Homotopy Perturbation Method for Thermal Stresses in an Annular Fin with Variable Thermal Conductivity

An approximate analytical solution method for thermal stresses in an annular fin with variable thermal conductivity is presented. Homotopy perturbation method (HPM) is employed to estimate the non-dimensional temperature field by solving nonlinear heat conduction equation. The closed-form solutions for the thermal stresses are formulated using the classical thermoelasticity theory coupled with HPM solution for temperature field. The plane state of stress conditions are considered in this study. The effects of thermal parameters such as variable thermal conductivity parameter (β), thermogeometric parameter (K), and the non-dimensional coefficient of thermal expansion (χ) on the temperature field and stress field are studied. The results for temperature field and stress field obtained from HPM-based solution are found to be in very close agreement with the results available in literature. Furthermore, the HPM solution is found to be very efficient and handles nonlinear heat transfer equation with greater convenience.     

Analytical solution of the parabolic and hyperbolic heat transfer equations with constant and transient heat flux conditions on skin tissue

In this article, the parabolic (Pennes bioheat equation) and hyperbolic (thermal wave) bioheat transfer models for constant, periodic and pulse train heat flux boundary conditions are solved analytically by applying the Laplace transform method for skin as a semi-infinite and finite domain. The bioheat transfer analysis with transient heat flux on skin tissue has only been studied by Pennes equation for a semi-infinite domain. For modeling heat transfer in short duration of an initial transient, or when the propagation speed of the thermal wave is finite, there are major differences between the results of parabolic and hyperbolic heat transfer equations. The non-Fourier bioheat transfer equation describes the thermal behavior in the biological tissues better than Fourier equation. The outcome of transient heat flux condition shows that by penetrating into the depths beneath the skin subjected to heat, the amplitude of temperature response decreases significantly. The blood perfusion rate can be predicted using the phase shift between the surface temperature and transient surface heat flux. The thermal damage of the skin is studied by applying both the parabolic and hyperbolic bioheat transfer equations.     

Estimation of heat flux imposed on the rake face of a cutting tool: A nonlinear,complex geometry inverse heat conduction case study

In this paper the sequential function specification method is used to estimate the transient heat flux imposed on the rake face of a cutting tool during the cutting operation with two different assumptions. In one of them the thermal conductivity is taken to be constant, and in the other one it varies with temperature. The cutting tool is modeled as a three dimensional object. The capabilities of the geometric modeling, mesh generation as well as solver of the commercial software ANSYS are utilized in order to reduce the time expended for modeling and direct heat conduction solution, in both linear and nonlinear problems. This way the inverse heat conduction algorithm employs ANSYS as a subprogram through the ANSYS Parametric Design Language (APDL). The stability as well as accuracy is compared for cases of linear and nonlinear heat conductions. The effect of nonlinearity, as well as different sensor locations is investigated in order to arrive at an optimal experimental procedure. Finally, a typical temperature data during the working condition are used to recover the heat flux at the cutting tool surface using linear as well as nonlinear solutions.     

An inverse problem of finding the time-dependent thermal conductivity from boundary data

We consider the inverse problem of determining the time-dependent thermal conductivity and the transient temperature satisfying the heat equation with initial data, Dirichlet boundary conditions, and the heat flux as overdetermination condition. This formulation ensures that the inverse problem has a unique solution. However, the problem is still ill-posed since small errors in the input data cause large errors in the output solution. The finite difference method is employed as a direct solver for the inverse problem. The inverse problem is recast as a nonlinear least-squares minimization subject to physical positivity bound on the unknown thermal conductivity. Numerically, this is effectively solved using the lsqnonlin routine from the MATLAB toolbox. We investigate the accuracy and stability of results on a few test numerical examples.     

Numerical Technique for Resolving the Dual Phase Lag Heat Conduction in Thin Film Metal

Abstract

In this article, a three-time level finite difference scheme is used to resolve the dual phase lag’s (DPL) heat conduction in a micro scale gold film subjected to spontaneous temperature boundary conditions without knowing the heat flux. Finite difference analog of DPL equation on applying to the intermediate grid points of the computational domain results into a system of linear, algebraic equations which can be solved using Thomas’ algorithm to finally obtain the transient temperature solution distributions in the film. The solution predicted by the DPL model is compared with that obtained by the single-phase Cattaneo–Vernotte’s model. Further, the way in which non-Fourier’s temperature distributions affected by the diffusion due to the increase in Heat Conduction Model numbers agree with the predecessor’s published results. The results by both the models revealed a finite thermal wave speed in the film contrasting the infinite speed of heat propagation as stated by the classical Fourier’s thermal model. Low spatial step and higher order finite difference schemes are recommended for better accurate numerical results of the non-Fourier’s temperature distributions occurring in the very short transient period between the instants of the suddenly applied spatial temperature gradient and the reaching of the steady state conditions.     

