A very long, cylindrical heating element of diameter d = 25 mm is h = 50 mm away from a reflective (adiabatic) wall, Fig. 5.80. The heating element has a temperature T = 700 K, the surroundings are at...

A very long, cylindrical heating element of diameter d = 25 mm is h = 50 mm away from a reflective (adiabatic) wall, Fig. 5.80.

The heating element has a temperature T = 700 K, the surroundings are at TS = 300 K. The heating element, wall and surroundings are all assumed to be black bodies. Only the heat transfer by radiation is to be considered. Determine the temperature of the wall surface as a function of the coordinate x and calculate T(x) for x = 0, x = h, x = 2h, x = 10h and x → ∞. Note: The view factor between a surface strip dA1 of infinitesimal width and any length (perpendicular to the drawing plane in Fig. 5.81) and a ruled or cylindrical surface 2 is given by

Here, the ruled surface 2 is produced by parallel straight lines of infinite length, perpendicular to the drawing plane in Fig. 5.81. The derivation of this equation is available in [5.37], p. 197–199.