Surface Radiation Heat Transfer Research Articles

A parallel Galerkin boundary element method for surface radiation and mixed heat transfer calculations in complex 3‐D geometries

AbstractThis paper presents a parallel Galerkin boundary element method for the solution of surface radiation exchange problems and its coupling with the finite element method for mixed mode heat transfer computations in general 3‐D geometries. The computational algorithm for surface radiation calculations is enhanced with the implementation of ideas used for 3‐D computer graphics applications and with data structure management involving creating and updating various element lists optimized for numerical performance. The algorithm for detecting the internal third party blockages of thermal rays is presented, which involves a four‐step procedure, i.e. the primary clip, secondary clip and adaptive integration with checking. Case studies of surface radiation and mixed heat transfer in both simple and complex 3‐D geometric configurations are presented. It is found that a majority of computational time is spent on the detection of foreign element blockages and parallel computing is ideally suited for surface radiation calculations. Results show that the decrease of the CPU time approaches asymptotically to an inverse rule for parallel computing of surface radiation exchanges. For large‐scale computations involving complex 3‐D geometries, an iterative procedure is a preferred approach for the coupling of the Galerkin boundary and finite elements for mixed mode heat transfer calculations. Copyright © 2004 John Wiley & Sons, Ltd.

Maintaining uniform surface temperature along pipes by insulation

An analytical solution is obtained for the insulation thickness variation over a pipe to maintain a uniform outer surface temperature. A high temperature fluid is considered to be flowing through the pipe. The amount of the insulation material is assumed to be limited. Heat transfer from the outer surface of the pipe is through convection and radiation. The solution of the insulation thickness is found to be independent from the outer surface convective and radiative heat transfer coefficients. In addition, the solution is found to be very close to linear variation which is very easy to implement in practice.

Numerical study of natural convection with surface radiation in side-vented open cavities

The paper presents a numerical study of steady combined laminar natural convection and surface radiation heat transfer in a two-dimensional side-vented open cavity for different aspect ratios, side-vent ratios, and surface emissivities using air as the fluid medium. Results have been compared with experimental results available in the literature. Surface radiation is found to alter the basic flow pattern as well as the thermal performance substantially. The numerical investigation provides evidence of the existence of thermal boundary layers along adiabatic walls of the cavity as a consequence of the interaction of natural convection and surface radiation. Based on numerical data correlations have been developed for convective as well as radiative heat transfer.

AN IMPROVED DISCRETE TRANSFER METHOD FOR 3-D SURFACE RADIATION CALCULATION

Surface radiation heat transfer may become a dominant mode of heat transfer in many engineering applications, and its accurate and efficient modeling is the key to the efficient design of the involved systems. In the study, an improved discrete transfer method (DTM) is developed to meet practical needs for surface radiation modeling. A direct application of the DTM to modeling surface radiative heat transfer usually leads to a large error, due to the strong ray effects. In order to eliminate the ray effects, a total of nine discrete directions over a control angle instead of a single discrete direction as used in the traditional DTM is selected, and the incident radiative intensity over this control angle is then replaced by a weighted-averaged intensity from these nine discrete directions. This approach provides a more accurate value on the mean radiative intensity over a control angle, while it does not increase the total number of radiative intensity to be solved at a surface element. Compared to the modified DTM we developed previously, the present approach is much simpler in terms of numerical treatment. In order to examine the accuracy of the present method, two 3-D benchmark problems are selected and investigated. With a reasonably fine angular discretization, the present solutions are found to match the exact solutions and they are much more accurate than the results from the traditional DTM.

Combined convective and radiative heat transfer in side-vented open cavities

Abstract Steady, combined laminar natural convection and surface radiation heat transfer from side-vented open cavities with top opening have been studied for different aspect ratios, surface emissivities and side-vents, using air as the medium. A single, isothermal, heated vertical wall formed the heat source for the cavity, and all other walls were insulated. An optical measurement technique using a shearing interferometer with two Wollaston prisms was used to obtain local values of the convective heat transfer coefficient along the heated wall of the cavity. The radiative heat transfer rates were estimated by a numerical procedure, by means of enclosure analysis using the radiosity-irradiation formulation. Parametric studies, for a range of parameters of practical interest, were carried out to understand the effect of interaction of surface radiation on natural convection. Results of a large number of systematic, controlled experiments that were carried out are presented, highlighting the effect of interaction.

PREDICTION OF SURFACE RADIATIVE HEAT TRANSFER USING THE MODIFIED DISCRETE TRANSFER METHOD

An ideal surface radiation model applied in many manufacturing and materials processing systems must be able to take into account specular, spectral, and shadowing effects with complex geometries, and must be computationally efficient to permit its inclusion in the fluid flow and heat transfer models. In this study, a novel surface radiative heat transfer method is developed to meet all these practical needs. The present model is based on the discrete transfer method (DTM). A direct application of the DTM to modeling surface radiative heat transfer may result in a large error due to strong ray effects. In order to eliminate these ray effects, the DTM is modified by considering radiation contribution from all surface cells intercepted by a control angle. Calculation of these surface cell areas represents one of the most important tasks in the modified DTM (MDTM), and it is described in detail in this study. To investigate the accuracy and efficiency of the MDTM, three benchmark problems covering different geometric and boundary conditions are considered, and the present solution is compared with the solutions from the exact approach, the DTM, and discrete ordinates method (DOM). For each problem, the accuracy of the MDTM, DTM, and DOM appears to be affected by the angular discretization. For a reasonable fine angular discretization, the solutions from the MDTM and DOM match the exact solution very well, while the solution from the DTM usually shows strong ray effects. The CPU times spent on the MDTM and DTM are very similar, but they are usually orders of magnitude less than that for the DOM. The present study indicates that the MDTM is not only accurate but also very efficient for modeling complicated surface radiation problems. Such a model will greatly benefit the simulation of many manufacturing and materials processing systems.

