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Proceedings Papers

*Proc. ASME*. HT2016, Volume 2: Heat Transfer in Multiphase Systems; Gas Turbine Heat Transfer; Manufacturing and Materials Processing; Heat Transfer in Electronic Equipment; Heat and Mass Transfer in Biotechnology; Heat Transfer Under Extreme Conditions; Computational Heat Transfer; Heat Transfer Visualization Gallery; General Papers on Heat Transfer; Multiphase Flow and Heat Transfer; Transport Phenomena in Manufacturing and Materials Processing, V002T08A008, July 10–14, 2016

Paper No: HT2016-7085

Abstract

This work investigates the influence of thermal conductivity ratio on energy and mass transport across a porous square cavity. Modeling of heat transfer from side to side of the enclosure assumed the hypothesis of thermal non-equilibrium between the solid matrix and the fluid phase. Transport equations were discretized using the control-volume method and the system of algebraic equations obtained was relaxed via the SIMPLE algorithm. Results showed that Sh w , mass flux of chemical species and heat flux in the solid phase are strongly dependent of k s /k f , significantly increasing their values as such ratio increases.

Proceedings Papers

*Proc. ASME*. HT2016, Volume 2: Heat Transfer in Multiphase Systems; Gas Turbine Heat Transfer; Manufacturing and Materials Processing; Heat Transfer in Electronic Equipment; Heat and Mass Transfer in Biotechnology; Heat Transfer Under Extreme Conditions; Computational Heat Transfer; Heat Transfer Visualization Gallery; General Papers on Heat Transfer; Multiphase Flow and Heat Transfer; Transport Phenomena in Manufacturing and Materials Processing, V002T15A013, July 10–14, 2016

Paper No: HT2016-7103

Abstract

This paper provides a solution for two-dimensional heating over a rectangular region on a homogeneous plate. It has application to verification of numerical conduction codes as well as direct application for heating and cooling of electronic equipment. Additionally, it can be applied as a direct solution for the inverse heat conduction problem, most notably used in thermal protection systems for re-entry vehicles. The solutions used in this work are generated using Green’s functions. Two approaches are used which provide solutions for either semi-infinite plates or finite plates with isothermal conditions which are located a long distance from the heating. The methods are both efficient numerically and have extreme accuracy, which can be used to provide additional solution verification. The solutions have components that are shown to have physical significance. The extremely precise nature of analytical solutions allows them to be used as prime standards for their respective transient conduction cases. This extreme precision also allows an accurate calculation of heat flux by finite differences between two points of very close proximity which would not be possible with numerical solutions. This is particularly useful near heated surfaces and near corners. Similarly, sensitivity coefficients for parameter estimation problems can be calculated with extreme precision using this same technique. Another contribution of these solutions is the insight that they can bring. Important dimensionless groups are identified and their influence can be more readily seen than with numerical results. For linear problems, basic heating elements on plates, for example, can be solved to aid in understanding more complex cases. Furthermore these basic solutions can be superimposed both in time and space to obtain solutions for numerous other problems. This paper provides an analytical two-dimensional, transient solution for heating over a rectangular region on a homogeneous square plate. Several methods are available for the solution of such problems. One of the most common is the separation of variables (SOV) method. In the standard implementation of the SOV method, convergence can be slow and accuracy lacking. Another method of generating a solution to this problem makes use of time-partitioning which can produce accurate results. However, numerical integration may be required in these cases, which, in some ways, negates the advantages offered by the analytical solutions. The method given herein requires no numerical integration; it also exhibits exponential series convergence and can provide excellent accuracy. The procedure involves the derivation of previously-unknown simpler forms for the summations, in some cases by virtue of the use of algebraic components. Also, a mathematical identity given in this paper can be used for a variety of related problems.