A NONLINEAR OPTIMAL CONTROL PROBLEM IN DETERMINING THE STRENGTH OF THE OPTIMAL BOUNDARY HEAT FLUXES

A nonlinear optimal control algorithm in determining the strength of optimal boundary heat fluxes utilizing the conjugate gradient method (CGM) of minimization is applied successfully in the present study based on the desired temperature distributions at the final time of heating. The thermal properties are assumed to be functions of temperature, and this makes the problem nonlinear. The accuracy of this optimal control analysis is examined by using the numerical experiments. Three different desired temperature distributions are given and the corresponding optimal control heat fluxes are to be determined. Results show that the optimal boundary heat fluxes can be obtained with any arbitrary initial guesses within a couple of seconds' CPU time on a Pentium III 600-MHz personal computer.     

Transient heat transfer in a U-tube borehole heat exchanger

A transient heat transfer model has been development for a thermal response test (TRT) on a vertical borehole with a U-tube. Vertical borehole heat exchangers are frequently coupled to ground source heat pumps, which heat and cool buildings. The model provides an analytical solution for the vertical temperature profiles of the circulating fluid through the U-tube, and the temperature distribution in the ground. The model is verified with data sets from a laboratory sandbox and field TRTs, as well as a previously reported numerical solution. Unlike previous analytical models, the vertical profiles for the circulating fluid are generated by the model without any assumption of their functional form.     

基于航空散热板的内嵌热管传热模型分析

对一种非规则截面的航空散热板轴向槽道热管,分别建立了基于SINDA软件HEATPIPE算法的一维模型和基于QFLOW算法的二维模型,比较了两种传热模型和算法下热管的暂态和稳态传热特性。结果表明,两种模型对热管平均工作温度的计算结果吻合较好,由于一维模型没有考虑热管壳体的周向传热以及热管的结构对边界条件施加的影响,最大传热能力的计算结果小于二维模型。一维模型适于对航空热管进行系统级的初步热设计,二维模型适于对非规则截面热管的定量传热分析。     

Analysis of transient heat transfer in multilayer thin films with nonlinear thermal boundary resistance

Transient energy transport in thin-layer films with a nonlinear thermal boundary resistance is analyzed theoretically within the framework of the dual-phase-lag heat conduction model. An iterative finite difference numerical method is used and is verified using a derived semi-analytical solution of the problem. Effects of the thermo-physical properties on energy transport when a two-layer film is exposed to a thermal pulse of certain duration and strength are presented. The thermal boundary resistance, the heat flux and temperature gradient phase lags and the thermal conductivities and heat capacities all are important factors that characterize energy transport through the interface and the temperature distribution in the two layers. The maximum interfacial temperature difference that takes place in the transient process of thermal pulse propagation is found to be the proper choice to measure the perfect-ness of the interface with a finite thermal boundary resistance. The results show that even with high values of the thermal boundary resistance the maximum interfacial temperature difference can be very small when the thermal pulse propagates from a high-thermal conductivity and heat capacity layer to a low-thermal conductivity and heat capacity layer. For a certain range of the thermal conductivities and heat capacities, the maximum interfacial temperature difference approaches zero even with high values of the thermal boundary resistance. Thermal conductivities and heat capacities are much more important in characterizing transient heat transfer through the imperfect interface than the phase lags of the heat flux and temperature gradient.     

Transient behavior of run-around heat and moisture exchanger system. Part IІ: Sensitivity studies for a range of initial conditions

Part І of this paper [17] developed and verified the numerical model for simultaneous heat and moisture transfer in the run-around membrane energy exchanger (RAMEE) system to determine the transient behavior of the system under different initial and operating conditions.This paper presents the transient response of the RAMEE system for step changes in the inlet supply air temperature and humidity ratio. Also the system quasi-steady state operating conditions are predicted as the system approaches its asymptotic operating condition. The transient responses are predicted with changes in various parameters. These include: the number of heat transfer units, thermal capacity ratio, heat loss/gain ratio, storage volume ratio and the normalized initial salt solution concentration. It is shown that the storage volume ratio and the initial salt solution concentration have significant impacts on the transient response of the system and heat transfer between the RAMEE system and the surrounding environment can change the system quasi-steady conditions substantially.     

