Air at ϑA = 40 ◦C and relative humidity ϕ = 0.2 flows over an irregular packing of spheres whose surface temperature is kept constant at the wet bulb temperature 21.5 ◦C by evaporating water. The air...

Air at ϑA = 40 ◦C and relative humidity ϕ = 0.2 flows over an irregular packing of spheres whose surface temperature is kept constant at the wet bulb temperature 21.5 ◦C by evaporating water. The air becomes loaded with water vapour. Calculate

 a) the heat transferred and

 b) the amount of water transferred

The following values are given: sphere diameter d = 0.02 m, channel cross section without the spheres A0 = 1m2, air velocity over A0: wm = 2 m/s, void fraction ε = 0.4, packing height H = 0.65 m, saturation pressure of water vapour pWS(40 ◦C) = 73.85 mbar, thermal conductivity of air at (ϑA + ϑ0)/2 = 30.75 ◦C : λ = 0.0267W/Km, Prandtl number P r = 0.71, kinematic viscosity ν = 1.63 · 10−5 m2/s, Enthalpy of evaporation of water at 21.5 ◦C: Δhv = 2450.0 kJ/kg.