Steady-state Temperature Distribution Research Articles

Analytical Solution for Temperature Distribution in a Multilayer Body With Spatially Varying Convective Heat Transfer Boundary Conditions on Both Ends

Abstract Analytical modeling of thermal conduction in a multilayer body is of practical importance in several engineering applications such as microelectronics cooling, building insulation, and micro-electromechanical systems. A number of analytical methods have been used in past work to determine multilayer temperature distribution for various boundary conditions. However, there is a lack of work on solving the multilayer thermal conduction problem in the presence of spatially varying convective heat transfer boundary condition. This paper derives the steady-state temperature distribution in a multilayer body with spatially varying convective heat transfer coefficients on both ends of the body. Internal heat generation within each layer and thermal contact resistance between layers are both accounted for. The solution is presented in the form of an eigenfunction series, the coefficients of which are shown to be governed by a set of linear, algebraic equations that can be easily solved. Results are shown to be in good agreement with numerical simulation and with a standard solution for a special case. The model is used to analyze heat transfer for two specific problems of interest involving spatially varying convective heat transfer representative of jet impingement and laminar flow past a flat plate. In addition to enhancing the theoretical understanding of multilayer heat transfer, this work also contributes toward design and optimization of practical engineering systems comprising multilayer bodies.

Investigation of displacements and stresses in thick-walled FGM cylinder subjected to thermo-mechanical loadings

In this paper, analytical and numerical solutions are presented for computing mechanical displacements and stresses in a thick-walled cylindrical made of functionally graded materials (FGMs) under mechanical and thermal loadings. The elastic modulus and thermal conductivity are assumed to vary in the radial direction, and the Poisson’s ratio is assumed constant. Navier’s ordinary second-order differential equation derived from the mechanical equilibrium equation was solved to obtain the exact solution of the displacement and stress distributions. Furthermore and in order to validate the accuracy of the analytical solution, a numerical model was construct using the finite element method. Very good agreement has been found between the analytical formulation and the predictions of numerical simulation which confirms the accuracy of the model in the case of a thick-walled tube made of FGM under steady state temperature distribution and a mechanical loading. These results clarify the influence of the thermal field, non-homogeneity parameter and internal pressure on the thermo-elastic response of the functionally graded cylindrical vessel.

Design of Electronic Moxibustion Instrument for Umbilical Therapy and Preliminary Analysis of Temperature Field

Moxibustion has a history of thousands of years. Umbilical moxibustion achieves prevention and treatment of diseases through moxibustion at the golden section of the human body-the umbilicus. It has enough clinical practice experience. Traditional treatment methods have problems such as irritating smoke, uncontrollable temperature, experience-based, and difficult to quantify. Based on the principle of traditional umbilical moxibustion, a structural design of an electronic smokeless umbilical moxibustion instrument is proposed, which belongs to indirect moxibustion and has the advantages of smokeless, electric heating, portability, temperature monitoring and controllability. The internal heat transfer process of the moxibustion instrument is mainly heat convection and heat radiation. Based on ANSYS software, the internal temperature field of the moxibustion instrument is analyzed, and the steady-state temperature distribution and the temperature change characteristic curve of different positions with time are obtained to verify the rationality of the structural design. At the same time, lay a research foundation for the measurable and quantifiable effects of moxibustion on umbilical therapy.

Measuring and modeling quasicontinuous wave operation of quantum cascade lasers for enhanced average brightness

Quasicontinuous wave operation of midinfrared quantum cascade lasers are shown to have increased average output power with good beam quality. The ability to enhance average power by a significant fraction of CW power motivates the development of a model to estimate and project performance at varying duty cycles based on a previously developed continuous wave power projection model. The model takes into account pulse to pulse changes in temperature profile to project a transient steady-state temperature distribution. This temperature distribution is used to project both peak and average power in agreement with measurements. Preliminary model projections suggest that high average brightness may be achieved using a reduced number of stages and a greater scaling of core width than would be permissible for CW lasing.

