Orthotropic Thermal Conductivity Research Articles

An inverse methodology to estimate the thermal properties and heat generation of a Li-ion battery

Accurate estimation of temperature-dependent orthotropic thermal properties and volumetric heat generation of a Li-ion battery is crucial for thermal modeling, thermal safety, and the design of thermal management systems for electric vehicles. Though various studies are available on estimating thermophysical properties and heat generation, simple and easily applicable methods are rare. Moreover, these studies failed to report temperature sensitivity and standard deviation of the estimates. In this study, the temperature-dependent orthotropic thermal conductivities (kr,kθ,kz), specific heat (cp), and volumetric heat generation (qv) of Panasonic NCR18650BD cylindrical battery are estimated using an inverse approach (Metropolis Hastings-Markov Chain Monte Carlo algorithm based Bayesian method) with the help of experimentally obtained surface temperatures measured at convenient locations on the battery. From the estimation, the average values of kr,kθ,kz and cv are observed to be 3.18 ± 0.19, 20.34 ± 1.26, 19.89 ± 1.29 (W/mK), and 3180 ± 202 (J/kgK), respectively. The average heat generation rates from the same battery obtained using the same methodology are 0.1 ± 0.005, 0.34 ± 0.012, and 1.51 ± 0.026 W for 0.5, 1, and 2C discharge rates, respectively. The estimated thermophysical properties and heat generation rates are in good agreement with the results obtained from both in-house experiments and literature. In addition to the estimation of thermophysical properties and heat generation, the proposed methodology opens vistas to predict the strength and location of hotspots in the battery domain, which helps in designing appropriate and effective thermal management systems for battery packs.

Prediction of Orthotropic Thermal Conductivities Using Bayesian-Inference from Experiments under Vacuum Conditions

This work reports a novel “divide and conquer” approach to estimate the principal thermal conductivities of an orthotropic material, specifically engineered with a view to demonstrate the potency of the inverse heat transfer method with unsteady temperature data. The sample is placed in a vacuum chamber maintained at a pressure of 8.6 mbar. The heat capacity of the engineered orthotropic material was determined via estimating the heat capacity of a solid SS304 in a sequential fashion. First steady-state experiments followed by a Bayesian estimation with the Metropolis Hastings-Markov Chain Monte Carlo method were done to obtain the thermal conductivity of a solid SS304 block. Using this as a prior, the heat capacity of solid SS304 was obtained through unsteady experiments followed by Bayesian estimation. The heat capacity of SS304 thus obtained is multiplied by the solidity of the engineered orthotropic material, and using this information, the three components of the orthotropic conductivity are estimated again using the Bayesian route. To expedite the estimation, a surrogate for the forward model was developed using artificial neural network. Finally, the retrieved parameters are used to determine the simulated temperatures through the forward model for the orthotropic material. These, when compared with the measured temperatures, gave excellent agreement.

Thermal Management of Serpentine Flexible Heater Based on the Orthotropic Heat Conduction Model.

Flexible heaters can perfectly fit with undevelopable surfaces for heating in many practical applications such as thermotherapy, defogging/deicing systems and warming garments. Considering the requirement for stretchability in a flexible heater, certain spacing needs to be retained between serpentine heat sources for deformation which will inevitably bring critical challenges to the thermal uniformity. In order to reconcile these two conflicting aspects, a novel method is proposed by embedding the serpentine heat source in orthotropic layers to achieve comprehensive performance in stretchability and uniform heating. Such a scheme takes advantage of the ability of orthotropic material to control the heat flow distribution via orthotropic thermal conductivity. In this paper, an analytical heat conduction model with orthotropic substrate and encapsulation is calculated using Fourier cosine transform, which is validated by finite element analysis (FEA). Meanwhile, the effects of the orthotropic substrate or encapsulation with different ratios of thermal conductivity and the geometric spacing on the thermal properties are investigated, which can help guide the design and fabrication of flexible heaters to achieve the goal of uniform heating.

