One method of storing solar energy for use during cloudy days, or at night, is to store it in the form of sensible heat in a rock bed. Suppose such a rock bed has been heated to 70?C and it is desired to heat a stream of air by blowing it through the bed. If the air inlet temperature is 10?C and the mass velocity of the air in the bed is 0.5 kg/(s m2), how long must the bed be in order for the initial outlet air temperature to be 60?C? Assume that the rocks are spherical, 2 cm in diameter, and that the bed void fraction is 0.5. Hint: The surface area of the rocks per unit volume of the bed is (6/Dp) (1 ?? ε).GIVENPacked bed of rocks with air blowing through itInitial temperature of rocks (Tr) = 70?CInlet air temperature (Ta,in) = 10?CMass velocity of air (m/A) = 0.5 kg/(s m2)Outlet air temperature (Ta,out) = 65?CSurface area per unit volume (As/V) = (6/Dp)(1 ?? ε)ASSUMPTIONSRocks are spherical with diameter (D) = 2 cm = 0.02 mVoid fraction of the bed (ε) = 0.5Rock temperature remains practicallyconstant

Ta,out = 65C L-? ,- D- 0.02 m e= 0.5 Alr m/A = 0.5 kg/(sm2) Ta,in- 10C