Axisymmetric Heat Transfer Research Articles

Coupled Electrochemical-Thermal Runaway Model of Lithium-Ion Cells Operating Under High Ambient Temperatures

The risk of thermal runaway (TR) in high energy density Lithium-ion batteries (LIBs), which may initiate at around 90 °C, is a critical safety concern, particularly in regions where summer temperatures can reach nearly 50 °C. While multiple exothermic reactions that cause TR and modeled using Arrhenius equations lead to good predictions in controlled oven tests, their use in practical applications is questionable as these do not consider internal electrochemical processes that cause temperature rise and trigger exothermic reactions. Further, limited literature focuses on coupling electrochemical thermal models with exothermic reactions. This study demonstrates a method to couple the electrochemical and thermal runaway models for a commercial cylindrical Lithium-ion cell. The proposed model averages pseudo-2D electrochemical heat and couples it to a two-dimensional, axisymmetric heat transfer model of 18650-type Lithium-ion cell. The jellyroll structure is approximated as a homogeneous and anisotropic domain for electrochemical and exothermic heating. Simulations are performed through several, uninterrupted charge-discharge cycles at different ambient temperatures and C-rates. We show that while cycling rate is critical in instigating and accelerating TR, parameters like ambient temperature, particle radii and initial electrolyte concentration also play a role in determining the core temperature and its rate of growth in the cell.

Axisymmetric stagnation-point flow of a fractional Oldroyd-B hybrid nanofluid over a vertical cylinder by improved Buongiorno's model

This paper investigated the unsteady axisymmetric stagnation-point flow, heat and mass transfer of Oldroyd-B hybrid nanofluid over a vertical cylinder by using Caputo time fractional derivatives for the first time, with the consideration of second-order velocity slip conditions. Improved Buongiorno's model was adopted to build the governing equations and finite difference combined with L1-algorithm was employed to solve the numerical solutions. Effects of key physical parameters on velocity, heat and mass transfer were presented graphically and discussed in detail. Outcomes show that the fractional derivatives are capable to describe the memory effect and thermoelasticity of viscoelastic nanofluids. Both Brownian motion and thermophoresis, especially Brownian motion, improve the heat transfer on the cylinder wall. In addition, the sensitivity of average Nusselt (or Sherwood) number to velocity fractional derivates α and β rises with increasing α and β, while the sensitivity to temperature fractional derivate γ declines with increasing γ. When γ increases from 0.2 to 0.3, the relative growth rate of average Nusselt number is about 9.26 %. This study provides a reference for exploring the stationary-point flow of fractional order nanofluids on vertical cylinders.

Numerical Computational of Chemically Reactive Hybrid Nanofluids with Melting Phenomena Passing Through a Disk: Comparative Study

This paper aims to investigate the solutions for the axisymmetric flow and heat transfer coming from a permeable disk in hybrid nanofluids. The nanofluids are under the influence of thermal radiation and contain magnetohydrodynamics and melting phenomena. For this, the momentum and temperature mathematical model is developed to investigate the axisymmetric flow of two-dimensional hybrid nanofluids, containing nanoparticles and a base fluid. Using appropriate similarity variables, nonlinear partial differential equations have been transformed into ordinary differential equations. These are further solved using the function bvp4c, which is built into MATLAB software. The physical behavior of parameters is discussed for the values on the basis of visuals and tables. The analysis further shows an increase in the local Nusselt number and skin frictional coefficient due to nonlinear thermal radiation and magnetic parameters. The results may be promising for the applications of hybrid nanofluids in heat transfer and cooling systems of all modern industries. The authors have confidence in their study due to the novelty of the results and underline the numerous practical utilities of hybrid nanofluids.

