Question

Cryogenic liquid storage. Liquid oxygen is stored in a thin-walled spherical container, 96 cm in diameter, which is further enclosed in a concentric container 100 cm in diameter. The surfaces facing each other at coated with an emittance of only 0.05. The inner surface is at 95 K, and the outer surface is at 280 K.
a. Draw an equivalent electrical circuit.
b. What is the heat exchange [W] between the two surfaces?

Answer 1

Answer:

The answer is "26.55 V"

Explanation:

Given values:

$d_i= 0.96m\\d_o= 1m\\\epsilon = 0.05\\T_0= 280k\\T_i= 95k$

For Answer  (a) please find the attachment.

Answer (b):

$q_{i-0}= \frac{\sigma (T_{0}^4)-(T_{i}^4)}{\frac{1-\epsilon i }{\epsilon_{i} A_{i}}+ \frac{1 }{\ f_{i o} A_{i}} +\frac{1-\epsilon_{0}}{\epsilon_{0} A_{0}}}$

$f_{i0}= 1 \ it \ is \ fully \ inside \ the \ large \ sphero$

$q_{i-0}= \frac{\sigma A_i (T_{0}^4)-(T_{i}^4)}{\frac{1 }{\epsilon_{i}} - 1+ 1 +\frac{1-\epsilon_{0}}{\epsilon_{0}} \times \frac{A_i}{A_0}}\\\\q_{i-0}= \frac{\sigma A_i (T_{0}^4)-(T_{i}^4)}{\frac{1 }{\epsilon_{i}} +\frac{1-\epsilon_{0}}{\epsilon_{0}} \times (\frac{d_i}{d_0})^2}\\\\q_{i-0}= \frac{\sigma (\pi d^2_i) (T_{0}^4)-(T_{i}^4)}{\frac{1 }{\epsilon_{i}} +\frac{1-\epsilon_{0}}{\epsilon_{0}} \times (\frac{r_i}{r_0})^2}$

$q_{i-0}= \frac{5.67 \times 10^{-8} \times 3.14 \times 9.62 \times 9.62 \times (280^4-94^4)}{\frac{1 }{0.05} +\frac{1-0.05}{0.05} \times (\frac{0.96}{1})^2}\\\\\ After \ solve the \ equation \ the \ answer \ is:\\\\q_{i-0} = 26.55 \ V$