Treatment of the interfacial temperature jump condition with non-Fourier heat conduction effects

Transient energy transport with non-Fourier heat conduction effects in a two-layer structure of dissimilar materials subject to ultra-fast laser heating is studied using the proper interfacial temperature jump condition. The solution obtained is compared with solutions available in literature that use diffusion-type interfacial conditions in conjunction with non-Fourier heat conduction effects. The dual-phase lag heat conduction model is used in this work as it includes both the temporal and spatial non-Fourier effects. It is found that the diffusion-type interfacial temperature jump condition with non-Fourier heat conduction models can lead to discrepancies and erroneous trends in theoretical predictions. Moreover, a comparison between the functional forms of the two solutions obtained utilizing both interfacial conditions shows that implementing the proper interfacial temperature jump condition does not add any complexity to the solution obtained. This study – implementing the proper interfacial temperature jump condition – is further extended to show the strong effects of the thermal contact conductance and the surface layer thickness on the transient thermal response of a two-layer material in a semi-infinite domain subject to ultra-fast laser heating processes in terms of the reflectivity change of the surface layer, the temperature distribution in the two-layer structure as well as the temporal variation of the interfacial temperature difference.     

Magneto-thermal coupled analysis of canned induction motor

The authors present the calculation of the distribution of the transient temperature in the rotor bars of a canned induction motor, during locked rotor conditions, where the phenomena of electromagnetically induced currents and heat transfer are coupled. They have developed a coupled finite element electromagnetic code called WEMAP in which the calculated power loss densities are used as the heat sources for a transient thermal solution in subregions of the original problem geometry. These subregions are enclosed by surfaces on which either temperature or a convection boundary condition is known. In addition, the change in rotor bar resistance as a function of the temperature is included in these calculations. The calculated temperatures are compared with test results, and favorable agreement is obtained     

Compound Material Thermal Parameters for a Layered Material Resembling an Automobile Firewall

Heat transmission through a layered compound material consisting of carbon steel backing and insulation (either aluminized silver or fiberglass) was examined to determine thermal properties. The heat flux impinged on the insulation material side of this simulated "firewall." A heat transfer model was developed that could, in principle, be used to predict the heat transfer through layered compound materials using techniques of thermal property parameter estimation. The parameter estimates are based on thermocouple measurements of surface temperatures during heating on both sides of the material. The experiment analyzed in this article involved a vertical plate exposed on the insulation side to a transient step-applied radiant heat flux. The transient temperature measurements were fitted to heat transfer models. Thermal diffusivity and Biot number were estimated using ordinary least-squares nonlinear regression.     

Numerical simulations and analyses of temperature control loop heat pipe for space CCD camera

As one of the key units of space CCD camera,the temperature range and stability of CCD components affect the image's indexes.Reasonable thermal design and robust thermal control devices are needed.One kind of temperature control loop heat pipe(TCLHP) is designed,which highly meets the thermal control requirements of CCD components.In order to study the dynamic behaviors of heat and mass transfer of TCLHP,particularly in the orbital flight case,a transient numerical model is developed by using the well-established empirical correlations for flow models within three dimensional thermal modeling.The temperature control principle and details of mathematical model are presented.The model is used to study operating state,flow and heat characteristics based upon the analyses of variations of temperature,pressure and quality under different operating modes and external heat flux variations.The results indicate that TCLHP can satisfy the thermal control requirements of CCD components well,and always ensure good temperature stability and uniformity.By comparison between flight data and simulated results,it is found that the model is to be accurate to within 1℃.The model can be better used for predicting and understanding the transient performance of TCLHP.     

Numerical simulation of thermal loading produced by shaped high power laser onto engine parts

Recently a new method for simulating the thermal loading on pistons of diesel engines was reported. The spatially shaped high power laser is employed as the heat source, and some preliminary experimental and numerical work was carried out. In this paper, a further effort was made to extend this simulation method to some other important engine parts such as cylinder heads. The incident Gaussian beam was transformed into concentric multi-circular patterns of specific intensity distributions, with the aid of diffractive optical elements (DOEs). By incorporating the appropriate repetitive laser pulses, the designed transient temperature fields and thermal loadings in the engine parts could be simulated. Thermal–structural numerical models for pistons and cylinder heads were built to predict the transient temperature and thermal stress. The models were also employed to find the optimal intensity distributions of the transformed laser beam that could produce the target transient temperature fields. Comparison of experimental and numerical results demonstrated that this systematic approach is effective in simulating the thermal loading on the engine parts.     

A distributed model of a space heat pump under transient conditions

A prototype heat pump was designed and tested, as means of active thermal management for electronics packages to be used on stratospheric balloon missions. The evaporator worked as a cold plate to absorb heat dissipated by the electronics, while the condenser rejected heat primarily by radiation to the rarified environment. To predict the transient performance of the heat pump under varying environmental temperature and cooling load conditions, a dynamic model of the heat pump is created with a graphical user interface (GUI). The simulation of the evaporator and condenser are fully transient and the components are segmented, whereas the compressor and expansion device are lumped models and assumed to be at quasi-steady state. A detailed model for the mass and energy conservation in the two heat exchangers is presented. The spatial and temporal variation of temperature and mass flow rate in the heat exchangers are predicted. Several types of transient conditions such as step changes of the space temperature and cooling load, system start-up, shutdown, and cycling, are studied. The space temperature, cooling load, compressor power, mass flow rates of the compressor and expansion device, pressures and refrigerant charges of the condenser and evaporator, and temperature distribution in the heat exchangers are dynamically displayed on the GUI. The simulation results are compared with experimental data for step changes in the cooling load and show good agreement in terms of trends. Copyright © 2002 John Wiley & Sons, Ltd.     

