RADIATION HEAT TRANSFER Heat Transferwhere:f_{a} = is the shape factor, which depends on the spatial arrangement of the two objects(dimensionless)f_{e} = is the emissivity factor, which depends on the emissivities of both objects(dimensionless)The two separate terms f_{a} and f_{e} can be combined and given the symbol f. The heat flowbetween two gray bodies can now be determined by the following equation:(2-13)QfsA(T^{4}_{1}T^{4}_{2} )The symbol (f) is a dimensionless factor sometimes called the radiation configuration factor,which takes into account the emissivity of both bodies and their relative geometry. The radiationconfiguration factor is usually found in a text book for the given situation. Once theconfiguration factor is obtained, the overall net heat flux can be determined. Radiant heat fluxshould only be included in a problem when it is greater than 20% of the problem.Example:Calculate the radiant heat between the floor (15 ft x 15 ft) of a furnace and the roof, ifthe two are located 10 ft apart. The floor and roof temperatures are 2000°F and 600°F,respectively. Assume that the floor and the roof have black surfaces.Solution:A_{1} = A_{2} = (15 ft) (15 ft) = 225 ft^{2}T_{1} = 2000^{o}F + 460 = 2460°RT_{2} = 600^{o}F + 460 = 1060°RTables from a reference book, or supplied by the instructor, give:f_{1-2}= f_{2-1} = 0.31Q_{1-2}= sAf(T_{1}^{4}- T_{2}^{4})= (0.174Btuhr ft^{2}^{o}R^{4}) (225 ft^{2}) (0.31) [(2460^{o}R)^{4}(1060^{o}R)^{4}]= 4.29 x 10^{14} Btu/hrHT-02 Page 28 Rev. 0

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