Radiation exchange area

Evaluation of the AS" s that charac terize an enclosure involves solution of a system of radiation balances on the surfaces. If the assumption is made that all the zones of the enclosure a re gray and emit and reflec t diffusely, then the direct-exchange area ij, as evaluated for the black-siirface pair A and Aj, applies to emission and reflections between them. If at a surface the total leaving-flnx density, emitted phis reflected, is denoted by W (and called by some the radiosity and by others the exitance), radiation balances take the form ... 

This means that the sum of the exchange areas associated with a surface in an enclosure must be same as the area of that surface. The principle of the summation rule may be extended to other geometries such as, for example, radiation from a vertical rectangle (area 1) to an adjacent horizontal rectangle (area 2), as shown in Figure 9.40iii, where they are joined to a second horizontal rectangle of the same width (area 3). In effect area 3 is an extension of area 2 but has a different view factor. 

RadiationExchangeArea=2.0 CellActiveArea % radiation exchange area is 2x cellactivearea since have 2 surfaces, and all wallsarea viewfactors add up to cellactivearea ... 

There are several possible mechanisms for the heat exchange between a reacting medium and a heat carrier radiation, conduction and forced or natural convection. Here we shall consider convection only. Other mechanisms are considered in the chapter on heat accumulation. The heat exchanged with a heat carrier (q ) across the reactor wall by forced convection is proportional to the heat exchange area (A) and to the driving force, that is, the temperature difference between the reaction medium and the heat carrier. The proportionality coefficient is the overall heat transfer coefficient (U) ... 

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. 

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... 

The exchange of radiation is based upon two laws. The first, known as Kirchoff s law, states that the ratio of the emissive power to the absorptivity is same for all bodies in thermal equilibrium. The emissive power of a body, E, is the radiant energy emitted from unit area in unit time. A body of area Ai and emissivity E, therefore, emits energy at a rate E A. If the radiation falling on unit area of the body is E, the rate of energy absorption is E, aiAi, where ui is the absorptivity. At thermal equilibrium, E aiAx. For another body in the same environment, E a Aj = EjAj, leading to Eq. (36)... 

Area is a derived, or secondary, physical quantity. It pltQ a significant role in many engineering problems. For example, the rate of heat transfer from a surface is directly proportional to the exposed sur ce area. That is why a motorcycle engine or a lawn mower engine has extended surfaces, or fins as shown in Figure 7.7. If you look closely inside buildings around your campus, you will also see heat exchangers or radiators with extended surfaces under windows and... 

The circumferential strip of the kiln freeboard (Figure 7.13) is isolated and subdivided in N small area elements. The portion of the kiln freeboard, approximately three kiln inside diameters in each axial direction viewed by these area elements, is subdivided into volume zones such as Vj comprising the freeboard gas, and the surface zones such as Aj that form the exposed bed and wall surfaces. The exchange areas between each of the zones and the elements of the circumferential strip are then evaluated and used to calculate the radiation streaming to these elements from the various volumes and surface zones, either directly or after undergoing one or two reflections. 

Because the evaporation of the solvent is an endothermic process, heat must be suppHed to the system, either through conduction, convection, radiation, or a combination of these methods. The total energy flux into a unit area of coating, is the sum of the fluxes resulting from conduction, convection, and radiation (see Heat exchange technology, HEAT thansfer). 

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