Question

a black body of total area 0.05 m² is completely enclosed in a space bounded by 15 cm thick walls. the walls have a surface area 0.5 m² and the thermal conductivity 1.07 w/m.°c. if the inner surface on the enveloping wall is to be maintained at 225 celsius and the outer wall surface is at 30 celsius , calculate the temperature of the black body. neglect the difference between inner and outer surfaces area of enveloping material.

Answer 1

Heat transfer due to conduction is

$Q c = k A d t/δ\\ = \frac{1.07*0.50(225-30)}{15*10^{-2}}\\ = 695.5 W.\\ Qr = σ Ab (T b^4 – Tw^4)\\ 695.5 = 5.67*10^{-8} * 0.05 * (Tb^4 - (225+273)^4)$

So the temperature of the black body is, T_b =  $744.3$ K