Transient Heat Conduction Model Research Articles

Experimental Observations and Modelling of Thermal Historywithin a Steel Plate During Water Jet Impingement

In order to investigate heat transfer of steel plates under a water jet impingement and to further simulate runout table operation in a hot strip mill, a full-scale pilot runout table facility was designed and constructed at the University of British Columbia (UBC). This paper describes the experimental details, data acquisition and data handling techniques for steel plates during water jet impingement by one circular water jet from an industrial header. Recorded visual observations at the impinging surface were obtained. The effects of cooling water temperature and impingement velocity on the heat transfer from a steel plate were studied. A two-dimensional finite element method-based transient inverse heat conduction model was developed. With the help of the model, heat fluxes and heat transfer coefficients along the impinging surface under various cooling conditions were calculated. The microstructural evolution of the steel plate was also investigated for the varying cooling conditions. Samples were obtained from each plate, polished, etched and then photographed.Afin d’étudier le transfert de chaleur de tôles d’acier sous l’impact d’un jet d’eau et afin de simuler l’opération d’un train à rouleaux de sortie d’un laminoir à feuillards à chaud, on a conçu et construit, à l’université de la Colombie britannique (UBC), une installation pilote à pleine échelle d’un train à rouleaux de sortie. Cet article décrit les détails expérimentaux, les techniques d’acquisition de données et de manipulation de données pour les tôles d’acier lors de l’impact de jet d’eau par un jet circulaire provenant d’un collecteur industriel. On a obtenu un enregistrement de l’observation visuelle à la surface d’impact. On a étudié les effets de la température de l’eau de refroidissement et de la vitesse d’impact sur le transfert de chaleur d’une tôle d’acier. On a développé un modèle de conduction de chaleur transitoire inverse basé sur une méthode des éléments finis à deux dimensions. À l’aide de ce modèle, on a calculé les flux de chaleur et les coefficients de transfert de chaleur le long de la surface d’impact sous diverses conditions de refroidissement. On a également étudié l’évolution de la microstructure de la tôle d’acier pour les diverses conditions de refroidissement. On a obtenu des échantillons de chaque tôle, puis on les a polis, ‘attaqués’ à l’acide et ensuite photographiés.

A rational method for the distribution of nodes in modelling of transient heat conduction in plane slabs

In this paper, the thermal response of a homogenous slab to both step and sinusoidal excitations of temperature at one boundary is examined. The distribution of nodes for the purposes of heat balance thermal modelling is discussed. Errors in the heat flux at the external boundary are examined when even and uneven gridding approaches are applied. A denser gridding close to the surface is adopted due to the fact that the curvature of the temperature gradient is greatest near the surface during the early stages of transient heat transfer. Example calculations demonstrate the potential of uneven gridding to obtain a rational compromise between accuracy and computational effort. Rational uneven gridding results in a more accurate solution with a smaller number of thermal nodes compared with even gridding.

A Closure Model for Transient Heat Conduction in Porous Media

Equations governing the transient heat conduction in porous materials consisting of solids and fluids of different thermal properties were derived with a volumetric average scheme under the assumption of nonthermal equilibrium. The derivation leads to a macroscopic two-equation system which requires the closure modeling of new unknown terms due to interfacial transport, namely, the tortuosity term and the interfacial heat transfer term. Closure relations were obtained from the microscopic equations for temperature fluctuation under quasi-steady assumption. The closure coefficients appeared in the closure relations then depend on the media geometry as well as thermal properties. To demonstrate these dependencies, the closure coefficient for the thermal tortuosity is evaluated based on the effective stagnant thermal conductivity model proposed by Hsu et al. (1995) for periodically packed cubes, and the coefficient for interfacial heat transfer based on a quasi-steady heat conduction of dispersed spheres immersed in fluids. The salient features as well as the applicability and limitation of the newly proposed transient heat conduction model were discussed.

