Non-uniform Heat Generation Research Articles

Predicting anisotropic thermophysical properties and spatially distributed heat generation rates in pouch lithium-ion batteries

This paper proposes a novel thermal characterization approach to determine the specific heat capacity, anisotropic thermal conductivities, and spatially distributed heat generation rates of pouch lithium-ion batteries (LIBs) through a combined experimental and numerical simulation process. Unlike cylindrical LIBs, pouch LIBs subjected to high C-Rates exhibit non-uniform heat generation distributions due to the combined effect of their low impedance, large size, and internal structure. These thermophysical properties and distributed heat generation rates are crucial for designing, modeling, and assessing the performance of pouch-based battery thermal management systems. The proposed thermal characterization approach does not require expensive lab equipment and extensive details of the battery internal structure. Instead, it relies on simple battery experiments integrated with numerical modeling to predict these properties through inverse heat transfer simulations. The characterization approach accounts for non-uniform heat generation distribution through a geometric factor that discretizes the battery volume into three regions, and concentration factors that determine the percentage of the total heat generation rate in each region. Finally, the validation of the characterization approach and its accuracy is assessed with experimental data independent of that used in the characterization process.

Concepts of static vs. dynamic current transfer length in 2G HTS coated conductors with a current flow diverter architecture

This paper uses both experimental and numerical approaches to revisit the concept of current transfer length (CTL) in second-generation high-temperature superconductor coated conductors with a current flow diverter (CFD) architecture. The CFD architecture has been implemented on eight commercial coated conductor samples from THEVA. In order to measure the 2D current distribution in the silver stabilizer layer of the samples, we first used a custom-made array of 120 voltage taps to measure the surface potential distribution. Then, the so-called ‘static’ CTL () was extracted using a semi-analytical model that fitted well the experimental data. As defined in this paper, the static CTL on a 2D domain is a generalization of the definition commonly used in literature. In addition, we used a 3D finite element model to simulate the normal zone (NZ) propagation in our CFD samples, in order to quantify their ‘dynamic’ CTL (), a new concept introduced in this paper and defined as the CTL observed during the propagation of a quenched region. The results show that, for a CFD architecture, is always larger than , whereas when the interfacial resistance between the stabilizer and the superconductor layers is the same everywhere. We proved that the cause of these different behaviors is related to the shape of the NZ, which is curved for the CFD architecture, and rectangular otherwise. Finally, we showed that the normal zone propagation velocity (NZPV) is proportional to , not with , which suggests that the dynamic CTL is the most general definition of the CTL and should always be used when current crowding and non-uniform heat generation occurs around a NZ.

Entropy minimization on magnetized Boussinesq couple stress fluid with non-uniform heat generation

This article aims to investigate the generation of entropy for the magnetized coupled stress fluid passed through a permeable stretching cylinder that creates the condition of convective heat transfer. Additionally, in the uneven heat source in the flow field, we also analyzed our research. The properties of heat transfer taking into account in the perspective of thermal radiation. The main nonlinear partial differential equations (NPDE) become ordinary nonlinear differential equations by adopting the corresponding dimensionless variables. The recognized repeated shooting technique combined with the fourth-order standard Runge-Kutta integration solution to evaluate the resulting nonlinear ODE numerically. The velocity, temperature profile, streamline, number of local entropy generations, Bejan number, local friction coefficient, and Nusselt number effects of the new flow parameters are explained by graphs and tables. The flow system’s physical properties and the correlation between the parameters were clarified by using statistical methods. The results show that the Bejan number is reduced due to the magnetic source. Generation of entropy promotes the growth of the magnetic field and the Brinkman number, but the coupling stress aspect shows a double effect. The coupled stress parameter reduces the number of Nusselt by a fraction of 4.46%, while in the attendance of a magnetic field, the radiant heat transfer rate increases at a rate of 2.65%. In the attendance of a magnetic field, skin friction reduces the coupling stress factor by a rate of 24.67%. Besides, the current outcomes have been verified by previously published studies and are very acceptable. For the stretched cylinder, which has a curvature parameter of γ = 1.0, and for the flat, stretched surface, γ = 0.0, the thickness of the momentum and the thermal boundary layer are greater.

Thermal Stresses Due to Non-Uniform Internal Heat Generation in Functionally Graded Hollow Cylinder

Thermal stresses of a functionally graded hollow thick cylinder due to non-uniform internal heat generation are studied in this paper. Analytical solutions are obtained with radially varying properties by using the theory of elasticity. Thermal stresses distribution for different values of the powers of the module of elasticity and varying power law index of heat generation are studied. The results have been computed numerically and illustrated graphically.