Steady-state temperature distribution under near-field radiative heat transfer inside a linear chain of polaritonic nanoparticles

Thermal transport mediated by near-field interactions is superdiffusive in an ordered network of nanoparticles, such as linear chains. Based on such nanostructures, here we study a classical thermal-nonequilibrium problem, that is, the steady-state temperature distribution inside the chain of equally spaced polaritonic nanoparticles. The existence of the linear temperature profile and anomalous temperature variations in the inner region and near the boundary of a dense chain embedded in vacuum, respectively, is demonstrated by analyzing the effective radiative thermal conductivity within the system. Such temperature distributions are closely relevant to the strength of propagating surface modes sensitive to the chain density and dielectric material. We also demonstrate that, the presence of a homogeneous nonabsorbing background medium renders the steady-state temperature profile of the dense chain nonlinear, as well as enhancing drastically the long-distance heat exchange by two orders of magnitude relative to the vacuum case. This enhancement is a result of the high density of propagating waves in the medium, and is further confirmed by analyzing the energy density distribution over the chain. Furthermore, in a complex system consisting of many parallel chains, we show that, in steady state, temperatures of the thermal drive chain are allowed to tailor by its neighboring chains due to many-body interactions. This work opens ways to qualitatively assess and manipulate the stationary temperature field in advanced nanostructures, such as topological plasmonic chains and nanoparticle arrays.

Sequential V ce(T) Method for the Accurate Measurement of Junction Temperature Distribution Within Press-Pack IGBTs

In this article, a sequential Vce(T) method with separated gate controller is proposed to measure the junction temperature distribution within press-pack insulated gate bipolar transistors (PP IGBTs), which is not possible for traditional temperature measurement methods due to the enclosed structure and external clamping force of the pressure-type package. This proposed method is integrated into a standard dc power cycling test and the steady-state junction temperature distribution is obtained to validate its applicability and effectiveness. The measured junction temperature exhibited a bathtub type distribution within PP IGBTs. The root cause is the deformation of the copper plate, which was also discussed by the finite-element simulation in previous literature. Furthermore, the influence of static characteristic dispersion is excluded by the chip transposition and the thermomechanical coupling effect is confirmed to be the dominant factor of this junction temperature distribution. Finally, the influence of heating current and heating time on junction temperature distribution is also investigated by the proposed method.

Research on Heat Dissipation Optimization of a Novel Liquid-Cooling Eddy Current Brake

As an auxiliary brake element, the eddy current brake is widely used to ensure safe driving in heavy vehicles due to its noncontact braking characteristics. It is important to increase the power density of the eddy current brake and suppress the thermal derating of its braking performance. According to the principle of the eddy current braking and current skin effect, a decline in temperature can greatly increase the eddy current density of the low-frequency electromagnetic device. In this paper, a new heat dissipation method is proposed to cool the heating surface of the eddy current brake directly. The electromagnetic field model and the flow-heat coupling model are established to predict and analyze the steady-state temperature distribution and braking torque. A new type of internal liquid cooling eddy current brake prototype was manufactured for a bench test. The experimental data prove that the computational model is effective. The calculation results show that the new internal liquid cooling eddy current brake has improved heat dissipation advantages.

Coupled Magnetic Field-Thermal Network Analysis of Modular-Spoke-Type Permanent-Magnet Machine for Electric Motorcycle

Brushless modular spoke type permanent magnet (MSTPM) machine has exhibited prior electromagnetic (EM) performance over conventional surface-mounted PM machines for in-wheel traction system in electric vehicles (EVs). However, analysis of thermal behavior of MSTPM machines is rather insufficient, even accurate thermal analysis is of significant importance due to poor heat dissipation condition inside the wheel hub. Conventionally, the losses produced in electrical machines by EM prediction is equivalent to the heat source in normal thermal analysis, and only the resultant thermal behavior is investigated. However, the reaction of temperature rising on the EM performance is neglected. In this article, a bi-directional coupled electromagnetic-thermal analysis method is proposed and carried out by a combination of lumped parameter thermal network (LPTN) model and finite element method (FEM), where both steady-state temperature distribution and transient-state temperature rise are investigated for MSTPM machines. By finite number of iterations between magnetic and thermal fields, the electromagnetic performance and thermal behavior can be predicted more accurately due to the coupling effect considered. The coupled model-predicted results are verified by 3D-FEM and experimental measurement, which shows that the proposed method has advantages in both computational efficiency and accuracy as well as can be applied to other electrical machines.

Effect of spherical pores coalescence on the overall conductivity of a material.

