CHAPTER
5 The calculation of radiant heat transfer rates, in detail, is beyond the scope of this book and for most food processing operations a simplified treatment is sufficient to estimate radiant heat effects. Radiation can be significant with small temperature differences as, for example, in freeze drying and in cold stores, but it is generally more important where the temperature differences are greater. Under these circumstances, it is often the most significant mode of heat transfer, for example in bakers' ovens and in radiant dryers. 
The basic formula for radiantheat transfer is the StefanBoltzmann Law
where T is the absolute temperature (measured from the absolute zero of temperature at 273°C, and indicated in Bold type) in degrees Kelvin (K) in the SI system, and s (sigma) is the StefanBoltzmann constant = 5.73 x 10^{8} J m^{2} s^{1}K^{4} The absolute temperatures are calculated by the formula K = (°C + 273). This law gives the radiation emitted by a perfect radiator (a black body as this is called though it could be a redhot wire in actuality). A black body gives the maximum amount of emitted radiation possible at its particular temperature. Real surfaces at a temperature T do not emit as much energy as predicted by eqn. (5.8), but it has been found that many emit a constant fraction of it. For these real bodies, including foods and equipment surfaces, that emit a constant fraction of the radiation from a black body, the equation can be rewritten
where e (epsilon) is called the emissivity of the particular body and is a number between 0 and 1. Bodies obeying this equation are called grey bodies. Emissivities
vary with the temperature T and with the wavelength of
the radiation emitted. For many purposes, it is sufficient to assume that
for: Just
as a black body emits radiation, it also absorbs it and according to the
same law, eqn. (5.8).
where 1/C = 1/e_{1} + 1/e_{2}  1, e_{1} is the emissivity of the surface at temperature T_{1} and e_{2} is the emissivity of the surface at temperature T_{2}.
where e is the emissivity of the body, T_{1} is the absolute temperature of the body and T_{2} is the absolute temperature of the surroundings. For many practical purposes in food process engineering, eqn. (5.11) covers the situation; for example for a loaf in an oven receiving radiation from the walls around it, or a meat carcass radiating heat to the walls of a freezing chamber. In order to be able to compare the various forms of heat transfer, it is necessary to see whether an equation can be written for radiant heat transfer similar to the general heat transfer eqn. (5.3). This means that for radiant heat transfer:
where h_{r} is the radiation heattransfer coefficient, T_{1} is the temperature of the body and T_{2} is the temperature of the surroundings. (The T would normally be the absolute temperature for the radiation, but the absolute temperature difference is equal to the Celsius temperature difference, because 273 is added and subtracted and so (T_{1}  T_{2}) = (T_{1}  T_{2}) = DT Equating eqn. (5.11) and eqn. (5.12)
= es(T_{1} + T_{2} ) (T_{1}^{2} + T_{2}^{2})mmmmmm If T_{m} = (T_{1} + T_{2})/2, we can write T_{1} + e = T_{m} and T_{2}  e = T_{m} where and then = 2T_{m}^{2} + 2e^{2} = 2T_{m}^{2} + (T_{1}  T_{2})^{2}/2 Therefore h_{r} = es(2T_{m})[2T_{m}^{2} + (T_{1}  T_{2})^{2}/2] Now, if (T_{1}  T_{2}) « T_{1} or T_{2}, that is if the difference between the temperatures is small compared with the numerical values of the absolute temperatures, we can write:
q = Aes(T_{1}^{4} T_{2}^{4} )
= 0.0645 x 0.85 x 5.73 x 10^{8} (450^{4} 373^{4}) By eqn. (5.13) q = 0.23e (T_{m}/100)^{3}A DT
= 0.23 x 0.85(411/100)^{3} x 0.0645 x 77 Notice
that even with quite a large temperature difference, eqn. (5.13) gives
a close approximation to the result obtained using eqn. (5.11).
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