A Mathematical Solution for Gas-to-Surface Radiative Exchange Area for a Rectangular Parallelepiped Enclosure Containing a Gray Medium

Abstract

The transfer of heat in a gas filled enclosure can be calculated by the zone method put forward by Hottel and Cohen [1, 2]. For a shape which can be divided into cylindrical or cubic zones, tabulated and graphical data on exchange areas are available, however, insufficient data exist for subdivision into rectangular zones. The present contribution provides a mathematical solution for the gas-to-surface exchange area between a rectangular parallelepiped gas volume and an adjacent face. The rules for manipulating and scaling of exchange areas are reviewed, and their application to the zoning of a rectangular furnace chamber into concentric rectangular volume elements is demonstrated.

The correlation based zonal method and its application to the back pass channel of oxy/air-fired CFB boiler

“…Hottel and Cohen [2] presented some charts for the calculation of DEAs where the optical thickness of the zones (bD) were less than 1.4, which limits the usage of these charts especially in non-gray modeling with the WSGG model, where b can even exceed 100 m À1 , and therefore, the size of the zones for implementing these charts is limited to very small zones, which consequently cause huge computational costs. Moreover, some minor inaccuracies have been reported in these charts [20]. The DEA between two surface zones (SS) is defined as the fraction of radiative energy emitted or reflected in the source surface zone that directly reaches the destination surface zone without being reflected by the surface zones or scattered by other volume zones in the system.…”

Effect of design parameters on performance of a top fired natural gas reformer

“…Then Hottel and Sarofim [12] tabulated direct exchange areas for cylindrical enclosures. Later on Becker [20], Tucker [21], Sika [22] and Modest [3] presented other techniques for calculating direct exchange areas.…”

Efficient numerical computation of direct exchange areas in thermal radiation analysis

“…For simple rectangular geometries consisting of cubes (N V ¼ 2 volume zones) and squares (N S ¼ 10 surface zones), exchange areas can be found in published tables and charts, [1,10,12,25]. In the following, a simple example of an industrial furnace presented in [10] is used as a benchmark.…”