DRYING PROBLEMS-

QUESTION -1 Mass transfer coefficient from a free water surface to an adjacent moving air stream has been found to be 0.015 kg/m²-s. Estimate the rate of evaporation from a surface of 1 m² at a temperature of 28 oc into an air stream with dry bulb temperature of 40 oc and relative humidity ( RH ) of 40 % . and the consequent necessary rate of supply of heat energy to effect this evaporation.

Solution - from charts, the humidity of saturated air at 40 oc temperature = 0.0495 kg/kg
Humidity of air at 40 oc and 40 % RH = 0.0495*40/100 =0.0198 KG/KG = Ya
From charts, the humidity of saturated air at 28 oc = 0.0244 kg/kg = Ys
Driving force = Ys - Ya = 0.0244- 0.0198) = 0.0046 kg/kg
Rate of evaporation = Kg.*A*(Ys - Ya ) =0.015 * 1*0.0046 = 6.9 *10 ^-5 kg/s
Latent heat of vaporization of water at 28 oc = 2.44 *1000 =24400 kj/kg
Heat energy supply rate / 1 m2 area = 6.9* 10^-5 * 24400 = 0.168 kj /s
= 0.168 kw

Part 2 - heat transfer in air drying -
Q = 168 j/s

Temperature difference = dry bulb temperature - wet bulb temperature = 40 -28 = 12 oc = Tb - Ts
Q = h. *A* ( Tb- Ts )
168 =h. *1* (12)
H = 168/12 =14 j/m2-s- 0c

Part -3 - Temperature and RH in air drying of carrots at 60 0c and 10 % RH is being passed over a bed of dished carrots at the rate of 20 kg dry air /s . if the rate of evaporation of water from the carrots ,measured by the rate of change of weight of the carrots = 0.16 kg/s. Estimate the temperature and RH of the air leaving the dryer.

Solution - from the psychometric chart -
Humidity of air at 60 oc and 10 % = 0.013 kg/kg
Humidity added to air in drying 0.16/20 = 0.008 kg/kg
Humidity of air leaving the dryer = 0.013 +0.008 = 0.021 kg/kg
Following on the psychometric chart the wet bulb line from the entry point at 60 oc and 10% RH upto the intersection of that line with a constant humidity of 0.021 kg/kg .

The resulting temperature = 41 0c and the RH = 42%
BECAUSE THE EQUATION FOR PREDICTING HEAT TRASNFER CO EFFICIENT CO EFFICIENT , FOR SITUATIONS COMMONLY ENCOUNTERED , ARE EXTENSION AND MUCH MORE WIDELY AVOIDABLE , THEN MASS TRANSFER COEFFICIENT , THE HEAT TRANSFER RATES CAN BE USED TO ESTIMATE DRYING RATES THROUGH THE LEWIS NUMBER ( RATIO)
AND, LEWIS NO = Le = hc/ Cs* Kg= 1