Energy Balances for Volume Zones—The Radiation Source Term

Energy Balances for Volume Zones—The Radiation Source Term Reconsider a generalized enclosure with N volume zones confining a gray gas. When the N gas temperatures are unknown, an additional set of N equations is required in the form of radiant energy 

The radiative source term is a discretized formulation of the net radiant absorption for each volume zone which may be incorporated as a source term into numerical approximations for the generalized energy equation. As such, it permits formulation of energy balances on each zone that may include conductive and convective heat transfer. For K— 0, GS — 0, and GG — 0 leading to S — On. When K 0 and S = 0N, the gas is said to be in a state of radiative equilibrium. In the notation usually associated with the discrete ordinate (DO) and finite volume (FV) methods, see Modest (op. cit., Chap. 16), one would write S /V, = K[G - 4- g] = Here H. = G/4 is the average flux 

Implementation of Eq. (5-152) necessitates the definition of two additional symmetric N x N arrays of exchange areas, namely, gg = [gi ] GG= [G,G,]. In Eq. (5-152) VI = [ Vj-8,] is an NxN diagonalmatrix of zone volumes. The total exchange areas in Eq. (5-151) are explicit functions of the direct exchange areas as follows Surface-to-gas exchange 

The matrices gg = [g g, and GG = [G,Gf] must also satisfy the following matrix conservation relations  

Direct exchange areas 4KVI1n = gs liw + gglw (5-154zr) 

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Energy Balances for Volume Zones—The Radiation Source Term. . 5-35... 

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