Effect of Chemical Reaction and Thermo-Diffusion in an Electrically Conducting Walters’ B Fluid over a Vertical Stretching Surface

In this article, the significance of chemical reaction and thermo-diffusion in Walters’ B fluid is examined with medium porosity under the influence of non-uniform heat generation\absorption. The nonlinear ordinary differential equations describing the flow are obtained via similarity variables and tackled by Homotopy Analysis Method. The results show among others that involvement of chemical reaction contributes to the shrinking of concentration buoyancy effect while dimensionless temperature overshoot with large values of convective heat parameter and heat generation\absorption which enable thermal potency to gain entrance to the quiescent-fluid, indicating that the two parameters can be used for drying of the components.

Investigation on battery thermal management system combining phase changed material and liquid cooling considering non-uniform heat generation of battery

In order to keep the working temperature of lithium-ion battery in desired range under harsh conditions, a novel coupled thermal management with phase changed material (PCM) and liquid pipe was proposed and numerically investigated for prismatic LiFePO4 battery pack. The verified non-uniform heat generation model of the battery was employed to simulate the real temperature distribution on battery surface. The effects of coolant velocity, pipe position and ambient temperature on cooling performance of coupled system were analyzed. Cycle test under harsh conditions was conducted to evaluate the thermal performance of the system. Simulation results showed that the coupled system exhibited good cooling performance even at ambient temperature of 45 °C, which suppressed the maximum temperature and temperature difference of battery pack to 47.6 °C and 4.5 °C, respectively. In addition, the system removed the heat stored in PCM and improved the liquid fraction of PCM effectively, especially in the area close to the electrode tabs. In cycles, properly reducing the coolant velocity during charge was feasible in saving power consumption of liquid cooling while keeping the cooling capacity. These results might be helpful for the application of PCM and liquid cooling in battery thermal management system for better cooling performance and lower power consumption under harsh conditions.

Modeling of induction heating of thermoplastic composites

In this article, a hybrid finite element model is presented for the simulation of induction heating of layered composite plates. Modeling includes the alternating electromagnetic field generated by an alternating current running through a coil, the current densities in the composite plate resulting from the electromagnetic field, the heat generation resulting from the current density distribution, and the heat transfer resulting from the nonuniform heat generation in the plate and the temperature distribution in the plate. The different elements of the model are shown to capture the time-dependent temperature distribution resulting from a coil moving over the surface of a composite laminate.

Constructal design of a non-uniform heat generating disc based on entropy generation minimization

Non-uniform heat generating phenomenon is ubiquitous in real electronic devices. Based on this point, this paper researches the entropy generation rate (EGR) performance of a non-uniform heat generating (NUHG) disc. In this NUHG model, constructal design of the radial-pattern disc is performed with the conditions of constant- and variable-cross-sectional highly conductive routes (HCRs), respectively. The overall generation of heat over the entire disc area stays invariable, while the geometry of the disc is free to morph. The influence of heat generation non-uniformity on the optimized geometry of the disc is studied. The results manifest that increasing the thermal conductivity ratio and area ratio of HCRs both can reduce the EGR. Increasing the number of elements involved in the disc will compel the optimal HCRs to stretch towards the centre. In the areas with more heat generation and severer heat conduction requirement, more high conductivity material should be arranged to converge more heat flow and reduce the EGR aroused during the heat transfer process. The dimensionless EGR slumps by 11.5% on account of the employment of variable-cross-sectional HCR stratagem. Henceforth, the variable-cross-sectional HCR structure can reduce the EGR and improve its thermal performance. Additionally, the results obtained by minimizing EGR are compared with those obtained by minimizing maximum temperature difference. The primary novelty of this paper is introducing entropy generation minimization theory into the constructal design of radial-pattern disc with both non-uniform heat generation and constant- and variable-cross-sectional HCRs, which can provide benefits to the designs of practical electronic devices and the improvement of heat transfer performance.

Estimation of effective thermal conductivity of packed bed with internal heat generation

Test Blanket Module (TBM) of the fusion reactor has the vital role of removing heat generated from the fusion reactor along with the heat generated internally due to tritium breeding reaction. In the initial startup phase of fusion reactor, neutron flux has a climbing ramp nature and heat gets generated in discrete locations of TBM due to non-uniform nature of neutron irradiation. Thus, there is need to establish mathematical method to estimate Effective Thermal Conductivity (ETC) of packed bed with randomly scattered internal heat sources. Novel Induction Heating technique was used to simulate above mentioned conditions in packed bed of Li2TiO3 pebbles. An input-output FDM (Finite Difference Method) based model has been developed to estimate ETC of packed beds with non-uniform and discrete Internal Heat Generation (IHG). The inputs to the FDM based model are experimental results along with various operating and process parameters of the packed bed system under consideration. Also, an empirical correlation has been proposed to yield ETC of above mentioned packed bed systems valid for bed voidage of 0.44-0.47. The experimental and analytical methods used for this study are detailed in this paper.