Proceedings Papers

*Proc. ASME*. HT2013, Volume 3: Gas Turbine Heat Transfer; Transport Phenomena in Materials Processing and Manufacturing; Heat Transfer in Electronic Equipment; Symposium in Honor of Professor Richard Goldstein; Symposium in Honor of Prof. Spalding; Symposium in Honor of Prof. Arthur E. Bergles, V003T23A002, July 14–19, 2013

Paper No: HT2013-17763

Abstract

Bubble column dehumidifiers are a compact, inexpensive alternative to conventional fin-tube dehumidifiers for humidification-dehumidification (HDH) desalination, a technology that has promising applications in small-scale desalination and industrial water remediation. In this paper, algebraic equations for relevant mean heat and mass transfer driving forces are developed for improved modeling of bubble column dehumidifiers. Because mixing in the column ensures a uniform liquid temperature, the bubble column can be modeled as two single stream heat exchangers in contact with the column liquid: the seawater side, for which a log-mean temperature difference is appropriate, and the gas side, which has a varying heat capacity and mass exchange. Under typical conditions, a log-mean mass fraction difference is shown to drive latent heat transfer, and an expression for the mean temperature difference of the moist gas stream is presented. These expressions will facilitate modeling of bubble column heat and mass exchangers.

Proceedings Papers

*Proc. ASME*. HT2013, Volume 3: Gas Turbine Heat Transfer; Transport Phenomena in Materials Processing and Manufacturing; Heat Transfer in Electronic Equipment; Symposium in Honor of Professor Richard Goldstein; Symposium in Honor of Prof. Spalding; Symposium in Honor of Prof. Arthur E. Bergles, V003T21A006, July 14–19, 2013

Paper No: HT2013-17733

Abstract

The paper reports on work in progress aimed at improving the prediction of heat transfer in turbulent separated flows. The cases considered here are the flow over a heated backward-facing step, and the periodic flow in a heated channel with square ribs. The predictions were obtained using two models not hitherto employed in these flows: a Reynolds-stress transport closure in which the model for the fluctuating pressure-strain correlations that satisfies the requirement of model objectivity while not requiring wall-damping functions, and a model for the turbulent heat fluxes that is explicit, algebraic and correctly allows for these fluxes to depend on the gradients of mean temperature and velocity. Both models have previously given good predictions in attached shear flows and the objective of this work was to determine whether this improvement carries over to separated flows. It was found that distinct improvements in the prediction of skin friction and Nusselt number can only be obtained by extending the models so as to allow the computations to extend through the viscous sub-layer directly to the wall.

Proceedings Papers

*Proc. ASME*. HT2013, Volume 4: Heat and Mass Transfer Under Extreme Conditions; Environmental Heat Transfer; Computational Heat Transfer; Visualization of Heat Transfer; Heat Transfer Education and Future Directions in Heat Transfer; Nuclear Energy, V004T14A019, July 14–19, 2013

Paper No: HT2013-17505

Abstract

Thermal efficiency of energy conversion systems such as gas turbines can be increased greatly with an increase in the turbine inlet temperature of combustion gases. However, this necessitates the use of efficient cooling techniques in addition to thermal barrier coatings (TBCs) to help significantly improve the life expectancy of gas turbine blades. The effect of TBC use is the formation of oxides, particularly alumina, at the interface of the ceramic top coat and bond coat material during in-service application. This effect is well known to cause failure of TBCs exposed to extreme high temperature environments. The objective of this paper is to present a micro-scale finite difference thermal model for the TBC-Substrate system that considers growth of the TGO layer and predicts in-situ thermal gradients. The governing equation is the transient heat diffusion equation discretized over a 1-D domain using mean value finite volume method with grid adaptation for zones involving depletion of bond coat (BC) material and TGO growth; hence, necessitating a moving interfacial boundary problem. The resulting algebraic equations are simultaneously solved in MATLAB to produce temperature distributions and BC/TGO interfacial locations. The model has utility in studying the evolution of residual stresses and hence prediction of TBC durability and failure.