The problem about steady-state temperature distribution in a homogeneous isotropic medium containing a pore or an insulating inhomogeneity formed by two coalesced spheres of the same radius, under arbitrarily oriented uniform heat flux, is solved analytically. The limiting case of two touching spheres is analyzed separately. The solution is obtained in the form of converged integrals that can be calculated using Gauss-Laguerre quadrature rule. The temperature on the inhomogeneity's surface is used to determine components of the resistivity contribution tensor for the insulating inhomogeneity of the mentioned shape. An interesting observation is that the extreme values of these components are achieved when the spheres are already slightly coalesced.

Oncological Study of Thin Layers of Imatinib Molecule Nanostructure for Chronic Myelogenous Leukemia (CML), Acute Lymphocytic Leukemia (ALL), Philadelphia Chromosome-Positive (Ph+), Gastrointestinal Stromal Tumors (GIST), Hypereosinophilic Syndrome (HES), Chronic Eosinophilic Leukemia (CEL), Systemic Mastocytosis and Myelodysplastic Syndrome Treatment

The interest in exploring more effective methods for cancer treatment has increased widely in recent years. In clinical studies it is difficult to determine the temperature distribution in both normal tissue and in tumor during hyperthermia treatment since temperature can be measured in limited number of positions in tissue or tumor. Simulation studies can play crucial role in physician's perception of the temperature distribution in tissue. Hyperthermia treatment is facing some unsolved problems such as the appropriate dosage of magnetic Nano particles required to achieve the optimum temperature which results in apoptosis in tumor cells. In this study, a 2D computational model is created in COMSOL Metaphysics in order to analyze temperature distribution in both normal tissue and tumor during hyperthermia treatment using various dosages of magnetic Nano particles. Temperature distribution is achieved by considering various layers from wave source through to the tumor and also by taking into account the amount of heat generated through the Brownian rotation and the Neel relaxation. Simulations of a spherical tumor located in ellipse tissue were designed. A systematical variation in dosage has been performed. Temperature distribution and maximum temperature in steady state and effect of the dosage of Nano particles.

Analysis of crack problems in functionally graded materials under thermomechanical loading using graded finite elements

This paper represents a comprehensive study of the fracture behaviour of linear elastic isotropic functionally graded materials (FGMs) subjected to mechanical and thermal loading. For this purpose, an improved graded 9-node quadrilateral finite element which includes the variation of elastic (Young's modulus and Poisson's ratio) and thermal properties (coefficient of thermal expansion and heat conductivity) at the element level is developed. The performance of the new element in conducting thermomechanical fracture analysis is evaluated by conducting a set of simulations to compare the fracture parameters in FGMs with sharp material and temperature gradients against those with mild material and temperature gradients. The reliability of the proposed element is verified by comparing with existing solutions. The thermomechanical coupling and its influence on the coupled modes of fracture which originates from the material gradient in FGMs are investigated. The influence of the steady-state temperature distribution, as well as the material gradient on the crack tip local fields and fracture parameters, such as stress intensity factors, mode mixity, and energy release rate, are studied. More importantly, it was found that compared with conventional homogeneous finite elements the current model is more reliable for modelling crack problems in FGMs.

A Fast Semi-Analytic Approach for Combined Electromigration and Thermomigration Analysis for General Multisegment Interconnects

Considering temperature gradient or thermomigration (TM) impacts on electromigration (EM) due to Joule heating was less studied in the past. In this article, we propose a new semi-analytical stress transient analysis method to consider both EM and TM effects for general multisegment interconnects. The new method is based on the separation of variables (SOVs) approach to find the analytic solution of coupled EM-TM partial differential equation (PDE). The algorithm consists of several steps. We first develop analytic solutions to compute the steady-state temperature distribution of multisegment wires. Based on this, we derive closed-form solutions for steady-state hydrostatic stress distribution in the context of thermal gradients due to Joule heating for multisegment interconnect wires. With the steady-state stress distribution, the coupled EM-TM PDE can be homogenized and solved by the SOV method. To deal with temperature/position-dependent diffusivity of metal migration process due to nonuniform temperature distribution, we utilize a piecewise linear technique to approximate the position-dependent diffusivity. The numerical results on multisegment interconnects show that the proposed method has negligible error loss compared to commercial finite element analysis software COMSOL but is about an order of magnitude faster than COMSOL with $10\times $ less memory footprint. The numerical results further show that temperature gradient due to Joule heating indeed has significant impacts on the EM failure process.