A fast convergent and accurate temperature model for phase-change heat conduction

This work proposes a temperature-based finite element model for transient heat conduction involving phase-change. Like preceding temperature-based models, it is characterized by the discontinuous spatial integration over the elements affected by the phase-change. Using linear triangles or tetrahedrals, integration can be performed in a closed analytical way, assuring an exact evaluation of the discrete balance equation. Because of its unconditional stability, an Euler-backward time-stepping scheme is implemented. A crucial fact is the computation of the exact tangent matrices for the Newton–Raphson solution of the non-linear system of discretized equations. Efficiency of the model is tested by means of the results obtained for the Neumann problem and the solidification of a steel ingot. Copyright © 1999 John Wiley & Sons, Ltd.

Determination of local heat transfer coefficient based on bulk mean temperature using a transient liquid crystals technique

Abstract Recent advances in thermochromic liquid crystal (TLC) thermography has improved its usefulness as a very effective technique for measurements of temperature and heat transfer. One of the approaches to determine the local heat transfer coefficient, known as the transient technique, is to monitor the temporal evolution of surface temperature in conjunction with the solution of a transient heat conduction model penetrating to the wall substrate. The local heat transfer coefficient resulted from such a transient test, by nature, has its reference temperature based on the inlet temperature of the test rig, rather than the local bulk mean temperature. The latter during a transient test varies with both time and streamwise location. The heat transfer coefficient based on the inlet temperature presents difficulty in data interpretation in designs of heat exchangers, particularly for flow channels with large length-to-diameter ratios. This study evaluates four different approaches and their theoretical background for determining the local bulk mean temperature and the sensible local heat transfer coefficient. Using a test model of a turbine blade cooling passage with delta-wing shaped vortex generators mounted on one of the passage walls, the magnitudes of the sensible heat transfer coefficient resulted from various approaches vary as much as 40%. Validated with the experimental data, two of the four methods yield superb data accuracy. Nevertheless, one of them stands out as the best choice, as it requires much less processing time and implementation effort.

Transient analysis of energy storage in a thermally stratified water tank

A one-dimensional transient heat conduction model to describe the decay of the thermocline in a stratified water tank is presented. The problem is formulated as an initial boundary value problem and the resulting governing equations in the fluid and in the storage wall are solved numerically to obtain the temperature profiles in the wall and the fluid. The formulation considers the axial conduction of heat, both in the fluid and in the solid wall. The mixing parameters introduced in the boundary conditions at the top and bottom of the tank in the fluid region account for mixing due to inlet and outlet streams with the stored fluid. The model is applicable to the storage of both hot and chilled water. The model is validated with experimental data from the literature. The parameters that influence the operation of a stratified thermal energy storage for both heat and cool storage are examined. © 1998 John Wiley & Sons, Ltd.

Transient analysis of energy storage in a thermally stratified water tank

A one-dimensional transient heat conduction model to describe the decay of the thermocline in a stratified water tank is presented. The problem is formulated as an initial boundary value problem and the resulting governing equations in the fluid and in the storage wall are solved numerically to obtain the temperature profiles in the wall and the fluid. The formulation considers the axial conduction of heat, both in the fluid and in the solid wall. The mixing parameters introduced in the boundary conditions at the top and bottom of the tank in the fluid region account for mixing due to inlet and outlet streams with the stored fluid. The model is applicable to the storage of both hot and chilled water. The model is validated with experimental data from the literature. The parameters that influence the operation of a stratified thermal energy storage for both heat and cool storage are examined. © 1998 John Wiley & Sons, Ltd.

