I had this problem while calculating the constant drying rate during flash/Pneumatic Drying. Drying rate is negative when I am calculating it.

During this type of drying, solid particle is freely flowing in a hot gas and free moisture evaporation occurs well below the boiling point near atmospheric pressure. Particle surface is saturated with water vapor.

First of all these are the conditions for drying and symbols used in equations.

T

_{s} = Particle temperature = 303 K/ 30 °C

T

_{g} = Gas temperature = 413 K/ 140 °C

P

_{sat} = Saturation vapor pressure of water at particle temperature = 4247 Pa

Source :

https://www.engineeringtoolbox.com/water-vapor-saturation-pressure-d_599.htmlP = atmospheric pressure = 101325 Pa

mole fraction of water vapor in gas is 0.15. Rest is dry gas.

P

_{H2O} = Partial pressure of water vapor in gas = 101325 × 0.15 = 15198 Pa

M

_{w} = molecular weight of water = 0.018 kg/mol

M

_{g} = molecular weight of dry gas = 0.030 kg/mol

w = drying rate (kg/m

^{2}s)

k = mass transfer coefficient

H = humidity of gas ( H

_{2}O kg / dry gas kg) =( 0.15 × 0.018 ) / ( 0.85 × 0.030 ) = 0.10588

R = universal gas constant = 8.314 J/mol K

In literature I found two equations to calculate the drying rate during flash/pneumatic drying.

This is the first one. It is for a particle.

I used trying \frac but it didn't work for me.

1. w = k ( P

_{sat}M

_{w}/RT

_{s} - P

_{H2O}M

_{w}/RT

_{g} )

However when I substitute the values the answer is negative. since 4247/303 - 15198/413 < 0

2. This is the second equation. This is for all the dispersed particles.

w = k [ ( M

_{w} P

_{sat} / M

_{g}(P - P

_{sat}) ) - H ]

However when I substitute the values the answer is negative.

Since [18 × 4247 / 30 ×(101325 - 4247) ] - 0.10588 < 0

Can anyone please tell me why the drying rate is negative when it should be positive?