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 65°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 –(?).)

Question

GIVEN

Packed bed of rocks with air blowing through it

Initial temperature of rocks (Tr) = 70°C

Inlet air temperature (Ta,in) = 10°C

Mass velocity of air (m/A) = 0.5 kg/(s m2)

Outlet air temperature (Ta,out) = 65°C

Surface area per unit volume (As/V) = (6/Dp)(1 –(?) )

FIND

Length of bed required (L)

ASSUMPTIONS

Rocks are spherical with diameter (D) = 2 cm = 0.02 m

Void fraction of the bed (?) = 0.5

Rock temperature remains practically constant

SKETCH

Answer 1

The Whitaker definition of the Reynolds number is





The heat transfer coefficient is given by



A local energy balance on the air flow through the bed yields



Checking the units, then eliminating them for clarity



Applying the above equation iteratively until the temperature reaches 65°C yields the following results