T. L. Bergman*, R. Viskanta**
*Department of Mechanical Engineering
The University of Texas at Austin, Austin, USA
**School of Mechanical Engineering
Purdue University, West Lafayette, USA

This review discusses radiation heat transfer which occurs in conjunction with a variety of manufacturing and materials processing applications. Practical needs in manufacturing and materials processing thermal analysis are noted, and the role of radiation heat transfer in meeting these requirements is discussed. Specifically, different types of radiative heating strategies are categorized, radiation sources commonly used are described, and issues which are somewhat unique to radiation heat transfer in manufacturing and materials processing operations, such as matching the spectral characteristics of the source and load, are identified. The need for development of robust inverse analysis tools for process and equipment design, as well as thermal process control is noted throughout the review.

Surface radiation heat transfer, although fairly well understood in principle, is used in many manufacturing operations (such as in electronics manufacturing) and needs for improved understanding and development of new analysis techniques are discussed. Specific topics include i)the practical need for improved surface exchange analysis techniques in complex geometries and/or in systems involving moving materials, ii) coupled macro- and microscale radiation heat transfer for process analysis, thermal control and inspection, and iii) forward analysis and identification of dimensionless parameters describing highly coupled and multiple mode heat transfer operations.

Volumetric radiative transfer in semitransparent materials at high temperature, important in a number of specific operations, such as fabrication of composite epoxy-fiber structures, crystal growth and glass manufacturing, is described. Here, the examples are selected to illustrate i) the importance of matching source and load spectral characteristics, ii) combined volumetric radiative and surface convective heating utilizing flames and other high temperature sources, and iii) the relevance and impact of dependent scattering phenomena.

Finally, needs and challenges in radiation thermometry in practical systems involving, for example, i) moving materials, ii) materials of high purity, or iii) radiatively participating process and/or plant gases are discussed, and recent advances in radiation thermometry theory and applications are reviewed.


M. Kassemi
Processing Science &Technology Branch
NASA Lewis Research Center
Cleveland, Ohio
M.H.N. Naraghi
Mechanical Engineering Department
Manhattan College

This paper studies the interaction of radiation heat transfer with conduction and convection during solidification of semitransparent oxide crystals. A comprehensive numerical model is presented for solidification of two important oxide crystals, BSO and YAG, by the vertical Bridgman technique. Bismuth Silicon Oxide (BSO) is an optically active semi-insulating material that is photoconductive and has widespread applications in optical information processing and computing components, such as spatial light modulators and volume holographic optical elements and filters. Yttrium Aluminum Oxide Garnet (YAG) is another important optically active oxide crystal which is used in many laser devices. These two materials were chosen because they have well-defined experimental counterparts and their thermophysical and radiative properties are relatively wellknown.

A schematic of the Bridgman crystal growth configuration is shown in Fig. 1. In solidification of semiconductors, usually both the crystal and the melt are opaque to thermal radiation. Furthermore, both phases typically have relatively high thermal conductivities. Therefore, conduction is the dominant mode of heat transfer in both the solid and the melt. Oxide crystals, on the other hand, are usually semi-transparent to thermal radiation in the solid phase and almost opaque in the melt. They also have relatively low thermal conductivities in both phases. Therefore, heat transfer during the solidification of oxide crystals is governed by an intricate balance between convection and conduction in the melt and conduction and radiation in the solid. In a sense, the solid acts as a light pipe through which the interface loses a considerable amount of heat (by emission) to the cold sections of the crucible wall or directly to the furnace (if the crucible is also transparent).

A radiation heat transfer model is developed based on exchange factors for multi-dimensional complicated geometries encountered in crystal growth. The radiation model takes into account the wavelength-dependant semi-transparency of oxide crystals such as BSO and YAG which are transparent to radiation below 6 microns and opaque to radiation in the rest of the spectrum. It is shown that the radiation model can be easily incorporated into existing finite element codes for fluid flow and heat transfer such as FIDAP. During numerical simulations the algorithm tracks the position and shape of the interface as the solidification process proceeds and updates the radiation exchange factors based on the changing geometry.

The model was applied to the processing of both YAG and BSO under realistic experimental conditions. From the numerical simulations the following conclusions can be drawn:

  1. Under the experimental conditions considered in this paper, radiation is the dominant heat transfer mode at the interface for solidification of BSO and YAG.
  2. For both BSO and YAG, the interface attains a highly stretched parabolic shape largely because of the nonuniform radiative loss from the interface. In both cases, the interface is convex into the melt and there are two vortices rotating near the interface with the flow rising from the region near the wall as shown in Fig. 2a.
  3. If radiation is neglected or the crystal is treated as opaque, the interface is only very mildly curved due to the mismatch among the thermal conductivities as shown in Fig 2b. The interface is usually convex into the phase with the lower conductivity. In the absence of radiation effects, the flow structure indicates two large vortices in the upper portion of the melt and two smaller vortices near the interface. The direction of the rotation of the smaller vortices depends on the shape of the interface.
  4. For YAG, because of its higher conductivity, conduction and radiation are the dominant heat transfer mechanisms. For BSO, convection plays a more important role and the recirculating flow can compensate for a significant amount of the radiant heat loss from the center of the interface rendering a much flatter interface in comparison to YAG.
Fig. 1 Fig. 2
Figure 1: Cross Sectional View of the Crucible in a Vertical Bridgman Furnace.Figure 2: Solidification of YAG for Gr=2053: a) Radiation Effects (Semitransparent Crystal), b) No-Radiation (Opaque Crystal).


Dept. of Mechanical Eng., Aeronautical Eng., and Mechanics
Rensselaer Polytechnic Institute
Troy, NY, USA

A numerical model of combined radiative and convective heat transfer in a fiber draw furnace was formulated and solved. The model was used to predict glass temperatures and identify important heat transfer modes. The energy equation, which included conductive, convective, and radiative terms, was discretized using a control-volume-based finite element technique. Thermal radiation within the glass was approximated by the P1 method using a two-band spectral absorption coefficient. Surface-to-surface radiation from the muffle wall to the outer surface of the class was computed by a full enclosure analysis. A cosinusoidal glass profile was assumed and a continuity-satisfying, velocity field was specified.

The results of the calculation showed that radiation was an important mode for air, arson and carbon dioxide purge gases, but that conduction was dominant for the case of a helium purge gas. The glass preform attains its asymtotic temperature higher in the furnace with helium than with any of the other gases studied. Temperatures are relatively insensitive to final fiber velocity and to the spacing, between the glass and the furnace wall.

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