Proceedings Papers

#### A Simple Model for Prediction of Preheating and Pyrolysis Time of a Thermally Thin Charring Particle

*Proc. ASME*. HT2012, Volume 2: Heat Transfer Enhancement for Practical Applications; Fire and Combustion; Multi-Phase Systems; Heat Transfer in Electronic Equipment; Low Temperature Heat Transfer; Computational Heat Transfer, 183-190, July 8–12, 2012

Paper No: HT2012-58233

Abstract

The aim of this paper is to present a simple model, based on a time and space integral method, for prediction of preheating and conversion time of a charring solid particle exposed to a non-oxidative hot environment. The main assumptions are 1) thermo-physical properties remain constant throughout the process; 2) temperature profile within the particle is assumed to obey a quadratic function with respect to the space coordinate; 3) pyrolysis initiates when the surface temperature reaches a characteristic pyrolysis temperature; 4) decomposition of virgin material occurs at an infinitesimal thin layer dividing the particle into char and virgin material regions; 5) the volume of the particle remains unaltered; 6) volatiles escape through the pores immediately after formation. Employing assumption (2) allows one to convert the energy conservation equation of the particle, which is basically described in the form of a partial differential equation (PDE), into an ordinary differential equation (ODE) by performing space integration. Next, by applying approximate time integration the ODE is transformed into an algebraic equation. Applying this approach to the preheating and pyrolysis stages of a thermally thin charring solid particle leads to a set of algebraic equations which provides reactor designers with a convenient means for computation of the heating up time, mass loss history and total conversion of particle. The accuracy of the simple model is assessed by comparing its prediction with that of a one-dimensional detailed pyrolysis model. Overall, good agreement is achieved indicating that this new model can be used for engineering and design purposes.

Proceedings Papers

*Proc. ASME*. HT2009, Volume 2: Theory and Fundamental Research; Aerospace Heat Transfer; Gas Turbine Heat Transfer; Computational Heat Transfer, 633-644, July 19–23, 2009

Paper No: HT2009-88098

Abstract

In recent years, there has been a great deal of interest in developing meshless methods for computational fluid dynamics (CFD) applications. In this paper, a meshless finite difference method is developed for solving conjugate heat transfer problems in complex geometries. Traditional finite difference methods (FDMs) have been restricted to an orthogonal or a body-fitted distribution of points. However, the Taylor series upon which the FDM is based is valid at any location in the neighborhood of the point about which the expansion is carried out. Exploiting this fact, and starting with an unstructured distribution of mesh points, derivatives are evaluated using a weighted least squares procedure. The system of equations that results from this discretization can be represented by a sparse matrix. This system is solved with an algebraic multigrid (AMG) solver. The implementation of Neumann, Dirichlet and mixed boundary conditions within this framework is described, as well as the handling of conjugate heat transfer. The method is verified through application to classical heat conduction problems with known analytical solutions. It is then applied to the solution of conjugate heat transfer problems in complex geometries, and the solutions so obtained are compared with more conventional unstructured finite volume methods. Metrics for accuracy are provided and future extensions are discussed.

Proceedings Papers

*Proc. ASME*. HT2009, Volume 1: Heat Transfer in Energy Systems; Thermophysical Properties; Heat Transfer Equipment; Heat Transfer in Electronic Equipment, 1-11, July 19–23, 2009