On the Effect of Complex Permeability and Thermal Material Properties for 3D-CFD Simulation of PEM Fuel Cells

Fuel cells are considered a key technology to decarbonize the power generation sector, thanks to the absence of pollutants emissions related to the direct chemical-electric energy conversion, their high global efficiency, and the possibility for on-board electricity production, overcoming the storage limits of batteries. An example of the renewed interest towards fuel cells is the research in Proton Exchange Membrane Fuel Cell (PEMFC) in the automotive sector, as a candidate alternative to fossil fuels-fed internal combustion engines (ICEs). The complex interplay of electrochemical and physical phenomena concurring in PEMFC makes their understanding and optimization a challenging task. This is a field of active research thanks to the development of advanced CAE tools, e.g., 3D-CFD simulations of non-isothermal reactive flows, in which all the relevant physics is numerically solved, allowing to identify governing mechanisms as well as system bottlenecks. Among the multiple complex aspects, the material property characterization of PEMFC components is one of the major modelling challenges for modern CAE tools. This is usually provided as a set of boundary conditions for the numerical model, having a large impact on the simulated results which is often motivated by an oversimplification of materials characteristics. Examples of commonly overlooked aspects are direction-independent thermal/flow properties for fibrous materials, the neglection on the deformed (compressed) status, and the simplified contact approach. All of these might alter the key parameters (e.g., water management) and mislead designers’ conclusions on PEMFC optimization. In this paper three-dimensional CFD simulations are used to weight the impact of orthotropic diffusion layer properties on both flow distribution and heat transfer. In the first part, a simplified test case from literature is created and used to investigate the flow convection/diffusion balance in the gas diffusion layer considering the orthotropic permeability typical of pressed fibrous layers. Differences with respect to the still widely used isotropic permeability will be assessed, and implications on channel bypass and mass transport to the catalyst layer will be provided. In the second part, the analysis moves to the use of orthotropic thermal conductivity for the fibrous gas diffusion layers, which is another commonly discarded aspect despite being well documented in literature. A critical analysis of heat transfer routes between parts of different heat capacity (membrane, diffusion layers, solid plates) and thermal field for all the components will be assessed. Finally, thermal contact resistance between adjacent pressed materials will be applied. The altered thermal pathways for heat removal will be critically analyzed, as well as the differences in temperature distribution and their implication on electricity production and water management. This hierarchical flow/thermal analysis will provide guidelines for more accurate 3D-CFD models for a deeper understanding of flow and heat dynamics in PEMFC.

Analysis for an infinite orthotropic elastic plane with a hole subjected to uniform heat flux

A general solution is derived for the thermal stresses of an infinite orthotropic plane with a hole subjected to uniform heat flux. A dislocation method is applied to solve uniform heat flux problem, in which the orthotropic thermal conductivities and coefficients of thermal expansion are considered. The dislocation functions for stress analysis are also considered. The dislocations of displacements for the x and y directions due to the thermal stress and the elastic stress at infinity must be zero. Thus, the dislocation functions regarding elastic stress are determined. Then, the stress analysis is carried out by two methods, that is, methods due to the Riemann-Hilbert method and Cauchy integral method. These methods are completely different. It is confirmed that the stress functions achieved are identical. The final exact stress functions as a general solution are derived as a closed form. The stress components are represented by one complex variable. Therefore, the calculation of the stress components is simple. Arbitrarily shaped hole problem can be solved by exchanging the mapping function. As an example, an infinite plane with a square hole subjected to uniform heat flux is analyzed. The heat flux and stress distributions are shown.

An efficient method to identify thermal conductivity of orthotropic material based on BP neural network algorithm

BP neural network algorithm is used to identify the three-dimensional orthotropic thermal conductivity. The finite volume method is used to solve the forward heat transfer problem, and the training samples for neural network inversion identification are obtained. According to the identification results, the temperature field is reconstructed. Through the analysis of the calculation results, it is found that the accurate identification of three-dimensional orthotropic thermal conductivity can be realized by using BP neural network algorithm. When the temperature measurement error is less than 0.5 °C, the maximum identification error of thermal conductivity is only 3.5%.

Analysis of the Effect of the Orthotropic Thermal Conductivity Tensor During Microwave-Based Heat Treatment of a Core–Shell Spherical System

In this article, we propose a numerical analysis of the effect of the orthotropic tensor of thermal conductivity during microwave heating of a heterogeneous core–shell morphology. The core is made of a material with high thermal conductivity, whose dielectric loss coefficient guarantees high microwave energy to heat conversion. This type of morphology has a high potential for use in the ablation of tumors, chemotherapy, drug release, and enhancing nano-catalysis, among other applications. Nonetheless, the effect of orthotropic thermal conductivity has not been extensively studied. The system under analysis is a core surrounded by two shells, which are made of materials whose thermal conductivities vary orthogonally. The thermal model consists of a system of three time-dependent coupled parabolic partial differential equations. Such a model is numerically solved using finite elements, and assuming a thermal conductivity tensor for each layer. A strong effect of this type of anisotropy was observed on temperature profiles compared to traditional isotropic materials. Besides, the symmetric release of its internally generated energy was seriously affected. Selected simulated experimental scenarios are presented.