Characteristics of Dimethyl Ether Oxidation in a Preheated Pt-γ-Al2O3 Catalytic Reactor

ABSTRACT An experimental study on the catalytic combustion of dimethyl ether under various oxidation conditions through a preheated tubular catalytic reactor filled with a lab-made Pt-γ-Al2O3 catalyst is presented in this paper. Both the transient variance of temperature distribution during the ignition process and the stationary results as the reactor reaches stable are delineated. The catalytic reactor is mounted in a tubular furnace to preheat and maintain an isothermal boundary. The reaction profiles and ignition processes are characterized by monitoring the temporal temperature traces, which is the steady-state axial distribution of temperature in the reactor. The average axial reaction temperature for different fuel quantities with various isothermal boundaries of the reactor was also evaluated. During the light-off process, the main exothermal reaction zone shift is found. The results demonstrate that a higher equivalence ratio of reactants produces a higher temperature, resulting in more heat transferring upstream and causes a higher conversion ratio. For the same equivalence ratio, a higher isothermal boundary temperature will result in a higher conversion ratio. The more extended reactor is required in one of the two conditions of a lower equivalence ratio of reactants and a lower isothermal boundary of the reactor. Finally, the energy balance and exergy analysis for the reactor was also performed; the results will be the basis for improving and optimizing designs.

Distributed Temperature Control in Laser-Based Manufacturing

Abstract Temperature control is essential for regulating material properties in laser-based manufacturing. Motion and power of the scanning laser affect local temperature evolution, which in turn determines the a posteriori microstructure. This paper addresses the problem of adjusting the laser speed and power to achieve the desired values of key process parameters: cooling rate and melt pool size. The dynamics of a scanning laser system is modeled by a one-dimensional (1D) heat conduction equation, with laser power as the heat input and heat dissipation to the ambient. Since the model is 1D, length and size are essentially the same. We pose the problem as a regulation problem in the (moving) laser frame. The first step is to obtain the steady-state temperature distribution and the corresponding input based on the desired cooling rate and melt pool size. The controller adjusts the input around the steady-state feedforward based on the deviation of the measured temperature field from the steady-state distribution. We show that with suitably defined outputs, the system is strictly passive from the laser motion and power. To avoid over-reliance on the model, the steady-state laser speed and power are adaptively updated, resulting in an integral-like update law for the feedforward. Moreover, the heat transfer coefficient to the ambient may be uncertain, and can also be adaptively updated. The final form of the control law combines passive error temperature field feedback with adaptive feedforward and parameter estimation. The closed-loop asymptotical stability is shown using the Lyapunov arguments, and the controller performance is demonstrated in a simulation.

Simulation of the shape deflection for the spherical shell of the space calibration-adjustment spacecraft

The spherical shell made with high accuracy is one of the possible geometric shapes for passive orbital signal repeaters and calibration-adjustment spacecrafts used to determine the energy potential of the radar channel of the ground-based complex needed to control the space object motion. Under the solar radiation, an uneven temperature distribution over the surface of such a shell causing a deviation of its shape from the spherical one occurs. To determine these deviations, the steady-state temperature distribution for the shell with a fixed orientation relative to the Sun obtained by solving the Fredholm integral equation of the second kind is used. A quantitative analysis of the possible alignment of a quasi-stationary distribution of the shell temperature in case of the shell rotation with a constant angular velocity around the axis perpendicular to the direction to the Sun is carried out.

Investigations into thermal resistance of tunnel lining heat exchangers

Geothermal energy is a promising and sustainable source that can reduce current dependence on conventional fuels for thermal energy production. To exploit this source of energy thermo-active geostructures such as tunnel lining heat exchangers are being investigated theoretically as well as experimentally. These geostructures are composed of concrete panels embedded with reinforcement cages fitted with absorber pipes. Several engineering projects in China, Finland and Italy have deployed such heat exchangers in tunnels. To achieve efficient energy production, characterisation of these systems require realistic models of the substructure heat exchanger. Therefore investigations into thermal resistance of the heat exchanger is vital. The present study is concerned with quantifying the thermal resistance of tunnel lining heat exchangers where the thermal boundary surfaces are applied at surfaces representing the adjacent ground and the exposed concrete, in addition to the pipe surface. Steady state temperature distribution in a two dimensional cross section of a tunnel lining heat exchanger is investigated using the boundary collocation least squares method. Design parameters including pipe and tunnel lining specifications are used as model inputs.