Paper No: HT2009-88014

Abstract

The method of spherical harmonics (or P N ) is a popular method for approximate solution of the radiative transfer equation (RTE) in participating media. A rigorous conservative finite-volume (FV) procedure is presented for discretization of the P 3 equations of radiative transfer in two-dimensional geometry—a set of four coupled second-order partial differential equations. The FV procedure, presented here, is applicable to any arbitrary unstructured mesh topology. The resulting coupled set of discrete algebraic equations are solved implicitly using a coupled solver that involves decomposition of the computational domain into groups of geometrically contiguous cells using the Binary Spatial Partitioning algorithm, followed by fully implicit coupled solution within each cell group using a pre-conditioned Generalized Minimum Residual (GMRES) solver. The RTE solver is first verified by comparing predicted results with published Monte Carlo (MC) results for a benchmark problem. For completeness, results using the P 1 approximation are also presented. As expected, results agree well with MC results for large/intermediate optical thicknesses, and the discrepancy between MC and P 3 results increase as the optical thickness is decreased. The P 3 approximation is found to be more accurate than the P 1 approximation for optically thick cases. Finally, the new RTE solver is coupled to a reacting flow code and demonstrated for a laminar flame calculation using an unstructured mesh. It is found that the solution of the 4 P 3 equations requires 14.5% additional CPU time, while the solution of the single P 1 equation requires 9.3% additional CPU time over the 10 equations that are solved for the reacting flow calculations.

Proceedings Papers

*Proc. ASME*. HT2007, ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference, Volume 2, 719-726, July 8–12, 2007

Paper No: HT2007-32139

Abstract

Compact Thermal Models (CTMs) are multi-nodal thermal resistor networks which predict the internal thermal response of an electronic package, in various environments, to within an accuracy of 2%. The junction temperature of the package is typically obtained by solving a set of linear algebraic equations wherein the heat transfer to the ambience is modeled by a convection coefficient obtained from hand-book data, assuming identical ambient conditions imposed at all nodal surfaces. In reality, this approach may give misleading results as the ambience at each of the nodal surfaces is different and depends on the cooling fluid flow behavior at that surface. In this work, a methodology is presented where the network equations of the CTMs are coupled with the governing fluid equations solved by computational fluid dynamics (CFD). The CTM+CFD approach predicts a significantly (28%) higher junction temperature as compared to the conventional CTM network solver method, even when the convection coefficient used in the latter is obtained more accurately from CFD, rather than from hand-book correlations. It is likely that the new approach offers a more effective prediction of the package thermal performance.

Proceedings Papers

*Proc. ASME*. HT2008, Heat Transfer: Volume 3, 465-471, August 10–14, 2008

Paper No: HT2008-56265

Abstract

A new finite difference method, which removes the need for staggered grids in fluid dynamic computation, is presented. Pressure checker boarding is prevented through a dual-velocity scheme that incorporates the influence of pressure on velocity gradients. A supplementary velocity resulting from the discrete divergence of pressure gradient, together with the main velocity driven by the discretized pressure first-order gradient, is introduced for the discretization of continuity equation. The method in which linear algebraic equations are solved using incomplete LU factorization, removes the pressure-correction equation, and was applied to rectangle duct flow and natural convection in a cubic cavity. These numerical solutions are in excellent agreement with the analytical solutions and those of the algorithm on staggered grids. The new method is shown to be superior in convergence compared to the original one on staggered grids.

Proceedings Papers

*Proc. ASME*. HT2008, Heat Transfer: Volume 3, 421-428, August 10–14, 2008

Paper No: HT2008-56076

Abstract

This paper describes the theoretical bases of the Radiative Exchange Method, a new numerical method for simulating radiation heat transfer. By considering radiative interaction between all points of the geometry and solving the radiation balance equation in a mesh structure coarser than the structure used in computational fluid flow calculation, this method is able to simulate radiative heat transfer in arbitrary 3D space with absorbing, emitting and scattering media surrounded by emitting, absorbing and reflecting surfaces. A new concept is introduced, that of the exchange factors between the different elements that are necessary for completing the radiative balance equation set. Using this method leads to a set of algebraic equations for the radiative outgoing power from each coarse cell being produced and the result of this set of equations was then used to calculate the volumetric radiative source term in the fine cell structure. The formulation of the exchange factor for a three-dimensional state and also a mesh size analysis that was conducted to optimize the accuracy and runtime are presented. The results of this model to simulate typical 3D furnace shape geometry, is verified by comparison with those of other numerical methods.

