Total Heat Generation Rate Research Articles

An Improved Heat Equation for Fully Coupled Thermal-Structural Finite Element Analysis Using Small Strain Formulation

In this paper an improved heat equation for fully coupled thermal structural finite element analysis is presented. In the problem solving process, mathematical formulation appropriate strain measures describing the onset and the growth of ductile and total damage and heat generation rate per unit volume for dissipation-induced heating have been employed. The model was implemented into a finite element code using an improved weak form for fully coupled thermal structural finite element analysis, an extended NoIHKH material model with internal damping for cyclic plasticity of metals capable of modelling ductile material behaviour in wide range of strain rates. A notched aluminium alloy specimen in cyclic tension using 2Hz excitation frequency and linearly increasing amplitude has been studied. The model verification showed excellent agreement with available experiments. A few selected analysis results are presented and briefly discussed.

An Improved Heat Equation to Model Ductile-to-Brittle Failure Mode Transition at High Strain Rates Using Fully Coupled Thermal-Structural Finite Element Analysis

In this paper a universal heat equation for fully coupled thermal structural finite element analysis of deformable solids capable of predicting ductile-to-brittle failure mode transition at high strain rates is presented. In the problem mathematical formulation appropriate strain measures describing the onset and the growth of ductile and total damage and heat generation rate per unit volume to model dissipation-induced heating have been employed, which were extended with the heat equation. The model was implemented into a finite element code utilizing an improved weak form for updated Lagrangian formulation, an extended NoIHKH material model for cyclic plasticity of metals applicable in wide range of strain rates and the Jaumann rate in the form of the Green-Naghdi rate in the co-rotational Cauchy’s stress objective integration. The model verification showed excellent agreement with the modelled experiment at low strain rates. Plastic bending of a cantilever has been studied at higher strain rates. A few selected analysis results are presented and briefly discussed.

Analysis of the heat generation of lithium-ion battery during charging and discharging considering different influencing factors

Operating temperature of lithium-ion battery is an important factor influencing the performance of electric vehicles. During charging and discharging process, battery temperature varies due to internal heat generation, calling for analysis of battery heat generation rate. The generated heat consists of Joule heat and reaction heat, and both are affected by various factors, including temperature, battery aging effect, state of charge (SOC), and operation current. In this article, a series of experiments based on a power-type lithium manganese oxide/graphite battery was implemented under different conditions. The parameters for Joule heat and reaction heat are determined, and the Joule heat, reaction heat as well as total heat generation rate is detailed and analyzed considering the influence of temperature, aging, SOC, and current. In order to validate the accuracy of heat generation rate, a lumped battery heat transfer model is applied to calculate the temperature variation, and the estimated temperature variation shows good correspondence with experimental results under different currents and aging conditions. Due to its simplicity, the temperature variation estimation method is suitable for real time applications.

Electrochemical–thermal analysis of 18650 Lithium Iron Phosphate cell

A pseudo two dimensional electrochemical coupled with lumped thermal model has been developed to analyze the electrochemical and thermal behavior of the commercial 18650 Lithium Iron Phosphate battery. The cell was cut to obtain the physical dimension of the current collector, electrodes, separator, casing thickness, gasket, etc. The layer structure of the spiral wound, cylindrical casing, gasket and heat shrink wrapping were modeled to understand better the temperature distribution across the cell. Natural convection and radiation were used to reflect the heat dissipation on the side surface. Experimental study was carried out to validate the simulation results. The simulation results suggested that the cell temperature and total heat generation rate have a positive correlation with the It-rates and these were inline with the experimental results. Reaction heat was the main heat source and it contributed about 80–85% of the total heat generated during charging and discharging of the cell. Based on the simulation results, the final temperature of the cell surface was elevated to 59°C using 10It of charging. The effect of electrical contact resistance between the connectors and terminals of the cell was also investigated. It was found that the electrical contact resistance caused a large temperature gradient across the cell. These effects are important and should be considered in the design of EV battery pack and thermal management system to reduce the maximum temperature and maintain the temperature uniformity of the cells.

Moving toward a more realistic material model of a ductile material with failure mode transition

AbstractIn this paper a universal mathematical model using fully coupled thermal‐structural finite element analysis capable of predicting ductile‐to‐brittle failure mode transition at high strain rates is presented. Appropriate equivalent strain measures describing the onset and the growth of ductile and total damage and heat generation rate per unit volume for dissipation‐induced heating have been proposed. The model was implemented into a finite element code using the updated Lagrangian formulation for finite strains, the von Mises material model with isotropic hardening and the Jaumann rate, in the form of the Green‐Naghdi rate, in the co‐rotational Cauchy's stress update calculation. Plastic bending of a cantilever was studied, applying constant pressure as stepped load to 1/3 of the upper surface of the beam. The analysis result shows that at higher strain rates the ductile damage value is significantly lower than the value of the total damage, while at low strain rates their values are approximately identical, thus the model is likely to open new perspectives in the study and numerical simulation of the behaviour of ductile materials.

