors in different environments, this paper, starting from the basic law of heat transfer, proposes an accurate macro model of the thermal wind sensor. The model proposed in this study accurately considers the influence of thermal and transport properties in different environments, and can be simulated together with the interface circuits in Cadence software. The results indicate that the variation of temperature and atmospheric pressure in the natural range can affect the sensor output by more than 15%, and the influence of relative humidity should not be ignored when the temperature is higher than 70 °C. Furthermore, the flow direction over the sensor can be further studied according to the 2D equivalent circuit model. The simulation results agree well with the experimental results, and the results can provide a valuable reference for the research and practical application of thermal wind sensors.

Maximizing power output of endoreversible non-isothermal chemical engine via linear irreversible thermodynamics

Maximum power performance of an endoreversible non-isothermal chemical engine (NICE) with simultaneous heat and mass transfer is investigated in this paper. The heat and mass transfer processes are assumed to obey Onsager equations in linear irreversible thermodynamics. The power output of the endoreversible NICE as well as the corresponding vector efficiency [See Eq. (13) in this paper for its definition] are obtained analytically. Special cases for an endoreversible Carnot heat engine with the linear phenomenological heat transfer law [q∝Δ(T−1)] and an endoreversible isothermal chemical engine with the linear mass transfer law [g∝Δ(μ)] are further derived based on the general optimization results. Some numerical examples are provided, and the effects of changes of absorbed energy flux rate, mass flux rate, and heat and mass transfer phenomenological coefficients on the optimization results are analyzed. The results show that there are optimal absorbed energy flux rate and optimal mass flux rate for the power output of the endoreversible NICE to approach to its maximum; the relationship between the power output of the endoreversible NICE and its vector efficiency is paraboloid.

Comparative performance for thermoelectric refrigerators with radiative and Newtonian heat transfer laws

Models of multi-element thermoelectric refrigerator (TER) with radiative heat transfer law (RHT) and Newtonian heat transfer law (NHT) are established based on finite time thermodynamics. The sameness and difference of the characteristics with different form of heat transfer are compared by numerical examples. It is found that for two heat transfer models, there is a set of optimal variables, i.e., an optimal working electrical current (WEC) and an optimal ratio of thermal conductance (RTC) of heat exchangers corresponding to the maximum cooling load, and there is another set of optimal variables corresponding to the maximum coefficient of performance (COP). For the same heat reservoir temperature difference (HRTD), both the cooling load and COP with RHT is larger than that with NHT, the optimal WEC at maximum cooling load with RTH is lager than that with NTH, and the optimal WEC at maximum COP with RTH is almost the same as that with NTH. With the increase of HRTD, both of the optimal WECs at maximum cooling load with RTH and NTH decrease, and both of the optimal WECs at maximum COP with RTH and NTH increase. The study with different heat transfer model for TER is necessary.

Development of leak detection methods using canister surface temperature change during gas leak from canister- leak evaluation using a 1/4.5-scale cask model -

It would be useful for improving the safety of the long-term storage to install a leak detector on a canister in a concrete cask. The phenomenon that the temperature at the bottom of the canister increases and the temperature at the top of the canister decreases during the gas leak from the canister has been confirmed in the previous study. We have proposed sealing performance monitoring by using this phenomenon. To quantitatively evaluate temperature values in the actual canister, we conducted tests and test analysis. We used a 1/4.5-scale cask model designed in consideration of a similarity law of heat transfer. The temperatures obtained in the tests were converted into the actual canister temperatures by dimensional analysis. Also, three leak detection methods were evaluated by using the obtained temperature data. In addition, a computational fluid dynamics calculation for analyzing the phenomenon that the temperatures change before and after the pressure drop was performed.

Spatio-temporal multi-scale observation of the evolution mechanism during millisecond laser ablation of SiCf/SiC

Millisecond laser processing has advantages in terms of depth, efficiency, and cost. The evolution mechanism of the laser ablation of SiCf/SiC fabricated through melt infiltration remains unclear. Therefore, spatio-temporal multi-scale observation is proposed. The information of gas, plasma, and droplets is collected and analysed. The results reveal that laser power and the type of assist gas considerably affect the material removal, hole morphology, and efficiency. Typical topographies, such as crack propagation, fibre fracture, recasting, and debonding are clarified with various melting temperatures and internal stress induced by temperature gradient. Additionally, the distribution of elements Si and C is exclusive, which is clarified with surface tension, melting temperature difference, chemical reaction, and intervention of assist gas. The simulation model based on heat transfer laws and the birth-death element method verifies the rationality of the evolutionary model of the hole morphology. Moreover, the simulation model established for first pulse ablation in N2 indicates that a limited increase in maximum depth at high power can be attributed to the plasma shielding effect. This study can guide the processing of parts in the aerospace and nuclear industries.

Research on water heat coupling model of riparian zone based on soil thermal conductivity model

In recent years, the research on the process of water and heat transfer in the riparian zone has become more and more extensive, a more accurate riparian water and heat coupling model is helpful for us to understand the law of water and heat transfer in the riparian zone. The hydro thermal coupling model of riparian zone is constructed based on different soil thermal conductivity models, the simulation effects of different models are verified and compared by using the experimental data, the parameter sensitivity analysis of the built model is carried out to determine the main parameters affecting the output of model temperature field, and the influence of revetment structure on the process of hydro thermal transport in riparian zone is simulated. The results show that: 1. the Hydrothermal Coupling Model of riparian zone based on Johansen thermal conductivity model has the best simulation effect and high reliability. 2. The permeability coefficient (ks ) and porosity (n) have the most significant influence on the temperature simulation results, and the parameter sensitivity is the highest. 3. The revetment structure hinders the infiltration of surface water into the riparian zone in the horizontal direction, reduces the infiltration water level and temperature fluctuation in the riparian zone.

