Question

Three thin walled infinitely long hollow cylinders of radii 5 cm, 10 cm and

15 cm are arranged concentrically as shown in Fig. 15.54. T1 = 1000 K and T3 = 300 K.

Assuming ε1 = ε2 = ε3 = 0.05 and vacuum in the spaces between the cylinders, calculate the

steady state temperature of cylinder surface 2 and heat flow per m2 area of cylinder 1

Answer 1

$Q_1=Q_2,$

$\frac{A_1\sigma(T_1^4-T_2^4)}{\frac{1-\varepsilon}{\varepsilon}+1+(\frac{1-\varepsilon}{\varepsilon})\frac{A_1}{A_2}}=\frac{A_2\sigma(T_2^4-T_3^4)}{\frac{1-\varepsilon}{\varepsilon}+1+(\frac{1-\varepsilon}{\varepsilon})\frac{A_2}{A_3}},$

where $T_2=770~K,$

and $Q=1250~W.$