Rotor Stress and Dynamics Analysis of a High-Speed Permanent Magnet Machine for a Micro Gas Turbine Considering Multiphysics Factors

For high-speed permanent magnet machines (HSPMMs), the precise analysis of rotor stress and rotor dynamics is essential to ensure the stable operation of rotor under high-speed conditions. This work conducts an in-depth research on the rotor of an HSPMM for a micro gas turbine with predetermined geometrical sizes. Firstly, the mechanical and electromagnetic losses are investigated by both, empirical methods and finite element method (FEM) respectively, and then the 3D steady-state temperature distribution of the HSPMM is evaluated on this basis. Then, considering the non-isothermal temperature field of the rotor, the 3D thermal-structural coupling method is adopted to analyze the influence of the carbon fiber wrapping direction and the epoxy resin adhesive between permanent magnets (PMs) and rotor core on the rotor thermal stress. Furthermore, in the steady-state thermal field, considering the change in elastic modulus and the generation of thermal stress caused by temperature rise, the results of the modal analysis are compared with those of room temperature to analyze the effect of temperature on the natural frequency of the rotor. Finally, two prototypes of 80 kW, 60000 rpm HSPMMs are fabricated to test the capability of the HSPMM. The experimental results of back-to-back drag test and modal test verify the accuracy of the temperature characteristics and modal analysis, respectively.

Influence of Turbulence Schmidt Number on Exit Temperature Distribution of an Annular Gas Turbine Combustor using Flamelet Generated Manifold

The Reynolds analogy concept has been used in almost all turbulent reacting flow RANS (Reynolds-averaged Navier-Stokes) simulations, where the turbulence scalar transfers in flow fields are calculated based on the modeled turbulence momentum transfer. This concept, applied to a lean premixed combustion system, was assessed in this paper in terms of exit temperature distribution. Because of the isotropic assumption involved in this analogy, the prediction in some flow condition, such as jet cross flow mixing, would be inaccurate. In this study, using Flamelet Generated Manifold as reaction model, some of the numerical results, obtained from an annular combustor configuration with the turbulent Schmidt number varying from 0.85 to 0.2, were presented and compared with a benchmark atmospheric test results. It was found that the Schmidt number σt in mean mass fraction f transport equation had significant effect on dilution air mixing process. The mixing between dilution air and reaction products from the primary zone obviously improved as σt decreased on the combustor exit surface. Meanwhile, the sensitivity of σt in three turbulence models including Realizable k-e, SST (Shear Stress Transport) and RSM (Reynolds Stress Model) has been compared as well. Since the calculation method of eddy viscosity was different within these three models, RSM was proved to be less sensitive than another two models and can guarantee the best prediction of mixing process condition. On the other hand, the results of dilution air mixing were almost independent of Schmidt number Sct in progress variable c transport equation. This study suggested that for accurate prediction of combustor exit temperature distribution in steady state reacting flow simulation, the turbulent Schmidt number in steady state simulation should be modified to cater to dilution air mixing process.

Thermal conductivity of cylindrical tanks for backup fuel of boiler rooms

In this paper, the method of determining the level of heat losses through structures of a cylindrical tank for backup fuel of boiler rooms and steady-state non-uniform temperature distribution in a multilayer tank have been considered, given that the heat transfer coefficient depends on r and z coordinates.

Temperature control in TTFields therapy of GBM: impact on the duty cycle and tissue temperature

In TTFields therapy, Optune® is used to deliver the electric field to the tumor via 4 transducer arrays. This device monitors the temperature of the transducers and reduces the current whenever a transducer reaches 41 °C. Our aim is to quantify Optune’s duty cycle and to predict the steady-state temperature distribution in the head during GBM treatment. We used a realistic head model and the finite element method to solve Pennes equation and to simulate how Optune operates considering that current reduces to zero when the thermal limit is reached. The thermal impact was evaluated considering the maximum temperature reached by each tissue and using the CEM 43 °C metric. We observed that Optune switches the current on and off intermittently. In our model, one transducer reached the temperature limit quicker than the others and consequently it was the one that controlled current injection. This led to different duty cycles for the anterior–posterior and left–right array pairs. The thermal analysis indicated that the highest temperature in the model, 41.7 °C, was reached on the scalp under a transducer. However, TTFields may lead to significant changes only at the brain level such as BBB permeability increase, cerebral blood flow variation and changes in the concentration of some neurotransmitters. The duty cycle may be increased, e.g. by controlling the current at the transducer level. These predictions should be validated by comparison with experimental data and reconciled with the lack of evidence of thermal impact in clinical trials.