Proceedings Papers

*Proc. ASME*. HT-FED2004, Volume 3, 843-850, July 11–15, 2004

Paper No: HT-FED2004-56844

Abstract

Industrial processes involving multi-phase flows such as flotation require an understanding of the relationships between bubbles, solid particles and the flow. For decades engineers and researchers based their calculations on algebraic formulas that model these interactions. These formulas were derived either from simple models, or from experimental data. Modern experimental tools are employed in this effort to measure with great accuracy the basic features of the motion of all three phases in turbulent flow. We employed a unique Digital Particle Image Velocimeter (DPIV) that can record with great accuracy and kHz temporal resolution, velocity vectors of all three phases, namely the fluid, the solid particles and the air bubbles. The interaction of these three phases was studied in grid turbulence. Flow was directed through a rectangular grid of circular rods and the resulting homogeneous isotropic turbulence was documented. Particles and bubbles were released and the motion of the three phases was monitored. The particle RMS was in good agreement with a model proposed by Shubert, having an average RMS velocity of about 13% of the free stream velocity in the fully developed region. A theoretical model, derived first by Levins and Glastonbury was found to underpredict the particle RMS. The bubble RMS was about 26% of the free stream in the homogeneous isotropic region, 100% greater than the particle RMS and not consistent with the model predictions.

Proceedings Papers

*Proc. ASME*. HT-FED2004, Volume 2, Parts A and B, 819-825, July 11–15, 2004

Paper No: HT-FED2004-56392

Abstract

A three-dimensional finite element-boundary integral formulation is presented for the analysis of the electric and magnetic field distribution, power absorption and the temperature distribution in electrically conduction and dielectric materials. For large-scale electromagnetic-thermal materials processing system analyses, the hybrid finite/boundary method represents an optimal approach. To further improve the efficiency, the present formulation also incorporates various efficient solvers designed specifically for the solution of large sparse systems of linear algebraic equations. The resulting algorithm with a compressed storage scheme is considered effective and efficient to meet the demand of 3-D large scale electromagnetic/thermal simulations required for processing industries. Examples of 3-D electromagnetic and thermal analysis are presented for induction and microwave heating systems. Numerical performance of the computer code is assessed for these systems. Computed results are presented for the electric field distribution, power absorption and temperature distribution in a food load thermally treated in an industrial pilot scale microwave oven designed for food sterilization.

Proceedings Papers

*Proc. ASME*. HT-FED2004, Volume 2, Parts A and B, 939-950, July 11–15, 2004

Paper No: HT-FED2004-56475

Abstract

We present a numerical software interface that can be integrated easily in a CFD or Heat transfer code and allows the systematic investigation of the efficiency of a broad class of solvers to optimize the code. We consider three classes of solvers that are respectively direct solver with LU decomposition, Krylov method with incomplete LU preconditionner and algebraic multigrid that have been implemented in Lapack, Sparskit, and Hypre. We systematically investigate the performance of these solvers with four test cases in ground flow, multiphase flow, bioheat transfer, and pressure solve in an Incompressible Navier Stokes code for flow in pipe with overset composite meshes. We show for each test case that the choice of the best solver may depend critically on the grid size, the aspect ratio of the grid, and further the physical parameters of the problem and the architecture of the processor. We have constructed an interface that allows to easily include in an existing CFD or heat transfer code any of the elliptic solvers available in Lapack, Sparskit and Hypre. This interface has the simplicity of Matlab command but keeps the efficiency of the original Fortran or C library. This interface can help us to investigate what would be the best solver as a preprocessing procedure. This work is a first step to construct intelligent software that will optimize an existing code automatically using the best algorithm for the application.

