Consider the packed bed ( = 0.5) of latent heat capsules (D c = 50 mm) described

Consider the packed bed (ε = 0.5) of latent heat capsules (D_c = 50 mm) described in Problem 7.102, but now for an application in which ambient air is to be heated by passing it through the bed. In this case the capsule contain an organic compound with a melting point of T mp = 50°C, and the air enters the vessel (4 = D_v = 0.40 m) at T_i = 20°C and V = 1.0 m/s.

(a) If the PCM in each capsule is in the liquid state at T mp as solidification occurs within the capsule what is the outlet temperature of the air? If the density and latent heat of fusion of the PCM are p = 900 kg/m³ and h_sf = 200 kJ/kg, what is the mass rate (kg/s) at which the PCM is converted from liquid to solid in the vessel?

(b) Explore the effect of the inlet air velocity and capsule diameter on the outlet temperature.

(c) At what location in the vessel will complete freezing of the PCM in a capsule first occur? Once complete freezing begins to occur, how will the outlet temperature vary with time and what is its asymptotic value?