An investigation of heat transfer and capacity fade in a prismatic Li-ion battery based on an electrochemical-thermal coupling model

A large format lithium-ion (Li-ion) battery significantly suffers from a nonuniform thermal distribution, which adversely affects the electrochemical reaction inside the battery and accelerates its degradation. In this work, a one-dimensional (1D) electrochemical-three-dimensional (3D) thermal coupling model is developed to investigate the heat transfer of a prismatic Li-ion battery when cooling different external surfaces. Simulation parameters are considered, including a forced convection cooling coefficient, h, the surface area of heat dispersion and the battery size. Despite the side surfaces of the prismatic Li-ion battery being small, the orthotropic thermal conductivity of the prismatic battery improves the planar heat transfer and effectiveness of forced convection cooling on the small side surfaces. It is found that the temperature distribution in the prismatic battery with forced convection cooling on the small side surfaces is more uniform than cooling the large front surfaces. At h = 100 W/m2 K, as the battery size increases, the maximum temperature difference of the prismatic battery with small side surface cooling stays at a constant value of 3.18 °C. In addition, the effect of operating temperature on the capacity fade of Li-ion batteries during cycling is investigated. It is found that a high operating temperature accelerates the parasitic lithium/solvent reduction reaction, and the above reduction reaction results in the loss of Li ions and increases the rate of capacity fade during the cycling process.

In Situ Measurement of Orthotropic Thermal Conductivity on Commercial Pouch Lithium-Ion Batteries with Thermoelectric Device

In this paper, the direct measurement of the orthotropic thermal conductivity on a commercial Li-ion pouch battery is presented. The samples under analysis are state-of-the art batteries obtained from a fully electric vehicle commercialized in 2016. The proposed methodology does not require a laboratory equipped to manage hazardous chemical substances as the battery does not need to be disassembled. The principle of the measurement methodology consists of forcing a thermal gradient on the battery along the desired direction and measuring the heat flux and temperature after the steady state condition has been reached. A thermoelectric device has been built in order to force the thermal gradient and keep it stable over a long period of time in order to be able to observe the temperatures in steady state condition. Aligned with other measurement methodologies, the results revealed that the thermal conductivity in the thickness direction (0.77 Wm−1K−1) is lower with respect to the other two directions (25.55 Wm−1K−1 and 25.74 Wm−1K−1) to about a factor ×35.

Reconstruction of an orthotropic thermal conductivity from non-local heat flux measurements

Raw materials are anisotropic and heterogeneous in nature, and recovering their conductivity is of utmost importance to the oil, aerospace and medical industries concerned with the identification of soils, reinforced fibre composites and organs. Due to the ill-posedness of the anisotropic inverse conductivity problem certain simplifications are required to make the model tracktable. Herein, we consider such a model reduction in which the conductivity tensor is orthotropic with the main diagonal components independent of one space variable. Then, the conductivity components can be taken outside the divergence operator and the inverse problem requires reconstructing one or two components of the orthotropic conductivity tensor of a two-dimensional rectangular conductor using initial and Dirichlet boundary conditions, as well as non-local heat flux over-specifications on two adjacent sides of the boundary. We prove the unique solvability of this inverse coefficient problem. Afterwards, numerical results indicate that accurate and stable solutions are obtained.

Reconstruction of an orthotropic thermal conductivity from non-local heat flux measurements

Raw materials are anisotropic and heterogeneous in nature, and recovering their conductivity is of utmost importance to the oil, aerospace and medical industries concerned with the identification of soils, reinforced fibre composites and organs. Due to the ill-posedness of the anisotropic inverse conductivity problem certain simplifications are required to make the model tracktable. Herein, we consider such a model reduction in which the conductivity tensor is orthotropic with the main diagonal components independent of one space variable. Then, the conductivity components can be taken outside the divergence operator and the inverse problem requires reconstructing one or two components of the orthotropic conductivity tensor of a two-dimensional rectangular conductor using initial and Dirichlet boundary conditions, as well as non-local heat flux over-specifications on two adjacent sides of the boundary. We prove the unique solvability of this inverse coefficient problem. Afterwards, numerical results indicate that accurate and stable solutions are obtained.