Two-dimensional transient conduction and radiation heat transfer with temperature dependent thermal conductivity

This paper deals with the effect of the temperature dependent thermal conductivity on transient conduction and radiation heat transfer in a 2-D rectangular enclosure containing an absorbing, emitting and scattering medium. The thermal conductivity of the medium is assumed to vary linearly with temperature. The radiative part of the energy equation was solved using the collapsed dimension method. To facilitate solution of the energy equation, which is a highly nonlinear one, time linearization was done first and then the equation was solved using the alternating direction implicit scheme. Results for the effects of the variable thermal conductivity were found for temperature and heat flux distributions.     

Dynamic Coverage Optimal Control for Multiple Spacecraft Interferometric Imaging

In this paper, we study and generalize a class of optimal control problems known in the literature as τ-elastic variational optimal control problems. In the τ-elastic optimal control, we want to minimize a cost function over trajectories that evolve on a Riemannian manifold and satisfy a second-order differential equation together with some smoothness and motion constraints. The cost function is a weighted sum of the squared norm of the acceleration and the squared norm of the velocity. Here, we generalize the τ-elastic variational problem to the dynamic coverage optimal control problem, which is a class of optimal control problems motivated by multiple spacecraft formation flying for imaging applications. The main novelty of this paper is an interesting connection between multiple spacecraft formation flying and the τ-elastic and coverage optimal control problems. This research is supported by NSF grants DMS-0103895, DMS-0305837, and CMS-0408542.     

Meshless element free Galerkin method for unsteady nonlinear heat transfer problems

In this paper, meshless element free Galerkin (EFG) method has been extended to obtain the numerical solution of nonlinear, unsteady heat transfer problems with temperature dependent material properties. The thermal conductivity, specific heat and density of the material are assumed to vary linearly with the temperature. Quasi-linearization scheme has been used to obtain the nonlinear solution whereas backward difference method is used for the time integration. The essential boundary conditions have been enforced by Lagrange multiplier technique. The meshless formulation has been presented for a nonlinear 3-D heat transfer problem. In 1-D, the results obtained by EFG method are compared with those obtained by finite element and analytical methods whereas in 2-D and 3-D, the results are compared with those obtained by finite element method.     

SIMULATION OF RAPID THERMAL PROCESSING IN A DISTRIBUTED COMPUTING ENVIRONMENT

Rapid thermal processing (RTP) has become a key technology in the fabrication of advanced semiconductor devices. As wafers get larger and chip dimensions become smaller, the understanding of the highly coupled physics, such as radiative heat transfer, transient fluid flow, heat transfer, and chemical reactions through numerical modeling using high-performance computing, is the key to the design, optimization, and control of RTP reactors. In this study, an accurate and efficient simulation tool for RTP in a distributed computing environment is developed by implementing various new models and algorithms. Thegoverning equations for highly coupled and transient transport phenomena inRTP are solved by anunstructured finite volume method (FVM). Surface radiative heat transfer is the most dominant mode of heat transfer in RTP and it is modeled by the modified discrete transfer method (MDTM). The radiative properties on the patterned wafer are quite different from those on the bare silicon and they are predicted by the matrix method. To enhance thecomputationefficiency, anefficient parallelalgorithmis implemented in the solution procedure. Data communication among the processors is carried out by the Parallel Virtual Machine (PVM). To evaluate the present simulation tool, an actual commercial RTP reactor is investigated under various conditions. The accuracy of the present model is validated through the comparisons of wafer temperature profile between different models for steady state andtransient flow andheat transfer cases. To demonstrate the importance of the pattern effects in RTP systems, a transient case containing the patterned wafer is investigated. The temperature profile and its uniformity for the patterned wafer are found to be quite different from those for the unpatterned wafer. To examine the performance on parallel computation, the previous transient case is studied with different processor numbers. As the processor number increases, the computationtime is seen to reduce; however, the parallel performance is seen to degrade A larger solution iteration number and higher communication overhead are believed to be the major reasons for the degradation of the parallel performance. The present case studies indicate that the simulation tool developed in this study can be used to systematically investigate various effects in RTP systems because of its high accuracy and efficiency.