Numerical heat generation analysis of the tabbed and novel tabless designs of cylindrical-type lithium-ion batteries

The heat generation behaviours of a traditional tabbed cylindrical lithium-ion (Li-ion) battery are known to greatly affect its performance, cycle life, and safety. In this study, we explore the heat generation behaviours of the tabbed and novel tabless designs of a 21,700 cylindrical cell with graphite anode and NCA/LiNi0.8Co0.15Al0.05O2 cathode, by coupling the discreet layers of a three-dimensional (3D) disassembled electrochemical (EC) model with a two-dimensional (2D) axisymmetric heat transfer (HT) model. The respective heat generation mechanisms of each battery components of tabbed and tabless designs are first compared, and it is observed that the tabbed design generates significantly more heat than the tabless design, with the negative current collectors (NCC) in the tabbed design accounting for over 80 % of the total heats at 1C-rate. Also, the tabless design reduces the cell voltage drop due to its lower ohmic impedance and promotes a more homogenous cell temperature than the tabbed design. Next, the effects of particle size (ω) for the tabless design on the ohmic, reversible, and polarization heats of the battery’s electrodes are investigated at a high discharge rate of 10C, and the results show that polarisation heat decreases significantly in both electrodes as ω decreases. At the Negative Electrode (NE), the ohmic heating decreases initially as ω decreases because the battery is not drawing significant current. As the current drawn increases, Li-ion transport resistance also increases and at depth of discharge (DoD) = 36 %, a reverse in the trend is observed leading to an increase in Ohmic heating up to the end of life. In contrast, the ohmic heating at the Positive Electrode (PE) increases throughout the discharge process as ω decreases. For the reversible heat, the heat is negative in the NE side initially and fluctuates with ω towards the end of life (DOD = 88 %) when it changes from heat sink to heat source, whereas in the PE it remains unchanged for all ω throughout the discharge process. The resulting temperature drop is caused by the increase in the overall reversible heat sink effect in the NE side, as well as the weakened polarization heat in both electrodes. On the other hand, miniaturising the electrode thickness (η) causes a considerable decrease in ohmic heating in both electrodes resulting in larger temperature drops and elevated voltage curve. This study provides relevant insights in support of the development of battery thermal management systems (BTMS) for the tabbed and novel tabless batteries in a realistic environment.

Modelling and simulation of heat flow in indexable insert drilling

In machining, the heat generated during the process deforms the components and the final shape might not meet specified tolerances. There is therefore a need for a compensation strategy which requires knowledge of the workpiece temperature field and the associated thermal distortions. In this work, a methodology is presented for the determination of the heat load for indexable insert drilling of AISI 4140. Compared to previous research, this work has introduced a varying heat load. The heat load is extracted from thermo-mechanical finite element simulations for different nominal chip thicknesses and cutting speeds using the coupled Eulerian-Lagrangian formulation of an orthogonal turning process. The heat load is then transferred to a simplified 2D axisymmetric heat transfer model where the in-process temperature field in the workpiece is predicted. To verify the methodology, the predicted temperatures are compared to the experimentally measured temperatures for various feed rates. It is found that the model is capable of predicting the workpiece temperatures reasonably well. However, the methodology needs to be further explored to validate its applicability.

Numerical investigation of time-dependent axisymmetric stagnation point flow and heat transfer of $$A{l}_{2}{O}_{3}-{H}_{2}O$$ and $$Cu-{H}_{2}O$$ nanofluid over a stretching sheet with variable physical features

Numerical investigation of time-dependent axisymmetric stagnation point flow and heat transfer of $$A{l}_{2}{O}_{3}-{H}_{2}O$$ and $$Cu-{H}_{2}O$$ nanofluid over a stretching sheet with variable physical features

Analytical solutions for hyaluronic acid flow and heat transfer between joints with periodic oscillations under the magnetic field

Osteoarthritis (OA) is a globally prevalent disease that poses significant challenges to the daily work and life of patients. Viscosupplementation is one of the most commonly used drug treatments for OA, which involves injecting hyaluronic acid (HA) into the joint cavity to alleviate synovial inflammation. The current research aims to explore the rheological and thermal behavior of HA between joints by studying the axisymmetric squeezing flow and heat transfer of incompressible Maxwell fluid under the action of static magnetic field between two rigid spheres with partial wall slip. The analytical solutions for velocity and temperature are obtained by using the Laplace integral variational theory. Detailed explanations are provided on the effects of different fluid parameters on velocity and temperature, presented in the form of charts. It can be shown that as the magnetic field intensity increases, the viscosity of HA increases with the increasing of relaxation time, thereby fluid motion is weakened and a strong damping effect is produced. As the frequency of joints motion increases, the velocity distribution becomes more uniform in the central region, and the overall distribution deviates from a parabolic distribution. In addition, as Reynolds number, Prandtl number and squeezing depth increase, the heat transfer capacity of the fluid decreases, resulting in a lower temperature at the top wall and a higher temperature at the bottom wall. This study provides theoretical support for exploring the rheological and thermal behavior characteristics of HA in the treatment of OA.

