Question

Radioactive wastes are temporarily stored in a spherical container, the center of which is buried a distance of 10 m below the earth's surface. The outside diameter of the container is 2 m, and 500 W of heat are released as a result of radioactive decay. If the soil surface temperature is 20°C, what is the outside surface temperature of the container under steady-state conditions? The thermal conductivity of soil is k = 0.52 W/mK.

Answer 1

Given:

outer radius, R' = 10 m

inner diameter, d = 2 m

inner radius, R =
`(d)/(2)` = 1 m

surface temperature, T' =
`20^(\circ)C`

Thermal conductivity of soil, K = 0.52 W/mK

Solution:

To calculate the thermal temperature of conductor, T, we know amount of heat, Q is given by :

Q =
`(T - T')/((R' - R)/(4\pi KRR'))`

500 =
`(T - 20)(4\pi *0.52* 1* 10)/(10 - 1)`

T = 68.86 +20 =
`88.865^(\circ)C`

Therefore, outside surface temperature is
`88.865^(\circ)C`