Suppose the rock bed in Problem 7.37 has been completely discharged and the entire bed is at 10?C. Hot air at 90?C and 0.2 m/s is then used to recharge the bed. How long will it take until the first rocks are back up to 70?C and what is the total heat transfer from the air to the bed?From Problem 7.37: 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. 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 itInlet air temperature (Ta,in) = 90?CMass velocity of air (m/A) = 0.5 kg/s m2Surface area per unit volume (As/V) = (6/Dp) (1 ?? ε)Length of bed (from solution to Problem 7.37) (L) = 19 cm = 0.19 mInitial temperature of rocks (Tr,i) = 10?CASSUMPTIONSRocks are spherical with diameter (D) = 2 cm = 0.02 mVoid fraction of the bed (ε) = 0.5The rock has the density and thermal conductivity of graniteThe specific heat of the rock is approximately the same as brick or concrete: c = 840 J/(kgK)

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T,-70°C D= 0,02 m e=0.5 Alr M/A = 0.5 kg/(sm2) Ta,In = 90°C