Isogeometric boundary element method for axisymmetric steady-state heat transfer

Isogeometric analysis (IGA) utilizes the Non-Uniform Rational B-Splines (NURBS) basis functions, which are commonly employed in Computer Aided Design (CAD), to both construct the problem’s geometry and approximate the field variables. In axisymmetric scenarios, the 3D problem can be simplified to 2D, requiring only the discretization of the 1D curve boundary for the boundary element method (BEM). This study proposes an isogeometric boundary element method (IGABEM) to simulate steady-state heat transfer in axisymmetric domains. Both the precise geometry of the boundary and the physical variables are approximated with the same NURBS basis functions, yielding higher-order continuity, superior accuracy per degree of freedom (DOF), and continuous nodal gradients with fewer DOFs than the traditional BEM. Additionally, a zoning method is introduced to handle heterogeneities. Five cases including a solid cylinder, a revolution hyperboloid with a coaxial cylindrical tube, an ellipsoid with a spherical cavity, a bimaterial ellipsoid and a complex geometry with a toroidal tube validate the accuracy, convergence, computational efficiency of IGABEM, and the applicability in addressing multiply-connected domains. The method outperforms Finite Element Method (FEM) and conventional BEM in accurately handling steady-state axisymmetric heat transfer issues under Dirichlet, Neumann, and Robin boundary conditions.

Dual solutions for axisymmetric flow and heat transfer due to a permeable radially shrinking disk in copper oxide (CuO) and silver (Ag) hybrid nanofluids with radiation effect

Purpose This study aims to investigate the dual solutions for axisymmetric flow and heat transfer due to a permeable radially shrinking disk in copper oxide (CuO) and silver (Ag) hybrid nanofluids with radiation effect. Design/methodology/approach The partial differential equations that governed the problem will undergo a transformation into a set of similarity equations. Following this transformation, a numerical solution will be obtained using the boundary value problem solver, bvp4c, built in the MATLAB software. Later, analysis and discussion are conducted to specifically examine how various physical parameters affect both the flow characteristics and the thermal properties of the hybrid nanofluid. Findings Dual solutions are discovered to occur for the case of shrinking disk (λ < 0). Stronger suction triggers the critical values’ expansion and delays the boundary layer separation. Through stability analysis, it is determined that one of the solutions is stable, whereas the other solution exhibits instability, over time. Moreover, volume fraction upsurge enhances skin friction and heat transfer in hybrid nanofluid. The hybrid nanofluid’s heat transfer also heightened with the influence of radiation. Originality/value Flow over a shrinking disk has received limited research focus, in contrast to the extensively studied axisymmetric flow problem over a diverse set of geometries such as flat surfaces, curved surfaces and cylinder. Hence, this study highlights the axisymmetric flow due to a shrinking disk under radiation influence, using hybrid nanofluids containing CuO and Ag. Upon additional analysis, it is evidently shows that only one of the solutions exhibits stability, making it a physically dependable choice in practical applications. The authors are very confident that the findings of this study are novel, with several practical uses of hybrid nanofluids in modern industry.

