Engineering Approximations for Directed Exchange Areas

It is clear that transfer from the gas to the surface and transfer from the surface into the gas are characterized by two different constants of proportionality, g and agi. To allow for the difference between gas emissivity and absorptivity, it proves convenient to introduce a single 

The calculation then proceeds by computing two values of 8 at the given Tg and Ti temperature pair and the two values of pLM and 2pLM- We thereby obtain the expression e = m(l - Tm). It is then assumed that 1 = 2 = g = m for use in Eqs. (5-171). This simplification may be used for M 2 as long as N= 1. This simplification is illustrated in Example 12. 

Example 12 WSGG Clear plus Gray Gas Emissivity Calculations Methane is burned to completion with 20 percent excess air (50 percent relative humidity at 298 K or 0.0088 mol water/mol dry air) in a furnace chamber of floor dimensions 3 x 10 m and height 5 m. The entire surface area of the enclosure is a gray sink with emissivity of 0.8 at temperature 1000 K. The confined gas is well stirred at a temperature of 1500 K. Evaluate the clear plus gray WSGG constants and the mean effective gas emissivity, and calculate the average radiative flux density to the enclosure surface. 

Two-zone model, M = 1, N = 1 A single volume zone completely surrounded by a single sink surface zone. 

The gas emissivities and absorptivities are then calculated from the two constant correlation in Table 5-5 (column 5 with pjpc - 2.0) as follows  

---