Fingerprinting Redox Heterogeneity in Electrodes during Extreme Fast Charging

Conventionally, battery electrodes are rationalized as homogeneous reactors. It proves to be an erroneous interpretation for fast transients, where mass transport limitations amplify underlying heterogeneities. Given the lack of observability of associated fast spatiotemporal dynamics, redox activity in inhomogeneous electrodes is superficially explored. We resort to a physics-based description to examine the extreme fast charging of lithium-ion battery electrodes. Representative inhomogeneity information is extracted from electrode tomograms. We discover such electrodes to undergo preferential intercalation, localized lithium plating and nonuniform heat generation as a result of distributed long- and short-range interactions. The spatial correlations of these events with the underlying inhomogeneity are found to be nonidentical. Investigation of multiple inhomogeneity fields reveals an exponential scaling of plating severity and early onset in contrast to the homogeneous limit. Anode and cathode inhomogeneities couple nonlinearly to grow peculiar electrodeposition patterns. These mechanistic insights annotate the complex functioning of spatially nonuniform electrodes.

Constructal design and experimental validation of a non- uniform heat generating body with rectangular cross-section and parallel circular cooling channels

Non-uniform heat generating phenomenon is omnipresent in real electronic devices. A three-dimensional model with non-uniform heat generation is established in this paper. Both fluid flow and heat transfer behaviors are uncovered with the consideration of constructal theory. Constructal theory enables a heat transfer system to evolve and generate to provide a better flow access for the currents that flow through it. Taking a complex function composed of hot spot temperature and pumping power as the performance indicator, the diameter of cooling channels and the aspect ratio of elemental body are optimized as two degrees-of-freedom. The physical problem is numerically solved by resorting to the finite element method. The optimization was performed by the exhaustive search technique, comparing all results generated by finite element method. The heat generation over the entire body and the volume ratio of cooling channels operate as the prior constraints. On this basis, the optimal geometries of the elemental component are obtained in cases of various heat generating premises. The obtained results demonstrate that the complex function behaves an extreme value for the dimensionless cooling channel diameter. It is observed that the minimum value of the complex function slumps by 29.3% as the number of elements increases from 10 to 30. The overall thermo-fluid performance of the non-uniform heat generating body can be elevated as the elemental body features a square cross-section by releasing the new degree-of-freedom of aspect ratio to morph. Furthermore, alumina ceramics are used as the heat generating substrate and water as the coolant. The validity of the mathematical model is corroborated by experiments. Oriented to industrial applications, it is implied that the coolant entryway should be placed prone to the place where more electronic components or heat generating devices situate. The optimization results can put new suggestions on the thermal design of actual electronic devices from both theoretical and experimental perspectives.

Multiscale prediction of localized hot-spot phenomena in solar cells

Hot-spot phenomena in photovoltaic (PV) devices may suppress the performance and cause irresistible damage. Traditional study focuses on hot spots caused by shade or faults of PV modules, discussing the systematic failure. Different from that, this study focuses on hot-spot phenomena due to nonuniform heat generation within a unit cell of the module, which is resulted from surface microstructures, locally enhanced absorption and uneven concentration of light. In this paper, the volume heat generation in a cell is derived by modeling interactions between photons, excited free electrons and lattice phonons. And significant unevenness of heat generation is found. Based on the 3D heat distribution, transient simulations of cell temperature are conducted. Although hot-spot phenomena are negligible in non-concentrated PV cells, in a 400 × (1000 × ) high concentrator photovoltaic(HCPV) cell, remarkable hot spot is found with maximum temperature difference of 68K(169K) and the local hottest spot reaches 372K(491K). More seriously, in cloudy or windy days, cells may be shaded constantly, leading to sharp and constant temperature variation at the hot spot area in tens of microseconds. All these results creatively reveal that localized hot-spot phenomena within a cell may significantly suppress the cell performance and shorten the lifespan.