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.

AN OPTIMUM SPACING PROBLEM FOR FIVE CHIPS ON A HORIZONTAL SUBSTRATE IN AN ENCLOSURE – NATURAL CONVECTION

International Journal of Computational Engineering ScienceVol. 01, No. 01, pp. 167-186 (2000) No AccessAN OPTIMUM SPACING PROBLEM FOR FIVE CHIPS ON A HORIZONTAL SUBSTRATE IN AN ENCLOSURE – NATURAL CONVECTIONYANG LIU, CHUN WAH LEUNG, TAL LEUNG CHANG, and PHAN-THUEN NHANYANG LIUDepartment of Mechanical Engineering, The Hong Kong Polytechnic University, Hum Hom, Kowloon, Hong Kong, P. R. China Search for more papers by this author , CHUN WAH LEUNGDepartment of Mechanical Engineering, The Hong Kong Polytechnic University, Hum Hom, Kowloon, Hong Kong, P. R. China Search for more papers by this author , TAL LEUNG CHANGDepartment of Mechanical Engineering, The Hong Kong Polytechnic University, Hum Hom, Kowloon, Hong Kong, P. R. China Search for more papers by this author , and PHAN-THUEN NHANInstitute of High Performance Computing, National University of Singapore, Singapore 119260, SingaporePermanent address: Department of Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia. Search for more papers by this author https://doi.org/10.1142/S1465876300000094Cited by:3 Previous AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractThe optimum spacing problem for five heated chips rested on a conductive substrate in a two dimensional enclosure filled with air is solved by an operator-splitting pseudo-time-stepping finite element method, which automatically satisfies the continuity of the interfacial temperature and heat flux. It is found that the conventional equi-spaced arrangement is not an optimum option. An optimum thermal performance can be obtained when the center-to-center distances between the chips follow a geometric series. The maximum relative temperature drop in the optimum configuration can be as much as 17% of the equi-spaced arrangement. FiguresReferencesRelatedDetailsCited By 3Optimal Distribution of Discrete Heat Sources Under Natural Convection Using ANN–GA Based TechniqueTapano Kumar Hotta and Shakkottai P. Venkateshan25 August 2014 | Heat Transfer Engineering, Vol. 36, No. 2Optimal Distribution of Discrete Heat Sources Under Mixed Convection—A Heuristic ApproachTapano Kumar Hotta, C. Balaji and S. P. Venkateshan29 July 2014 | Journal of Heat Transfer, Vol. 136, No. 10Effect of surface radiation heat transfer on the optimal distribution of discrete heat sources under natural convectionTapano Kumar Hotta, Pullarao Muvvala and S. P. Venkateshan18 October 2012 | Heat and Mass Transfer, Vol. 49, No. 2 Recommended Vol. 01, No. 01 Metrics History Received 2 August 1999 Accepted 4 November 1999 PDF download

An analysis of a heat transfer model for situations involving gas and surface radiative heat transfer

An algorithm for total heat transfer in a furnace chamber was analysed for various operating conditions. The emphasis is on radiative heat transfer by carbon dioxide and water vapour, and methods of calculating their overlap. The algorithm was used for real-time monitoring of the reheating of slabs in a pusher furnace. The measured and calculated heating-up curves for a test slab are shown in diagrams. Copyright © 1999 John Wiley & Sons, Ltd.

An analysis of a heat transfer model for situations involving gas and surface radiative heat transfer

An algorithm for total heat transfer in a furnace chamber was analysed for various operating conditions. The emphasis is on radiative heat transfer by carbon dioxide and water vapour, and methods of calculating their overlap. The algorithm was used for real-time monitoring of the reheating of slabs in a pusher furnace. The measured and calculated heating-up curves for a test slab are shown in diagrams. Copyright © 1999 John Wiley & Sons, Ltd.

Two dimensional numerical simulation of transient natural convection in freezer

A two dimensional model of the transient natural convection in a freezer is studied numerically by finite volume approach. The temperatures of the freezer outside surfaces and the evaporator vary in specified manners, which were taken from an experimental work. The fluid in the freezer is of the Bousinnesq type and the flow is assumed laminar. The transient heat conduction in the insulating layers and the temperature and velocity fields of the fluid are solved conjugately. The radiation heat transfer between the freezer inner surfaces is taken into account by using the additional source term method. The distributions of the local Nusselt number along the upper and lower surfaces of the evaporator and their average values in the period of periodically unsteady operation are calculated. Comparisons are made between the results with and without consideration of inner surface radiative heat transfer. It is found that the radiative heat transfer between the inner surfaces has a profound effect on the evaporator heat transfer characteristics.

Interaction of surface radiation with convection in crystal growth by physical vapor transport

Growth of single crystals from vapor in closed ampoules is governed by an intricate interplay between mass, momentum and heat transfer processes. The objective of this study is to examine and isolate the effects of surface radiation heat transfer on the vapor transport process using a mathematical model. The model consists of a set of coupled nonlinear partial differential equations for conservation of mass, momentum, energy and species, and the integrodifferential equations which represent radiative exchange. It depends on five important physical parameters. These are Grashof number, Prandtl number, Schmidt number, aspect ratio and the radiation-conduction number. The effects of these dimensionless groupings are systematically investigated. From the cases examined, it is concluded that surface radiation can change the flow structure appreciably. This is especially true in microgravity environment where radiation competes primarily with conduction in modifying the thermal profiles. The numerical results also show that in the presence of radiation, the top heating configuration (source on top) is no longer stable and that near the growing crystal, radiation-induced vortices can introduce significant nonuniformities in the growth flux.