Calculation of convection coefficient during steel hardening of axisymmetric probes in thermal oils

The paper presents the results of the convection coefficient during the process of two-dimensional axisymmetric steel hardening of in two different thermal oils used in the area of thermal treatment of steel. One thermal oil was Isorapid 277 HM preheated to the set temperature, and the other one was Marquench 722 also preheated to the set temperature. The experimental work setup consists of six quenches, three dimensionally different axisymmetric probes in two different thermal oils. Steel hardening was done under strictly controlled conditions: heating the sample to the tempering temperature of most steels in a nitrogen atmosphere, vertical slow immersion of the test sample in the opposite flow of thermal oil. The temperature of the thermal oil was kept constant, stopping the test sample in the sample steel hardening area and non-stationary data collection until thermal oil equilibrium temperature with interruption of data collection. The data collection rate was two probes/second in parallel from four points located within the test cylinder. Three measuring points were located directly below the surface of the cylinder distributed along the height of the cylinder, while the fourth one was in the centre of gravity of the cylinder. Time-measured temperature values in the indicated four points of each probe were written in a text file. The set mathematical model describes the non-linear two-dimensional axisymmetric non-stationary heat transfer through the cylinder. The set mathematical model requires the inverse solution of the heat conduction problem, that is, ill-conditioned problems, so the solution of the problem came down to a sufficiently accurate estimation of the unknown convection coefficient imposed on the outer surface of the probe. The chosen solution algorithm was the one from previously published works. The solution algorithm was based on a iterative combination of the finite element method (FEM), while the second part of the solution algorithm is the Levenberg Marquardt method (LMM) from the line of optimization deterministic algorithms, which takes the calculation results of the temperatures at the points of the computational domain from the FEM, and for comparison, that is, error minimization, using the experimental results of temperature measurements at the same place.

BEM for transient nonhomogeneous heat conduction in axisymmetric solids with heat source

Boundary equation approach is revisited and extended to be applicable for axisymmetric transient heat transfer applications with spatially varying field variables and heat sources. For the derivation of axisymmetric formulation, three-dimensional fundamental solutions are integrated with respect to the circumferential direction and then the radial integration procedure using the stabilized temperature values is implemented to convert axisymmetric plane integrals to axisymmetric line integrals. All integrals are evaluated numerically. Four Numerical examples are given in order to assess the reliability of the proposed formulation.

Numerical study on thermal characteristics under external short circuit for Li||Bi liquid metal batteries

As one of the most potent battery technology, liquid metal battery (LMB) plays an important role in addressing the requirement of grid energy storage. However, up to now, few attention has been paid to the heat generation characteristics and thermal safety of LMB, including the conventional and abusive conditions. In this paper, a 2D axisymmetric multi-physics field model coupling electrochemistry, heat transfer, and laminar flow is proposed to evaluate the electro-thermal behavior of 200 Ah Li||Bi LMBs under the states of constant current (CC) cycle and external short circuit (ESC). Verified by the experimental data, the maximum fitting errors of the voltage and temperature are 4.61% and 0.42%, respectively. The reversible and irreversible electrochemical heat generation rates are calculated to assess the total heat power (9.14 W during 0.2 C discharge and −5.06 W during 0.2 C charge). The reversible heat rate is found to occupy a large proportion in the total heat generation, while the percentage of irreversible heat is shown to increase with the increasing current rate. Based on the analysis of CC cycle, the model is applied to investigate the battery electro-thermal performance in ESC failure. The results show that the ESC current and surface temperature vary with the short-circuit resistance and initial state of charge (SOC). The lower ESC resistance and initial SOC may lead to a severer temperature rise due to the unique entropic heat behavior. The maximum current and temperature reach 455.8 A and 549.3 °C in 5 min (100% SOC, 0.1 mΩ). This work provides an important opportunity to advance the understanding of heat generation and abuse phenomena induced by ESC in LMB.

A study on heat transfer enhancement of Copper [formula omitted]-Ethylene glycol based nanoparticle on radial stretching sheet

Copper nanoparticles are getting attention because of their outstanding physical characteristics and wide range of uses. The motivation of this research is to investigate axisymmetric flow and heat transfer for various shapes (Cylinder, Platelets and Sphere) of Copper (Cu) nanoparticles on a radial stretching sheet. Energy and momentum partial differential equations are transformed into nonlinear ordinary differential equations (ODE). The dimensionless equations are solved using the BVP4C method to yield numerical solutions for the represented problem. The impacts of multi-shape Copper (Cu) nanoparticles are thoroughly examined, as are other parameters such as solid volume fraction (ϕ), Prandtl number Pr, unsteadiness parameter S, magnetic parameter M, slip parameter k, and Eckert number EC. According to the findings, Platelet shape Copper (Cu) nanoparticles have the highest flow and Sphere shape particles contain maximum heat transfer rate.