Constructal design of nonuniform heat generating area based on triangular elements: A case of entropy generation minimization

This paper reports a constructal investigation of heat transfer in a nonuniform heat generating triangular area, and numerically studies the entropy generation performance over the area inserted with constant and discrete variable cross-sectional high conductive channels (HCCs), respectively. The effects of the nonuniform heat generating (NUHG) coefficient and width coefficient on the overall thermal performance are also analyzed with several conditions of heat distributions. This model has two constraints: the area ratio of HCCs to the whole heat generating area and the global heat generation (the heat is nonuniformly distributed over the area). The structure of the HCCs is free to morph in order to present a better thermal performance. The numerical results show that for an elemental triangle, the optimal structure tends to elongate as the NUHG coefficient increases. It is also indicated that the dimensionless entropy generation rate for the first-order construct constituting of six elements is decreased by 20.0% in comparison with the counterpart constituting of four elements, which means that increasing the number of incorporated elements makes it favorable to improve the overall thermal performance. Additionally, the quartic minimized dimensionless entropy generation rate of the first-order construct with discrete cross-sectional HCCs performs 14.2% better than the counterpart with constant highly conductive routes. In this context, the thermal performance can be improved reasonably by intruding the variable cross-sectional architecture into the heat generating area. In general, the effects of the nonuniform heat generating coefficient p, width coefficient m and the number of triangular elements n on the overall thermal performance are studied. The pivotal innovation of this paper is introducing entropy generation minimization theory into the constructal design of triangular assemblies with both nonuniform heat generation and discrete variable cross-sectional HCCs, which can contribute to the design of practical electronic devices to a promising heat transfer performance.

Three- Dimensional Hydromagnetic Convective Flow of Chemically Reactive Williamson Fluid with Non-Uniform Heat Absorption and Generation

Abstract The electrically conducting three-dimensional Williamson fluid flow produced by the movement of sheet via porous medium under non-uniform heat sink and source, thermal radiation and convective boundary condition is examined. The system of nonlinear expressions is transformed into nonlinear ordinary differential system of equations. These governing expressions are evaluated numerically with the help of boundary value problem default solver in MATLAB bvp4c package. Pertinent results are demonstrated graphically to execute the effects of various governing parameters on dimensionless fields. The aspects of constraints on skin-friction, mass and heat transport rates are characterized via numerical benchmarks. It is noticed that the transverse and axial velocities are depreciated by respective Williamson fluid parameters, while the opposite trend is noticed on concentration and temperature fields.

Investigation of Two‐Dimensional Viscoelastic Fluid with Nonuniform Heat Generation over Permeable Stretching Sheet with Slip Condition

Here, in this research article, we have investigated an incompressible viscoelastic fluid flow over a uniform stretching surface sheet along with slip boundary conditions in the presence of porous media. The partial differential equations which govern the fluid flow are changed into ordinary differential equations through suitable similarity transformation variables. Finally, the transformed ordinary differential equations are solved with the help of a seminumerical technique known as the homotopy analysis method (HAM). The uniqueness of our study is not only to analyze and carry out the effect of the elastic parameter but also to account for viscous dissipation which is important in the case of optically transparent flow. The novel effects for the parameters which affect the flow and heat transfer, such as the Eckert number, porous medium parameter, and the velocity slip parameter, are studied through graphs. Also, the convergence analysis for the proposed method is addressed. Additionally, for the sake of validation, the present work is also compared with the already published work and an outstanding agreement is found.

Effect of cladding on thermal behavior of nuclear fuel element with non-uniform heat generation

In nuclear power reactors if the maximum temperature (2000ᵒC) of the fuel element like Uranium-dioxide increments and reaches 2865ᵒC then the fuel element melts down leading to heavy loss and damage. To maintain this maximum temperature well below the allowable limit the heat in the fuel element should be conducted and dissipated to the surrounding medium. In this article, the numerical prediction and comparison of thermal performance characteristics of a nuclear fuel element with and without cladding (bare fuel element) having non-uniform energy generation in axial direction is studied in detail. Accordingly, the two-dimensional heat conduction equation having a cosine variation of heat generation term in the axial direction, along with appropriate boundary conditions is solved using second order accurate finite difference schemes. The results are presented for a wide range of parameters like Aspect Ratio Ar, Biot number, Bi, Conductivity ratio, Cr, Thickness ratio, Th, and total heat generation parameter, Qt in the form of transverse temperature profiles and axial temperature profiles. Effect of Cr and Th due to presence of cladding is thoroughly studied. Different range of parameters for which the temperature of the fuel element is within the maximum temperature range is obtained. Critical values of these parameters for which the temperature increments above maximum temperature is also investigated. From the detailed discussion of the results it is concluded that the maximum temperature attained in the fuel element without cladding (bare fuel element) is very much higher than that attained in fuel element with cladding. Also it is observed that for fixed values of Ar, Cr and Th, there exists a critical value of Qt and Bi beyond and below which maximum temperature in the fuel element exceeds its allowable limit.

