Estimate the minimum depth at which one must place a water main below the surface to avoid freezing. The soil is initially at a uniform temperature of 20°C. Assume that under the worst conditions...

Estimate the minimum depth at which one must place a water main below the surface to avoid freezing. The soil is initially at a uniform temperature of 20°C. Assume that under the worst conditions anticipated it is subjected to a surface temperature of –15°C for a period of 60 days, and use the following proper ties for soil (300 K):
 = 2050 kg/m³, k = 0.52 W/m K, c = 1840 J/kg K,
 = 0.138
10^–6
m²
/s.