An Introduction To a User-Friendly Numerical Fire Endurance Algorithm

This paper adopts the simplest numerical procedure for solving the multi-dimensional nonlinear transient heat conduction model, which "occasionally" is used to simulate fire endurance and related fire engineering problems. Due to its superb simplicity, average fire professionals can easily implement this relatively user-friendly algorithm customized for the rarely published fire (convective or Robin) boundary conditions. Further, the danger of constant incident (Neumann) flux is discussed. This paper also discusses the cogent investigation of converging solutions, numerical difficulties, comparisons of analytical solutions of a simple benchmark case, and nonlinear problems arising from thermophysical properties, temporal fire including variable combined heat transfer coefficient, and a heat source or sink. Language: en

The Effect of Pressure on Power Transfer in Electron Beam Remelting of Cylinders

Measurements have been made in a laboratory scale furnace to examine the effect of chamber pressure on power deposition in electron beam remelting. Both commercial purity titanium and tantalum cylinders instrumented with embedded thermocouples have been used as targets in the study. Owing to the fact that a direct measurement of the power distribution was not possible, a finite element based transient heat conduction model has been employed to analyze the measurements. The results of the analysis indicate that the distribution of power density can be adequately described as a normal Gaussian and that the beam is focused as the pressure is increased from low to moderate pressures (0.004 to 0.15Pa) then gradually defocused as the pressure continues to increase (0.15 to 0.8Pa). A detailed examination of the data with the model indicates that the predominant effect of pressure is to alter the beam focus and not the amount of power deposited. A comparison of the results obtained from the tantalum target, where no liquid metal was present, and the titanium target, where liquid metal was present, indicates that liquid metal vapor acts to defocus the beam. Finally, an examination of the effect of pressure on the behavior of the liquid pool indicates that the predominant effect of defocusing is to alter the pool depth.

Simulation of the Cyclic Injection Mold-Cooling Process Using Dual Reciprocity Boundary Element Method

The cyclic, transient heat transfer within an injection mold is analyzed using iterative DRBEM/FDM based on transient heat conduction model in a decoupled sequence. It is found that the transient temperature fluctuation at mold cavity surface is much larger than that away from it. Simulated results from the present method are also compared with those calculated by a modified boundary element method based on a cycle-averaged approach and combined with a one-dimensional transient analysis

Hyperbolic temperature profiles for laser surface interactions

This study theoretically analyzes the transient temperature distributions in laser irradiated materials by considering a hyperbolic heat conduction model. Exact and limiting mathematical solutions for the temperature distributions are developed and important parameters are identified. Traditional Fourier transient heat conduction models are parabolic in nature, which imply an infinite speed of propagation of the thermal signal in the material. Hyperbolic non-Fourier models have been introduced to account for the finite speed of the thermal wave. The effects of finite speed are significant in short-pulse applications where the time period of the laser input is comparable to the thermal characteristic time of the material, and the resultant temperature variations are significantly different from that of traditional infinite-speed Fourier predictions. Two different types of materials, biological materials and inorganic solids, are considered for laser-surface interactions in the study. The parameter of greatest significance is found to be the ratio of thermal characteristic length to the laser beam width. Values of this parameter in the range between 0.1 and 3, corresponding to different applications, are examined and local temperature maximas, or hot spots, are found to occur at initial time periods for values greater than ∼0.2.

Numerical simulations of the cyclic, transient mold heat transfer in injection mold cooling process

In the present study, simulations of mold heat transfer in injection mold cooling system are developed using a dual reciprocity boundary element technique. The cyclic, transient characteristics of mold heat transfer is calculated based on a transient heat conduction model coupled with polymer melt temperature analysis satisfying compatible boundary conditions along cavity surface. The cyclic, transient variations of mold temperatures are clearly illustrated through the analysis of a plate mold. The present method provides a more realistic description of mold temperature variation within the steady cyclic period than that calculated by the modified boundary element method on a cycle-averaged basis. The latter overestimates the temperature variation rate within a steady cycle.

Modeling of Temperature Distributions in the Workpiece During Abrasive Waterjet Machining

Modeling of temperature distributions in a block-type workpiece during cutting with an abrasive waterjet (AWJ) was the subject of an analytical/experimental investigation in the present study. The experiments included measurement of detailed time-temperature distributions in the workpiece for selected AWJ/workpiece operational parameters. Mathematical modeling of the problem made use of a two-part process. In the first part, the measured experimental data were fed into an inverse heat conduction algorithm, which determined the corresponding heat flux in the workpiece. In the second part, this heat flux was fed into a two-dimensional transient heat conduction model that calculated the corresponding temperature distributions in the workpiece. It is demonstrated that the proposed model can serve as a useful thermal analysis tool for AWJ cutting processes so long as a quasi-steady-state condition can be established in the workpiece.