Swirling flow analysis of Eyring–Powell fluid between coaxial disks with variable property

Abstract The main objective of this study is to examine an unsteady swirling flow of a non-Newtonian Eyring–Powell fluid between two coaxial disks. The lower and upper disks are considered to rotate with different angular velocities. The three-dimensional axisymmetric flow phenomenon and heat transfer mechanism are observed with the consequences of the magnetic field and variable thermal conductivity of the fluid. The variable thermal conductivity is taken to be dependent on the fluid temperature. The implementation of the Von Karman similarity transformations on the constituting equations of the flow phenomenon yields the dimensionless system of the non-linear equations. An optimal homotopy analysis technique is adopted to obtain analytical solutions for highly non-linear equations. In view of the same and opposite directions of disks rotation, the various aspects of the flow system corresponding to the pertinent parameters are discussed with physical significance. The obtained results indicate that both radial and axial fields are the escalating functions of the Eyring–Powell fluid parameter. Moreover, the heat transfer rate enhances with the improving variable thermal conductivity parameter.

The effect of particle shape on flow and heat transfer of Ag-nanofluid along stretching surface

The primary objective of the present work is to examine the axisymmetric flow and heat transfer over an unsteady radially stretching surface for different shapes of silver (Ag) nanoparticles. Due to their remarkable electrical conductivity and chemical stability for a variety of applications, silver nanoparticles are attracting attention. So, we consider five different shapes of silver nanoparticles. By using suitable transformation energy and momentum equations are transformed into nonlinear ordinary differential equations. The dimensionless equations are solved by BVP4C technique to get numerical results for the modeled problem. For velocity, temperature, skin friction coefficient, and Nusselt number, numerical values are obtained using and are also graphically displayed. Comprehensive discussion is given on the effects of many factors, including solid volume fraction, Prandtl number, unsteadiness parameter, magnetic parameter, slip parameter, and Eckert number. For both velocity and temperature Platelet shapes nanoparticles shows maximum flow and heat transfer. Sphere shape nanoparticles possess the highest skin friction coefficients values and lowest value of Nusselt number.

Axisymmetric Flow and Heat Transfer in TiO2/H2O Nanofluid over a Porous Stretching-Sheet with Slip Boundary Conditions via a Reliable Computational Strategy

In this investigation, the motion of TiO2/H2O nano-structures towards heated and porous sheets by considering the MHD effect and partial slip at the boundary is inspected. The non-linear PDEs that correspond to the basic conservation laws are converted into ODEs with the help of suitable similarity transformation. Furthermore, the shooting method is used to solve these transformed ODEs and boundary conditions. The impact of thermophoresis properties has been shown graphically and the effect of these properties on the skin friction coefficient (Cf) and Nussetl number (Nu) are given in table form. The comparison between the present exploration and published work is carried out and validation among results is prepared. The enhancement in thermophysical parameters showed contrary results to the velocity profile of the TiO2/H2O nanofluid as compared with temperature profile. Moreover, it is observed that the higher estimation in the velocity slip parameter retards the flow and an enhancement in volume fraction increases the fluid’s temperature. Furthermore, it has been discovered that the geometry of nanoparticles has a major impact on the flow behaviour. The temperature distribution diminishes when the shape of the nanoparticles changes from platelet to spherical.

Fully analytical solution in time and space domains on temperature in multi-barrier nuclear waste repository

Temperature evolution is one of the crucial factors in safe operation and geometric design of high-level radioactive waste disposal repositories. A three-dimensional two-layer axisymmetric heat transfer model was established to study the temperature evolution of the repository in the case of single canister. Applying a series of mathematical tools such as the finite Fourier sine transform, separation of variables and Duhamel's theorem, a fully analytical solution was obtained, which can visually and quickly represent the temperature evolution in both time and space. The validity of the model and solution was confirmed by comparing it with the existing line heat source solution, semi-analytical solution and finite element simulation results. The canister surface temperature was obtained by superimposing the temperature difference between the internal and external surfaces of buffer layer on the rock wall temperature. A single-panel calculation model was established, and dimensional and parameter analysis were carried out using the obtained fully analytical solution. According to the quantitative analysis using the obtained solution, increasing the canister spacing has a better effect on reducing the peak temperature than increasing the tunnel spacing. The effect of the two ways in reducing the peak temperature weakens with increasing the spacings.