Metal frame structures with controlled anisotropic thermal conductivity

The summation law (kxx+kyy+kzz=(1−ε)ks) for those structures made of the same metal frames has been generalized in terms of the thermal conductivity tensor kij=∑n=1Nsnks(g→n·e→i)(g→n·e→j) in order to identify the conditions for orthotropic thermal conductivity and the level of the anisotropy of thermal conductivity in metal frame structures. A novel design strategy was proposed for controlling the anisotropy of the effective thermal conductivity tensors in various metal frame structures. Both three-dimensional lattice frame structurers and two-dimensional prismatic cellular honeycomb structures were considered to achieve their desired levels of the anisotropy in the thermal conductivity tensors. The relationships between the level of the anisotropy and frame design parameters are found for rectangular frame structures, deformed octet-truss structures, deformed tetrakaidecahedron structures and various kinds of honeycomb structures. The relationships analytically obtained for these structures agree well with the full 3D numerical results, and thus can serve as a theoretical basis to design the anisotropy of the effective thermal conductivity in metal frame structures according to their particular thermal applications.

An adaptation of the Lewis-Nielsen equations for the thermal conductivity of short fiber reinforced hybrid composites

Estimating the thermal conductivity of fiber reinforced plastics can be challenging, as they typically have anisotropic properties due to filler orientation during processing. Several analytical models for the thermal conductivity of multiphase materials are proposed in the literature. However, these are typically aimed at particulate fillers or fibers with an idealized orientation. In this work, the orthotropic thermal conductivity of multiphase compounds containing reinforcement fibers as well as different types of spherical particles were calculated using an analytical approach based on the Lewis-Nielsen model. The fiber orientation, which was determined from microsections, was converted into an orientational parameter that can be used within the Lewis-Nielsen set of equations. The results of this homogenization approach were compared to measurements. Good agreement between the model and the experimental results could be achieved for composites in which the reinforcing fibers are the dominant component influencing the thermal conductivity. For composites that comprise two strongly conductive components, the effective conductivity tends to be underestimated.

Thermal Numerical Analysis of the Primary Composite Structure of a CubeSat

A thermal computational analysis for the composite structure of a CubeSat is presented. The main purpose of this investigation is to study the thermal performance of carbon fibre/epoxy resin composite materials with Zinc Oxide nanoparticles in order to be used in the panels of the primary structure of a CubeSat. The radiative heat fluxes over each composite panel are computed according to the orbit trajectory and they are utilized as boundary conditions for the analysis. The direct solar, albedo and Earth infrared radiation fluxes are considered in this study. The model implementation, including the computation of the orthotropic thermal conductivity of the composite material is presented. The thermal simulations were performed for three different orbit inclination angles: the selected mission ( β = 57 ∘ ), the worst hot ( β = 90 ∘ ) and the worst cold ( β = 0 ∘ ). The temperature ranges in the electronic boards are analyzed in order to show that are into the operating limits of each electronic component.

Integration of Direction Fields with Standard Options in Finite Element Programs

The two-dimensional differential equation y’ = f(x,y) can be interpreted as a direction field. Commercial Finite Element (FE) programs can be used for this integration task without additional programming, provided that these programs have options for the calculation of orthotropic heat conduction problems. The differential equation to be integrated with arbitrary boundaries is idealized as an FE model with thermal 2D elements. Its orthotropic thermal conductivities are specified as k1 = 1 and k2 = 0. In doing so, k1 is parallel to y´, and k2 is oriented perpendicular to this. For this extreme case, it is shown that the isotherms are identical to the solution of y’ = f(x,y). The direction fields, for example, can be velocity vectors in fluid mechanics or principal stress directions in structural mechanics. In the case of the latter, possibilities for application in the construction of fiber-reinforced plastics (FRP) arise, since fiber courses, which follow the local principal stress directions, make use of the superior stiffness and strength of the fibers.

Thermophysical properties of OSB boards versus equilibrium moisture content

The basic thermophysical properties of oriented strand boards were determined experimentally for use in humid conditions (OSB3) depending on the moisture content. The dependency between the thermal conductivity, thermal diffusivity, specific heat capacity, and the moisture content in the range of 0% to 10%, was examined. The non-stationary extended dynamic plane source (EDPS) experimental method was used. EDPS method was modified for anisotropic materials, i.e. with special considerations of heat-loss effect occurring at the edge of measuring samples, finite geometry of the sample and orthotropic thermal conductivity, for use with anisotropic materials. The validity of the experimental method was verified on polymethylmethacrylate (PMMA) samples. The error rate of measurements conducted on PMMA samples was less than 3%, and for OSB3 boards it was less than 5.5%. Based on the experimental results, regression equations of the dependency between the monitored properties and the moisture content were determined. In the case of thermal conductivity and thermal capacity, the determined dependencies showed a high correlation rate.