Material Pyrolysis Properties, Part I: An Integral Model for One-Dimensional Transient Pyrolysis of Charring and Non-Charring Materials

A new integral thermal pyrolysis model for the transient pyrolysis of charring and on-charring materials has been developed and evaluated by comparison of the results with exact solutions. The purpose for the development of this simple model has been the desire for predicting pyrolysis histories of materials exposed to pre heat fluxes by using “equivalent” properties tailored to the present model and common flammability test measurements. The pyrolyzing material is divided into a char layer and a unpyrolyzed (virgin) layer where the material has not yet pyrolyzed. These two layers are separated by an isothermal interface which is at a pyrolysis temperature (characteristic of the material). At this interface, heat is transferred to the virgin layer, causing further pyrolysis of the material (namely a thermal pyrolysis model is used). A one-dimensional transient heat conduction model is used to predict the heat transfer within the material. Exponential temperature profiles were assumed for the heat conduction model. Using a rwo-equation 9-moment method, the original partial differential equations were transformed into a set of two ordinary differential equations for each layer. These equations were numerically salved to I) determine the pyrolysis rate. regression depth and surface temperature, and 2) establish a dimensional and sensitivity analysis. The model has been shown to be very accurate (errors ~ 2%) from comparisons between numerical results and exact solutions. Despite the neglect of derailed chemical kinetic (Arrhenius) pyrolysis expressions, the accuracy of the integral model together with its simplicity has allowed the deduction of pyrolysis properties of materials by using common flammability test data as it ';ill be proved in a subsequent paper.

FINITE-ELEMENT MODELING OF HEAT FLOW IN DEEP-PENETRATION LASER WELDS IN ALUMINUM ALLOYS

A two-dimensional finite-element nonlinear transient heat conduction model was developed and used to simulate deep-penetration keyhole laser welds in aluminum alloys. The weld thermal profiles were calculated in an arbitrary reference plane as the laser beam approached and passed the plane. From the calculated thermal profiles, three-dimensional quasi-steady-state shapes of the weld pools were determined. The predicted weld bead shape and dimensions were in good agreement with the experimental results. The experimental laser welds in aluminum alloys contained large amounts of porosity. The model predicted large mushy zones for aluminum laser welds during solidification, which in turn increase the probability of porosity formation by increased bubble entrapment.

Phenomena at the advancing ice-liquid interface: solutes, particles and biological cells.

Ice formation in aqueous solutions and suspensions involves a number of significant changes and processes in the residual liquid. The resulting effects were described concerning the redistribution of dissolved salts, the behaviour of gaseous solutes and bubble formation, the rejection and entrapment of second-phase particles. This set of conditions is also experienced by biological cells subjected to freezing. The influences of ice formation in that respect and their relevance for cryopreservation were considered as well. A model of transient heat conduction and solute diffusion with a planar ice front, propagating through a system of finite length was found to be in good agreement with measured salt concentration profiles. The spacing of the subsequently developing columnar solidification pattern was of the same order of magnitude as the pertubation wavelengths predicted from the stability criterion. Non-planar solidification of binary salt solutions was described by a pure heat transfer model under the assumption of local thermodynamic equilibrium. The rejection of gaseous solutes and the resulting gas concentration profile ahead of a planar ice front has been estimated by means of a test bubble method, yielding a distribution coefficient of 0.05 for oxygen. The nucleation of gas bubbles has been observed to occur at slightly less than 20-fold supersaturation. The subsequent radial growth of the bubbles obeys a square-root time dependence as expected from a diffusion controlled model until the still expanding bubbles become engulfed by the advancing ice-liquid interface. The maximum bubble radii decrease for increasing ice front velocities. The transition between repulsion and entrapment of spherical latex particles by an advancing planar ice-front has been characterized by a critical value of the velocity of the solidification interface. The critical velocity is inversely proportional to the particle radius as suggested by models assuming an undisturbed ice front. The increase of the critical velocity for increasing thermal gradients shows good agreement with a theoretically predicted square-root type of dependence. Critical velocities have also been measured for yeast and red blood cells. The effect of freezing on biological cells has been analyzed for human lymphocytes and erythrocytes. The reduction of cell volume observed during non-planar freezing agrees reasonably well with shrinkage curves calculated from a water transport model. The probability of intracellular ice formation has been characterized by threshold cooling rates above which the amount of water remaining within the cell is sufficient for crystallization.(ABSTRACT TRUNCATED AT 400 WORDS)

