Estimate the depth in moist soil at which the annual temperature variation will be 10% of that at the surface.

GIVEN

Moist soil

FIND

The depth in moist soil at which the annual temperature variation will be 10 per cent of that at the surface

ASSUMPTIONS

Conduction is one dimensional

The soil has uniform and constant properties

Annual temperature variation can be treated as a step change in surface temperature with a 6 month

response time

SKETCH


The geometry of this problem is a semi infinite solid as covered in Section 3.4. The transient temperature for a change in surface temperature is given by



Where Ti is the temperature of the soil until the surface temperature is increased to Ts. For an annual

temperature variation of less than 10% of that of the surface





Physics & Space Science

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