Non-destructive infrared inspection of dry multilayer carbon fibre preforms

Thermography was used for performing non-destructive inspection of dry carbon fibre textile preforms used in manufacturing carbon fibre polymer-matrix composites (CF-PMCs). The aim was to probe the feasibility of identifying defects in thick carbon fibres preforms made from multiple layers of industrial textile reinforcements, before composites are manufactured. Inspecting dry preforms will not replace the inspection of final CF-PMC parts but it can avoid costly and wasteful manufacturing of CF-PMC parts from defective preforms, as the defects sought in this paper cannot be observed by visual inspection. The preforms tested were made of two or four layers of industrial carbon fibre textile reinforcements. They featured defects of different widths, types and orientations. Results show that thermography can identify defects in preforms successfully, and that detection is influenced by the orthotropic thermal conductivity of carbon fibres, by yarn and fabric architecture, by the relative orientations of defects and yarns, and by the number of layers.

A CFD study of Screw Compressor Motor Cooling Analysis

Screw compressors use electric motors to drive the male screw rotor. They are cooled by the suction refrigerant vapor that flows around the motor. The thermal conditions of the motor can dramatically influence the performance and reliability of the compressor. The more optimized this flow path is, the better the motor performance. For that reason it is important to understand the flow characteristics around the motor and the motor temperatures. Computational fluid dynamics (CFD) can be used to provide a detailed analysis of the refrigerant’s flow behavior and motor temperatures to identify the undesirable hot spots in the motor. CFD analysis can be used further to optimize the flow path and determine the reduction of hot spots and cooling effect. This study compares the CFD solutions of a motor cooling model to a motor installed with thermocouples measured in the lab. The compressor considered for this study is an R134a screw compressor. The CFD simulation of the motor consists of a detailed breakdown of the stator and rotor components. Orthotropic thermal conductivity material properties are used to represent the simplified motor geometry. In addition, the analysis includes the motor casings of the compressor to draw heat away from the motor by conduction. The study will look at different operating conditions and motor speeds. Finally, the CFD study will investigate the predicted motor temperature change by varying the vapor mass flow rates and motor speed. Recommendations for CFD modeling of such intricate heat transfer phenomenon have thus been proposed.

Electro-deposition of graphene nanoplatelets on CPU cooler—experimental and numerical investigation

ABSTRACTThis manuscript deals with to improve knowledge of the mechanisms of deposition of graphene on a flat surface. The analysis has been developed on a CPU cooler with experimental results and FEM analysis. The experiments are conducted by mounting the system over a heat source, while the force convection is facilitated by means of a blower. The transient temperature distribution in the CPU cooler is also observed. A model has been performed for modeling the thermal behavior of assembly structures with thin layers. The experimental observations are verified by simulation using a commercial FEM software. It was used a model of orthotropic thermal conductivity with variable values. The goal of the simulation has been to individuate the value of coefficient of thermal conductivity of the layer of graphene. The FEM results show how the graphene was deposited on the surface of CPU cooler and consequently, how this determine the coefficient of thermal conductivity.

Topology optimization for the conduction cooling of a heat-generating volume with orthotropic material

In this paper the two dimensional numerical topology optimization of a high conductive conduit material, distributed within a heat-generating material, is investigated with regards to the effect of orthotropic materials. Specifically, materials with orthotropic thermal conductivities (different primary and secondary principal thermal conductivities).Two cases are considered in this study, namely the optimal distribution of an isotropic conduit material within an orthotropic heat generating material; and the optimal distribution of an orthotropic conduit material within an isotropic heat-generating material. A finite volume method (FVM) code, coupled with the method of moving asymptotes (MMA); the solid isotropic with material penalization (SIMP) scheme; and the discrete adjoint method, was used to find the optimal distribution of the high conductive conduit material within the heat generating material.For the optimal distribution of an isotropic conduit material within an orthotropic heat-generating material is was found that a heat-generating material angle 10°⩽θ0⩽60° is preferred, for a higher thermal performance, and a heat-generating material angle θ0<10° and θ0>60° should be avoided.For the optimal distribution of an orthotropic conduit material within an isotropic heat-generating material is was found that an optimal conduit material angle exists giving the best thermal performance (lowest τmax). It was found that the optimal conduit material angle remains the same for different conductivity ratios and different heat-generating material angles. It was also found that the optimal conduit material angle directly corresponds to the domain aspect ratio, θ1,opt=tan-1(2H/L), with a minimum improvement of 3% and a maximum improvement of 50% of the thermal performance when using an orthotropic conduit material over that of an isotropic conduit material. A 50% improvement of the thermal performance effectively translates to either double the allowable heat generation or half the peak operating temperature of the isotropic heat-generating material.