A thermal storage medium consists of a large mass of limestone. Ambient air is pumped through a 30-mm-high, 5-m-long 5-m-wide fissure within the limestone at a velocity of 2m/s. providing a heat transfer coefficient between the air and the limestone of h = 10 W/m2 ∙ K. Over a 24-hour time period, the temperature of the surface of the limestone adjacent to the air stream near the inlet exhibits periodic behavior with maximum and minimum values of 302 and 298 K, respectively.

(a) Determine the minimum and maximum values of the temperature of the air near the inlet.

(b) Determine the maximum heat flux to the air during a 24-hour time period near the inlet. Determine the air inlet and outlet temperatures at the time corresponding to the maximum air heat flux.

(c) Determine the air outlet temperatures at the times corresponding to the maximum and minimum air inlet temperatures.

(d) Plot the inlet air temperature, the limestone surface temperature, and the heat transfer rate to the limestone over 48 hours.

(e) What is the required thickness of limestone necessary to ensure that the limestone may be viewed as a semi-infinite medium?