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Oksanka
2 months ago
13

Radioactive wastes are temporarily stored in a spherical container, the center of which is buried a distance of 10 m below the e

arth'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.
Engineering
1 answer:
mote1985 [299]2 months ago
4 0

Given:

outer radius, R' = 10 m

inner diameter, d = 2 m

inner radius, R = \frac{d}{2} = 1 m

surface temperature, T' = 20^{\circ}C

Thermal conductivity of soil, K = 0.52 W/mK

Solution:

In order to determine the thermal temperature of the conductor, T, we know the amount of heat, Q is defined as:

Q =  \frac{T - T'}{\frac{R' - R}{4\pi KRR'}}

500 =  (T - 20)\frac{4\pi \times0.52\times 1\times 10}{10 - 1}

T = 68.86 + 20 = 88.865^{\circ}C  

Thus, the temperature at the outer surface can be stated as 88.865^{\circ}C  

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