Numerical study of heat and mass transfer enhancement in Prandtl fluid MHD flow using Cattaneo-Christov heat flux theory

Heat and mass transfer have numerous industrial applications. The classical heat and mass transfer laws (Fourier and Fick laws) do not predict thermal and solute relaxation time phenomena. However, in this article, generalized modeling related to simultaneous heat and mass transfer in non-Newtonian fluid in the presence of chemical reaction and heat generation is presented and models are numerically solved by the finite element method (FEM). Hybrid nanoparticles A g and F e 3 O 4 are considered and novel correlations are inserted during numerical simulations. The present results have a good agreement with already published benchmark. Thermal relaxation time is the characteristics of the fluid due to which it avoids or tries to avoid the thermal changes. The fluid with thermal relaxation characteristic tries to restore the thermal equilibrium and hence the temperature of the fluid is decreased. The solute relation is incorporated in the concentration equation from generalized Fick's law and solute relaxation time has shown a decreasing tendency in the concentration field. The solute boundary layer region can be controlled via an increase in the solute relaxation parameter. Ohmic dissipation in hybrid nanofluid A g − F e 3 O 4 − Prandtl fluid) is stronger than that in mono nanofluid ( A g − Prandtl fluid). Hybrid nanofluid ( A g − F e 3 O 4 − Prandtl fluid) produces more heat due to Joule heating than that produced by mono nanofluid ( A g − Prandtl fluid).

Investigation of Leakage and Heat Transfer Properties of the Labyrinth Seal on Various Rotation Speed and Geometric Parameters

To investigate the influence of the variation of geometric parameters on the leakage and heat transfer characteristics of labyrinth seals at various rotational speeds, the labyrinth seal models with different geometric parameters were numerically simulated based on the control variable methods. Results show the aerodynamic mechanism of leakage characteristics changing with rotational speed, as well as the leakage characteristics of labyrinth seals under the coupling action of geometric parameters and rotating speeds. When the characteristic scale changes along the direction of centrifugal force, the variation trend of labyrinth seal leakage characteristics is consistent at different rotational speeds. However, the leakage characteristics of labyrinth seals show the difference of rotational speed when the feature scale changes along the axis. At the same time, the laws of convective heat transfer on the surface of the rotor and stator are shown by the results of the studies, which provides reference for the thermodynamic analysis of labyrinth seals.

Collapse of Coherent Large Scale Flow in Strongly Turbulent Liquid Metal Convection.

The large-scale flow structure and the turbulent transfer of heat and momentum are directly measured in highly turbulent liquid metal convection experiments for Rayleigh numbers varied between 4×10^{5} and ≤5×10^{9} and Prandtl numbers of 0.025≤Pr≤0.033. Our measurements are performed in two cylindrical samples of aspect ratios Γ=diameter/height=0.5 and 1 filled with the eutectic alloy GaInSn. The reconstruction of the three-dimensional flow pattern by 17 ultrasound Doppler velocimetry sensors detecting the velocity profiles along their beam lines in different planes reveals a clear breakdown of coherence of the large-scale circulation for Γ=0.5. As a consequence, the scaling laws for heat and momentum transfer inherit a dependence on the aspect ratio. We show that this breakdown of coherence is accompanied with a reduction of the Reynolds number Re. The scaling exponent β of the power law Nu∝Ra^{β} crosses eventually over from β=0.221 to 0.124 when the liquid metal flow at Γ=0.5 reaches Ra≳2×10^{8} and the coherent large-scale flow is completely collapsed.

Thermoelectric generator in endoreversible approximation: The effect of heat-transfer law under finite physical dimensions constraint.

We revisit the optimal performance of a thermoelectric generator within the endoreversible approximation, while imposing a finite physical dimensions constraint in the form of a fixed total area of the heat exchangers. Our analysis is based on the linear-irreversible law for heat transfer between the reservoir and the working medium, in contrast to Newton's law usually assumed in literature. The optimization of power output is performed with respect to the thermoelectric current as well as the fractional area of the heat exchangers. We describe two alternate designs for allocating optimal areas to the heat exchangers. Interestingly, for each design, the use of linear-irreversible law yields the efficiency at maximum power in the well-known form 2η_{C}^{}/(4-η_{C}^{}), earlier obtained for the case of thermoelectric generator under exoreversible approximation, i.e., assuming only the internal irreversibility due to Joule heating. On the other hand, the use of Newton's law yields Curzon-Ahlborn efficiency.

Scaling laws for two-phase flow and heat transfer in high-temperature heat pipes

Heat pipes are high efficiency passive two-phase heat transfer devices utilizing the cyclical evaporation and condensation of a working fluid to transfer heat between two interfaces. High-temperature heat pipes are used in a variety of applications that require high operating temperatures such as nuclear microreactors, solar thermal reactors, furnaces, and aerospace systems. The high operating temperatures, and the reactivity of certain working fluids such as liquid metals, dictate stringent safety precautions and require high startup costs. The present work describes the scaling laws for two-phase flow and heat transfer in heat pipes and thermosyphons, that allows the use of low-temperature working fluids to study various phenomena in high-temperature heat pipes. Similarity parameters which were obtained from the non-dimensionalized governing equations and constitutive relations were tabulated and discussed. A case study involving the scaling of a microreactor heat pipe for the purpose of investigating the pressure and temperature profiles was given. In addition, a parametric study was conducted on the effects of the liquid and vapor Prandtl numbers on the steady state pressure and temperature profiles.