Question

g A spherical container of inner diameter 0.9 meters contains nuclear waste that generates heat at the rate of 872 W/m3. Estimate the total rate of heat transfer from the container to its surroudings ignoring radiation.

Answer 1

Answer: The total rate of heat transfer from the container to its surroundings ignoring radiation is 332.67 W.

Explanation:

Given: Inner diameter = 0.9 m

q = 872 $W/m^{3}$

Now, radii is calculated as follows.

$r = \frac{diameter}{2}\\= \frac{0.9}{2}\\= 0.45 m$

Hence, the rate of heat transfer is as follows.

$Q = q \times V$

where,

V = volume of sphere = $\frac{4}{3} \pi r^{3}$

Substitute the values into above formula as follows.

$Q = q \times \frac{4}{3} \pi r^{3}\\= 872 W/m^{3} \times \frac{4}{3} \times 3.14 \times (0.45 m)^{3}\\= 332.67 W$

Thus, we can conclude that the total rate of heat transfer from the container to its surroundings ignoring radiation is 332.67 W.