Bubble Dynamics in Confined Spaces: Effect on Heating Surface

A theoretical study of the dynamics of a single vapour bubble growing between two close surfaces is presented. The results show that the existence of a solid wall situated opposite to the heating surface influences the bubble shape and tends to divert its geometry from the spherical to the ellipsoidal one. One also observes a slower growth rate in the direction perpendicular to the surface. Considering the forces responsible for the bubble detachment, it was found that the bubble departure radius and departure time increase when the width of the gap between the two surfaces is reduced. A close look at the mechanism leading to the heating surface “Departure from Nucleate Boiling” (DNB) in confined spaces indicated that the heating surfaces DNB is increased and the local “Critical Heat Flux” (CHF) is considerably reduced. The development of this phenomenon is explained and supported by previous experimental findings. Two transient heat conduction models are used to estimate the local heating surface (hot spot) temperature in the confined dry areas. The results show that, within a few seconds, the hot spot temperature excursion occurs and may lead to local surface damage.

Photopyroelectric thin-film instrumentation and impulse-response detection. Part II: Methodology

Frequency-modulation time-delay spectrometry (FM-TDS) has been implemented in photopyroelectric measurements of thermal diffusivity, on a series of well-characterized samples. The strategy of FM-TDS is sample excitation by a fast linear frequency sweep, whose autocorrelation function is mathematically equivalent to a Dirac delta function. The method permits the fast recovery of high-quality frequency and impulse-response information. Impulse responses recovered in the time-delay domain showed good agreement with a Green’s function model of transient heat conduction. The present work demonstrates that the FM-TDS measurement strategy yields photothermal information equivalent to that obtainable from a pulsed laser system, with much lower excitation power.

Analysis of the accuracy in modelling of transient heat conduction in plane slabs

The accuracy achieved by modelling unidimensional, thermal conduction using lumped representation is assessed. The transient responses of one surface of a plane, infinite, homogeneous slab when the other surface is subjected to unit step or linear ramp excitations of temperature or heat flux are analysed. The results are expressed in dimensionless form and are compared as a function of the Fourier variable. The lumping errors are assessed by the calculation of the percentage error. Graphs collecting the possible pairs m.β by which a prefixed percentage error is found are shown and discussed.

A quasi transient heat conduction model of heat transfer in fuel-coolant interaction in LMFBRs

In this paper, we have studied the effect of fuel temperature profile, that builds up in the fuel particles during the transient heat conduction from fuel to the coolant in the mixing zone of molten fuel-coolant interaction (MFCI) in LMFBRs, on the thermal to mechanical work energy conversion efficiency. The results have been compared with the transient heat conduction model of Cho, Ivins and Wright who assumed a linear fuel temperature profile over the fuel particles during the transient. It has been found that whereas the linear fuel temperature profile model of Cho et al. and the present model give almost similar results for smaller fuel particles with radius less than 10 μ, the results of these two models differ for bigger fuel particles. Hence, the present model of quasi-transient heat conduction which is an improvement over the linear temperature profile approximation of Cho et al. may be used when the fuel particles interacting with the cold sodium are coarse size.