If the temperature profile through the ground is linear, increasing from 35 F at the surface by 0.5 F per foot of depth, how long will it take for a pipe buried 10 ft below the surface to reach 32 F...

If the temperature profile through the ground is linear, increasing from 35F at the surface by 0.5F per foot of depth, how long will it take for a pipe buried 10 ft below the surface to reach 32F if the outside air temperature is suddenly dropped to 0F. The thermal diffusivity of soil may be taken as 0.02 ft²/h, its thermal conductivity is 0.8 Btu/h ft
F, and the convective heat-transfer coefficient between the soil and the surrounding air is 1.5 Btu/h ft²
F