Flow and heat transfer of non-Newtonian Sisko fluid past a nonlinearly stretching sheet with heat generation and viscous dissipation

This work will scrutinize the flow of non-Newtonian Sisko fluid owing to a nonlinearly stretching sheet. The mingle effect of viscous dissipation and non-uniform heat generation are also supposed in this work. In our work, we contribute toward gaining the similar solution for our problem. Eventually, the group of equations controlling the problem is reduced to a couple of characteristic equations, the first represents the momentum whereas the second is the energy equation. Shooting method is then applied further to get the numerical solution for this yielded set of equations. Also, this proposed model may enable us to evaluate both the skin friction coefficient and the Nusselt number. Finally, our proposed research agrees very well with related works.

Constructal Optimization for Cooling a Non-Uniform Heat Generating Radial-Pattern Disc by Conduction.

A heat conduction model in a radial-pattern disc by considering non-uniform heat generation (NUHG) is established in this paper. A series of high conductivity channels (HCCs) are attached on the rim of the disc and extended to its center. Constructal optimizations of the discs with constant and variable cross-sectional HCCs are carried out, respectively, and their maximum temperature differences (MTDs) are minimized based on analytical method and finite element method. Besides, the influences of the NUHG coefficient, HCC number and width coefficient on the optimal results are studied. The results indicate that the deviation of the optimal constructs obtained from the analytical method and finite element method are comparatively slight. When the NUHG coefficient is equal to 10, the minimum MTD of the disc with 25 constant cross-sectional HCCs is specifically reduced by 48.8% compared to that with 10 HCCs. As a result, the heat conduction performance (HCP) of the disc can be efficiently improved by properly increasing the number of HCCs. The minimum MTD of the disc with variable cross-sectional HCC is decreased by 15.0% when the width coefficient is changed from 1 to 4. Therefore, the geometry of variable cross-sectional HCC can be applied in the constructal design of the disc to a better heat transfer performance. The constructal results obtained by investigating the non-uniform heat generating case in this paper can contribute to the design of practical electronic device to a better heat transfer performance.

(Invited) In Situ Measurement of Temperature Distributions in Lithium-Ion Cells Under Extreme Conditions for Failure Analysis

Lithium-ion (Li-ion) batteries are susceptible to failures, even thermal runaway, when operating under extreme conditions that exceed safety limits, such as overcharge, overheating and short circuit. Temperature plays an important role in such failures due to its interaction with electrochemical reactions and heat generation (1). With very low thermal conductivity of battery materials (2, 3) and typically non-uniform heat generation under such extreme conditions, the local temperatures inside Li-ion cells can be very different from surface temperature. In situ measurement of temperature distributions in Li-ion cells can be therefore very useful for safety and failure analysis. Various efforts have been reported in measuring Li-ion cells internal temperatures with insightful findings obtained, typically using embedded thermocouples (4-18), RTD (19, 20) or fiber optic sensors (21-23), or via electrochemical impedance (24-27). But most of these studies only address normal operating conditions. In the few studies that address extreme conditions, only one internal temperature sensor was embedded (4, 10, 18), providing very limited information. In this research temperature distributions in Li-ion cells under extreme conditions are measured for detailed failure analysis. The progress will be reported in the presentation.

Mitigating non‐uniform heat generation induced hot spot(s) in multicore processors using nanofluids in parallel microchannels

The present paper illustrates experimentally the impact of non-uniform heat generation in a microprocessor on the hot spot distribution and the method to cool the same, efficiently employing parallel microchannel cooling configurations. It is often assumed during design of microprocessor cooling systems that the heat load emitted by the device is uniform, however real time tracking of the device shows that such assumptions are far from the reality. An Intel® Core™ i7–4770 3.40 GHz quad core processor has been experimentally mimicked using heat load data retrieved from a real microprocessor with non-uniform core activity. Parallel microchannel based heat spreader configurations using U, I and Z type flow configurations have been employed to mitigate the thermal load from the mimicked device. The observations clearly show that the microchannel cooling system experiences two forms of hot spots, one due to the flow maldistribution within the system and the other due to the additional non-uniform heat generation by the device. The hot spots have been shown to exhibit drastically different shapes and core temperatures and this has been verified through simulations and infrared thermography. To efficiently cool hot spot core temperatures, nanofluids have been employed and ‘smart cooling’ has been observed and the same has been explained based on nanoparticle slip mechanisms. The present work shows that the notion that high flow maldistribution leads to high thermal maldistribution, is not always true and existing maldistribution can be effectively utilized to tackle specific hot spot location. The present work can be important to design cooling mechanisms for real microprocessors with high core activity leading to non-uniform hot spot formation probabilities.