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In this chapter, we will deal with transient cooling of vertically hanged hot special steel plates by radiation and natural convection heat transfer. In engineering calculations of radiation heat transfer, a real surface emitting thermal radiation at a temperature Ts has a total emissive power less than the total emissive power of a black surface at Ts, namely less than σ× T4s. The ratio of a real surface’s emissive power to a black surface’s emissive power at the same Ts is called the emissivity of a surface. Emissivity of a surface is a function of surface temperature, wavelength and direction of radiation emission. In engineering calculation, we deal with total hemispherical emissivity, εTs, which is the emissivity of a surface that is averaged over all wavelengths and hemispherical directions and which is only a function of surface temperature as given in Equation 2-1.