Computational fluid dynamic analysis of core bypass flow phenomena in a prismatic VHTR

The core bypass flow in a prismatic very high temperature reactor (VHTR) is an important design consideration and can have considerable impact on the condition of reactor core internals including fuels. The interstitial gaps are an inherent presence in the reactor core because of tolerances in manufacturing the blocks and the inexact nature of their installation. Furthermore, the geometry of the graphite blocks changes over the lifetime of the reactor because of thermal expansion and irradiation damage. The occurrence of hot spots in the core and lower plenum and hot streaking in the lower plenum (regions of very hot gas flow) are affected by bypass flow. In the present study, three-dimensional computational fluid dynamic (CFD) calculations of a typical prismatic VHTR are conducted to better understand bypass flow phenomena and establish an evaluation method for the reactor core using the commercial CFD code FLUENT. Parametric calculations changing several factors in a one-twelfth sector of a fuel column are performed. The simulations show the impact of each factor on bypass flow and the resulting flow and temperature distributions in the prismatic core. Factors include inter-column gap-width, turbulence model, axial heat generation profile and geometry change from irradiation-induced shrinkage in the graphite block region. It is shown that bypass flow provides a significant cooling effect on the prismatic block and that the maximum fuel and coolant channel outlet temperatures increase with an increase in gap-width, especially when a peak radial factor is applied to the total heat generation rate. Also, the presence of bypass flow causes a large lateral temperature gradient in the block and also dramatically increases the variation in coolant channel outlet temperatures for a given block that may have repercussions on the structural integrity of the graphite, the neutronics and the potential for hot streaking and hot spots occurring in the lower plenum.

Effect of entropy change of lithium intercalation in cathodes and anodes on Li-ion battery thermal management

The entropy changes (Δ S) in various cathode and anode materials, as well as in complete Li-ion batteries, were measured using an electrochemical thermodynamic measurement system (ETMS). LiCoO 2 has a much larger entropy change than electrodes based on LiNi x Co y Mn z O 2 and LiFePO 4, while lithium titanate based anodes have lower entropy change compared to graphite anodes. The reversible heat generation rate was found to be a significant portion of the total heat generation rate. The appropriate combinations of cathode and anode were investigated to minimize reversible heat generation rate across the 0–100% state of charge (SOC) range. In addition to screening for battery electrode materials with low reversible heat, the techniques described in this paper can be a useful engineering tool for battery thermal management in stationary and transportation applications.

Benchmark of Computational Fluid Dynamics Simulations Using Temperatures Measured Within Enclosed Vertical and Horizontal Arrays of Heated Rods

Experiments and computational fluid dynamics/radiation heat transfer simulations of an 8 × 8 array of heated rods within an air-filled aluminum enclosure are performed. This configuration represents a region inside the channel of a boiling water reactor fuel assembly between two consecutive spacer plates. The rods are oriented horizontally or vertically to represent transport or storage conditions. The measured and simulated rod temperatures are compared for three different rod heat generation rates to assess the accuracy of the simulation technique. Simulations show that temperature gradients in the air are much steeper near the enclosure walls than they are near the center of the rod array. The measured temperatures of rods at symmetric locations are not identical, and the difference is larger for rods close to the wall than for those far from it. Small but uncontrolled deviations of the rod positions away from the design locations may cause these differences. The simulations reproduce the measured temperature profiles. For a total rod heat generation rate of 300 W, the maximum rod-to-enclosure temperature difference is 150°C. Linear regression shows that the simulations slightly but systematically overpredict the hotter rod temperatures but underpredict the cooler ones. For all rod locations, heat generation rates, and rod orientations, 95% of the simulated temperatures are within 11°C of the correlation values. For the hottest rods, which reside in the center of the domain where the air temperature gradients are small, 95% of the simulated temperatures are within 4.3°C of the correlation values. These results can be used to assess the accuracy of using simulations to design spent nuclear fuel transport and storage systems.

Natural Convection in an Array of Vertical Channels with Two-Dimensional Heat Sources: Uniform and Non-Uniform Plate Heating

An experimental and numerical analysis was performed to investigate the conjugated conduction–convection heat transfer problem in an array of vertical, parallel plates forming open channels with heated protruding elements attached to one of the walls. Uniform and non-uniform heating of the plates was analyzed. Both the distance between plates and power dissipated per plate was varied. In non-uniform heating in each plate and for a specified total heat generation rate, one element was electrically supplied with a different power level from the others, and the influence of the location of this element on the temperature distribution was investigated. The SIMPLEC algorithm, based on the finite volume method, was used to solve the pressure velocity coupling. Numerical and experimental temperature profiles were compared and good agreement was observed.

Optimal distribution of discrete heat sources on a wall with natural convection

This paper is an application of the constructal method to the discovery of the optimal distribution of discrete heat sources cooled by laminar natural convection. The global objective is to maximize the global conductance between the wall and the fluid, or to minimize the hot-spot temperatures when the total heat generation rate and global system dimensions are specified. Two scenarios are investigated: (i) a large number of small heat sources mounted on a vertical wall facing a fluid reservoir, and (ii) a small number of finite-size heat sources mounted on the inside of the side wall of a two-dimensional enclosure. It is shown that the optimal distribution is not uniform (the sources are not equidistant), and that as the Rayleigh number increases the heat sources placed near the tip of a boundary layer should have zero spacings. In both (i) and (ii), the optimal configuration of the wall with discrete sources is generated by the pursuit of maximal global performance subject to global constraints.