Proceedings Papers

*Proc. ASME*. HT-FED2004, Volume 2, Parts A and B, 807-814, July 11–15, 2004

Paper No: HT-FED2004-56387

Abstract

The thermal energy balance for emplacement drift ventilation is solved analytically by using “well-mixed” volume elements that discretize the domain down the length of a drift. The solution technique is based on the use of a lumped parameter quasi-steady-state approximation, and the principle of superposition. The lumped parameters are convective and linearized radiation heat transfer coefficients. The quasi-stead-state approximation allows the energy balance equations to be written without time derivatives and solved algebraically for a single time step. The progress of the heat transfer analysis through time is like that of integrating a function using Euler’s method. The principle of superposition is used to calculate the temperature response of the drift wall due to an arbitrary heat flux and a given set of thermophysical rock properties. The results of this calculation are used as a “multiplier” on the drift wall heat flux in the algebraic solution of the four energy balances, and eliminates the need to solve the conduction heat transfer in the rock mass at every time step. The results of the analysis are compared to a similar numerical model and include time and location dependent waste package, in-drift air, and drift wall temperatures, and ventilation efficiencies.

Proceedings Papers

*Proc. ASME*. HT-FED2004, Volume 2, Parts A and B, 1237-1245, July 11–15, 2004

Paper No: HT-FED2004-56777

Abstract

A finite element method is presented for the solution of a free boundary problem which arises during planar melting of a semi-infinite medium initially at a temperature which is slightly below the melting temperature of the solid. The surface temperature is assumed to vary with time. Two different situations are considered (I) when thermal diffusivity is independent of temperature and (II) when thermal diffusivity varies linearly with temperature. The differential equation governing the process is converted to initial value problem of vector matrix form. The time function is approximated by Chebyshev series and the operational matrix of integration is applied, a linear differential equation can be represented by a set of linear algebraic equations and a nonlinear differential equation can be represented by a set of nonlinear algebraic equations. The solution of the problem is then found in terms of Chebyshev polynomial of second kind. The solution of this initial value problem is utilized iteratively in the interface heat flux equation to determine interface location as well as the temperature in two regions. The method appears to be accurate in cases for which closed form solutions are available, it agrees well with them. The effect of several parameters on the melting are analysed and discussed.

Proceedings Papers

*Proc. ASME*. HT2003, Heat Transfer: Volume 1, 711-716, July 21–23, 2003

Paper No: HT2003-47360

Abstract

In this paper, it is shown that the Arithmetic Mean Temperature Difference, which is the difference between the average temperatures of hot and cold fluids, can be used instead of the Log Mean Temperature Difference (LMTD) in heat exchanger analysis. For a given value of AMTD, there exists an optimum heat transfer rate, Q opt , given by the product of UA and AMTD such that the rate of heat transfer in the heat exchanger is always less than this optimum value. The optimum heat transfer rate takes place in a balanced counter flow heat exchanger and by using this optimum rate of heat transfer, the concept of heat exchanger efficiency is introduced as the ratio of the actual to optimum heat transfer rate. A general algebraic expression as well as a chart is presented for the determination of the efficiency and therefore the rate of heat transfer for parallel flow, counter flow, single stream, as well as shell and tube heat exchangers with any number of shells and even number of tube passes per shell. In addition to being more intuitive, the use of AMTD and the heat exchanger efficiency allow the direct comparison of the different types of heat exchangers.

Proceedings Papers

*Proc. ASME*. HT2003, Heat Transfer: Volume 2, 87-93, July 21–23, 2003

Paper No: HT2003-47311

Abstract

The smoldering of cigarettes without drawing is described by a simple analytical model. A burning cigarette is assumed to be divided in 4 zones: unburned tobacco, dry tobacco, char and ash, separated by infinitesimally thin fronts of drying, pyrolysis and char oxidation. Circumferential heat losses and the convective-diffusive processes in the boundary layer are considered. A set of non-linear algebraic equations is solved to determine smoldering rates, drying lengths and pyrolysis lengths and to obtain the profiles of temperature. The influence coefficients of several parameters on smolder characteristics are calculated. Theoretical burn rates have shown a good agreement to experiments.