Total Exchange Areas

GS = total-exchange area between gas and surface subscript R... 

If the gas volume is not isothermal and is zoned, an additional magnitude, the gas-to-gas total-exchange area QGj, arises (see Hottel and Sarofim. Radiative Tran.sfer, McGraw-Hill, New York, 1967, chap. 11). Space does not permit derivations of special cases only the single-gas-zone system is treated here. 

These three expressions suffice to formulate total-exchange areas for gas-enclosing arrangements which include, for example, the four cases illustrated in Table 5-10. 

HEAT AND MASS TRANSFER TABLE 5-10 Total-Exchange Areas for Four Arrangements of Two-Zone-Surface Enclosures of a Gray Gas... 

Total-exchange areas for the basic one-gas two-surface model [Eqs. (5-160) to (5-162)], used to evaluate the cases in Table 5-10, take the following form when converted by the above described procedure to their nongray form ... 

Modification of Table 5-10 to make the total-exchange areas conform to the gray-plus-clear gas model is straightforward, following the instructions presented above. The results are given in Table 5-11. 

TABLE 5-11 Conversion of Some Total-Exchange Areas to Their Gray-Plus-Clear Values... 

The bracketed term is called (GSi)r, the total exchange area from G to A] with assistance from a refractory surface. In summaiy. 

The total exchange areas allow one to account for the surface emissivity. The calculation of these quantities is shown in Hottel and Sarofim (1967). 

Most of the existing HEN synthesis methods rely on either heuristic rules (for example, pinch analysis method [2]) or mathematical programming (for example, simultaneous optimization approach [3-6]). And further, to some typical objectives considered in the HEN synthesis such as utility consumption, total number of matches, and total exchanger area, the flexibility of the HENs for feasible operation under possible variation of source-stream temperatures and/or heat-capacity flow rates has been emphasized in some recent articles [6-10]. For HEN synthesis, the analysis of this flexibility, defined as the size of the region of feasible operation in the space of desired or undesired deviations of pa-... 

An air-to-air heat recovery unit uses a cross-flow exchanger with both fluids unmixed and an air flow rate of O.S kg/s on both sides. The hot air enters at 40°C while the cool air enters at 20°C. Calculate the exit temperatures for U = 40 W/m2 °C and a total exchanger area of 20 m2. 

Method Explicit Matrix Relations for Total Exchange Areas, Int.J. Heat Mass Transfer, 18, 261-269 (1975). Rhine, J. M., and R. J. Tucker, Modeling of Gas-Fired Furnaces and Boilers, British Gas Association with McGraw-Hill, 1991. Siegel, Robert, and John R. Howell, Thermal Radiative Heat Transfer, 4th ed., Taylor Francis, New York, 2001. Sparrow, E. M., and R. D. Cess, Radiation Heat Transfer, 3d ed., Taylor Francis, New York, 1988. Stultz, S. C., and J. B. Kitto, Steam Its Generation and Use, 40th ed., Babcock and Wilcox, Barkerton, Ohio, 1992. 

Total Exchange Areas When an enclosure contains reflective surface zones, allowance must be made for not only the radiant energy transferred directly between any two zones but also the additional transfer attendant to however many multiple reflections which occur among the intervening reflective surfaces. Under such circumstances,... 

Explicit Matrix Solution for Total Exchange Areas For gray or monochromatic transfer, the primary working relation for zoning calculations via the matrix method is... 

In Eq. (5-118), SS and SG are defined as the required arrays of total surface-to-surface exchange areas and total gas-to-surface exchange areas, respectively. The matrices for total exchange areas are calculated explicitly from the corresponding arrays of direct exchange areas and the other enclosure parameters by the following matrix formulas ... 

Finally the four matrix arrays ss, gs, SS, and SG of direct and total exchange areas must satisfy matrix conservation relations, i.e.,... 

The total exchange areas for the four geometries shown in Fig. 5-18 follow directly from Eqs. (5-126) and (5-127). 

Consider the special situation where Mj = 2, with any number of refractory zones Mr > 1. By use of appropriate row and column reduction of the reflectivity matrix R, an especially useful relation can be derived that allows computation of the conventional total exchange area S, Sj from the corresponding refractory augmented black view factor Fy... 

Temporarily denote SiS2]R as the value of SiS2 computed from Eq. (5-128 ) which assumes er = 0. It remains to demonstrate the relationship between and the total exchange area SiS2 computed from... 

S3Si + S3S2]. Thus SiS2]K is clearly the refractory-aided total exchange area between zone 1 and zone 2 and not SiS2 as calculated by the matrix method in general. That is, includes not only the radiant... 

Numerically the matrix method predicts SSAi2 = 1.0446 m2 for Q3 = 0 and 3 = 0.55, which is identical to SSRi for the SSR model. Thus SSRi = SSAi2 is the refractory-aided total exchange area between zone 1 and zone 2. The SSR model also predicts Er = 247.8 kW/m2 versus the experimental value E3 = 219.1 kW/m2 (1172.6C vs. 1128.9C), which is also a consequence of the actual 25.0-kW refractory heat loss. 

Another particularly interesting limit of Eq. (5-134) occurs when A2 Ai, which might represent a small sphere irradiated by an infinite surroundings which can reflect radiation originating at Ab back to Ai. That is to say, even though A2 — , the self total exchange area does not necessarily vanish, to wit... 

Subject to the restrictions of no scatter and diffuse surface emission and reflection, the above equations are the most general matrix statement possible for the zone method. When P = 1, the directed exchange areas all reduce to the total exchange areas for a single gray gas. If, in addition, K = 0, the much simpler case of radiative transfer in a transparent medium results. If, in addition, all surface zones are black, the direct, total, and directed exchange areas are all identical. 

For the WSGG clear gas components we denote SS ]K 0 = SSQ an( Sf K o = SG0 = 0. Finally the WSGG arrays of directed exchange areas are computed simply from a-weighted sums of the gray gas total exchange areas as... 

Total exchange areas for WSGG clear gas component ... 

---