Experimental Study on Heat Generation Behavior of Small Lithium-Ion Secondary Batteries

The overpotential resistance and the entropy change of two small lithium-ion secondary batteries, which are the heat source terms to increase the battery temperature, have been measured by several methods, changing the battery temperature and the state of charge. The temperature increase and the total heat generation rate of the batteries were calculated during the discharge cycle by using the measured resistance and entropy, being compared with the experimental results of the temperature increase and the total heat generation rate. The overpotential resistance was estimated by four measurement methods, i.e., the battery voltage-current characteristics during the constant current discharge, the difference between the open-circuit voltage and the cell voltage, the voltage change during the intermittent discharge for 60 s, and the ac impedance measurement. The overpotential resistance by the voltage-current characteristics is almost the same as by the difference between the open-circuit voltage and the cell voltage. However, in some cases the resistances by the intermittent discharge and the ac impedance are smaller than the former two resistances. The entropy change measured by the temperature change of the open-circuit voltage agrees almost with the measured by the heat production difference between the charge and discharge cycle. The temperature increases and the total heat generation rates estimated from the overpotential resistances by the voltage-current characteristics and by the temperature change of open-circuit voltage agree well with the measured ones for the two batteries during the constant current discharge. © 2003 The Electrochemical Society. All rights reserved.

Resistance jumps and hysteresis in ferromagnetic wires

A phenomenological theory leading to the principle of minimum heat generation is presented for the recently discovered exotic electric transport in ferromagnetic wires with a domain wall. In our theory, the lifetime (steadiness) of a local magnetic configuration of localized spins trapped by an impurity is assumed to be a decreasing function of the corresponding local temperature. The local temperature is an increasing function of the heat generation rate due to the conduction electron's inelastic scattering induced by the local combination potential of the impurity and the magnetic configuration. As a result, the whole magnetic structure of the system as well as the current distribution is realized as the nonequilibrium steady state to minimize the total heat generation rate of the system. Relying on this phenomenological principle of minimum heat generation, we provide a unified explanation of the negative and positive jumps and of the hysteresis loops observed in the magnetoresistance experiments. Our argument is based on a microscopic calculation as well as the principle. The result shows that the presence of a domain wall sometimes enhances the transmission probability of the conduction electrons through an impurity potential.

Steady-State Analysis of Visco-Elastic Material Generating Internal Heat for Vibration Damping. Method of Analysis and Two-Dimensional Problem under Fixed Thermal Boundary Condition.

When a viscoelastic material is applied by a sinusoidal excitation of which frequency is relatively high and amplitude large, we can recognize a phenomenon that the temperature of the material increases, while the apparent dynamic stiffnesses decrease. It is considered that the phenomenon is caused by the temperature dependence of the dynamin properties of the material and internal heat generetion for mechanical damping. There are, however, few papers on the vibration analysis of the viscoelastic materials taking into consideration the temperature dependence of the dynamic properties and internal heat generation. In this paper, a new analysis method is presented in order to examine the vibrating viscoelastic material on the steady-state response, and then the method applyed to two dimensional problem of viscoelastic material undergoing a sinusoidal displacement, under the fixed thermal boundary condition. Analytical results were reduced to the mean temperature, the total heat generation rate and the apparent dynamic stiffnesses, and the relationships between each quantites are found. As a result of consideration for the relationships, new equation for mean temperature was derived, moreover it is shown that apparent dynamic stiffnesses are also determined by the solution of the equation.

Constructal-theory network of conducting paths for cooling a heat generating volume

This paper develops a solution to the fundamental problem of how to collect and ‘channel’ to one point the heat generated volumetrically in a low conductivity volume of given size. The amount of high conductivity material that is available for building channels (high conductivity paths) through the volume is fixed. The total heat generation rate is also fixed. The solution is obtained as a sequence of optimization and organization steps. The sequence has a definite time direction, it begins with the smallest building block (elemental system) and proceeds toward larger building blocks (assemblies). Optimized in each assembly are the shape of the assembly and the width of the newest high conductivity path. It is shown that the paths form a tree-like network, in which every single geometric detail is determined theoretically. Furthermore, the tree network cannot be determined theoretically when the time direction is reversed, from large elements toward smaller elements. It is also shown that the present theory has far reaching implications in physics, biology and mathematics.

On the “surface law” and basal metabolic rate

It is shown on a theoretical basis that the existence of a “power law” relationship between body mass M and total metabolic heat generation rate Q of the form Q = kM α does not uniquely determine the dependence of metabolic rate on body temperature. However, it is shown that a particular assumption for this temperature dependence, successful in other problems, does predict a “power law” similar to the empirical one. At the same time it also accounts satisfactorily for the linear dependence of metabolic rate on ambient temperature.