BIE formulation for axisymmetric transient heat conduction applications

Boundary integral equation method is proposed for axisymmetric transient heat transfer applications covering spatially varying heat sources. The radial integral approach using the normalized temperature, thus, eliminating temperature gradients involved, is utilized to switch two-dimensional integrals to the equivalent line-related integrals. The derivative of the temperature is approximated using the finite difference method. To evaluate time-depended equations, the time-marching scheme is adopted. The proposed boundary integral formulation is implemented into axisymmetric applications to assess its accuracy.

Verification of Dual Solutions for Water and Kerosene-Based Carbon Nanotubes over a Moving Slender Needle

This article focuses on the boundary layer for an axisymmetric flow and heat transfer of a nanofluid past a moving slender needle with single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs). In this study, the streamlines of the flow are symmetrically located along the needle’s surface. Water and kerosene are two types of base fluids that are considered in this study. This analysis is presented with needle thickness, the ratio of velocity, nanoparticle volume fraction, and Prandtl number. The partial differential equations (PDEs) are transformed into dimensionless ordinary differential equations (ODEs) by adopting relevant similarity transformations. The bvp4c package is implemented in MATLAB R2018a to solve the governing dimensionless problems numerically. The behaviors of various sundry variables on the flow and heat transfer are observed and elaborated further. The magnitude of the skin friction, heat transfer rate, as well as velocity and temperature distributions are demonstrated in graphical form and discussed. It is worth mentioning that kerosene-based CNTs have the largest skin friction coefficient and heat transfer rate compared to water-based CNTs. The thin wall of the needle and the single-walled carbon nanotubes also contributes to high drag force and heat transfer rate on the surface. It is revealed from the stability analysis that the first solution exhibits a stable flow. Obtained results are also matched with the present data in the restricting situation, and excellent agreement is noticed.

Numerical investigation on the thermal behavior of cylindrical lithium-ion batteries based on the electrochemical-thermal coupling model

• HET model and LET model are proposed. • Radial temperature gradient of cylindrical LIB is non-negligible. • Inhomogeneous discharge due to non-uniform temperature distribution inside cylindrical LIB is investigated. • This work provides insights to choose appropriate electrochemical-thermal coupling models. In this paper, a one-dimensional electrochemical model and a three-dimensional axisymmetric heat transfer model are coupled to simulate the electrochemical and thermal behavior of cylindrical lithium-ion batteries (LIBs). The model is verified against the experimental data of discharge voltage and surface temperature of LIBs under different discharge rates. First, the holistic electrochemical-thermal coupling (HET) model and the layered electrochemical-thermal coupling (LET) model are established. In contrast to the traditional HET model, the advantage of the LET model is that it can realize the investigation on the inhomogeneous discharge and aging induced by the non-uniform temperature distribution inside the battery. We demonstrate the radially inhomogeneous discharge of cylindrical LIBs with a 4-layer LET model in this work. It is also found that the HET model can provide desirable simulation accuracy in temperature with less computational cost. This provides insights for researchers to choose more appropriate electrochemical-thermal coupling models in accordance with the different scenarios. Second, the thermal behavior of cylindrical LIBs at different discharge rates is studied by analyzing the heat generation rate and heat dissipation characteristics during the discharge process. The study reveals that, unlike pouch LIBs, there is a significant temperature gradient in the radial direction of cylindrical LIBs. Finally, the factors that affect the temperature uniformity of the battery, such as cooling conditions, ambient temperature, discharge rate, radial dimension, and radial thermal conductivity are analyzed in detail. Meanwhile, some suggestions are provided to improve the temperature uniformity. The findings in this work are of benefit to obtain profound understading of thermal behavior in cylindrical LIBs. Besides, they also have potential applications in improving the prediction accuracy of the temperature signal in the battery thermal management system of LIBs.