Example 2.2: ( Process design )

A rotary drier using counter current flow is to be used to dry 25000 lb/hr of wet solid (PTA) containing 5 weight percent water to a water content of 0.10 weight per cent. The wet solid enters at 30°C (86°F). Ambient air at 30°C (86°F) will be heated to 156°C (313°F). Specific heat of solid is 0.2871. Estimate the length and diameter of the drier.

H_mG Humidity of air at temperature T_G° F

H_mW Humidity of air at temperature T_W ° F

T_G Temperature of inlet air °F; T_W Wet bulb temperature ° F

M Molecular weight of air; λ_W Latent heat of vaporization at T_W ° F

h_G /(mPk_G ) = 0.26 for air at T_W and here m = 29.

First Trail : assume wet bulb temperature is 90°C = 194°F

Hence at T_W = 194 ° F, H_mW = 0.046  ∴ H_mW - H_mG = 0.046- 0.002 = 0.044: λ_W = 547.3

φ = (0.26(313-194)/547.3) = 0.056                         

Second Trial : Assume a wet bulb temperature of 180 ° F

H_mW = 0.065 ∴ H_mW - H_mG = 0.065 – 0.002 = 0.063 ; λ_W = 532

φ = (0.26 (313-180)/532) = 0.063

Therefore wet bulb temperature assumed is true i.e. T _W = 180°F

The temperature of the outlet air should be selected on the basis of an economic balance between dryer and the fuel costs. Empirically it is found that drier operates economically when total number of transfer units (NTU) is between 1.5 to 2. (Badger and Banchero, Pg 508)

NTU = ln(T_G1 - T_W)/(T_G2 - T_W )

Take NTU = 1.5 = ln (313 -180)/( T_G2 - 180) ∴ T_G2 = 209°F