I had this problem while calculating the constant drying rate during flash/ pneumatic drying.
Drying rate can be calculated by two ways. These are the equations I found in literature for calculating the constant drying rate for flash/pneumatic drying. (Free moisture is only evaporated. particle temperature normally doesn't exceed 50 Celsius)
w = drying rate (kg/ m2 s)
k = mass transfer coefficient
Ts = Solid temperature = 303 K = 30 C
Tg = Gas temperature = 413 K = 140 C
Mw = molecular weight of H2O (18 e-3 kg/mol)
Mg = molecular weight of dry gas (30 e-3 kg/mol)
R = Gas constant (8.314 J/mol K)
P = atmospheric pressure (101325 Pa)
Psat = Saturation water vapor pressure at solid temperature, 303 K = 4247 Pa
Source: https://www.engineer...sure-d_599.html
Drying gas has 12% moisture by volume.
PH2O = partial pressure of gas =101325*0.12 = 12159 Pa
H = humidity in gas (H2O kg/ dry gas kg) = (0.12*18) / (0.88*30) = 0.0818
1) First Method (for single particle)
w = k (Psat *Mw / R*Ts - PH2O*Mw / R*Tg)
However, the drying rate is negative. since (4247/303 - 12159/413) < 0
2) Second method (for bulk of the particles)
w = k { [Mw*Psat / Mg*(P - Psat) ] - H }
However drying rate is negative. since [ 18*4247/30*(101325 - 4247) ] - 0.0818 < 0 is negative.
Can anyone please explain why the drying rate is negative. Is there anything wrong with the equations or my calculations?