Math Problem Help, anyone?

Chemical Engineering - Fluid Dynamics

In a bubble phase after mixing 2 substances, given that the bubble moisture is as:

o ́ρ_ε (∂H_b)/∂t+G_gh (∂H_b)/∂Z = m

during a heat transfer while mixing, Solve for moisture (m) content when

H_b = Y_g⇝ʎ+(C_phb+Y_g c_pvb )x(T_gb-T_r)

and Y_g^x is a constant equilibrium to Y_g

with an error rate of +/- .5 C @ .25 seconds/phase

While the air humidity ( Y_g ) being 0.009

and the heat transfer coefficient is

h = (k_(gl))/(d_p) x ( X_(1) Re_p^x^2)

given that

x = area @ 0.38 m^2 per 5 seconds for 1 minute of mixing

Y = Water Content in dry basis

T = Temp @ 15 C at dry basis

t = Time @ 1.73 sec for phase rate to vapor

δ = volumetric bubble concentration at initiated time

λ = latent heat of vaporization @ 5 J kg^-1

ρ = density @ 1 kg m^-3

G = air mass flow rate per cross section @ .5 kg m^-2^s-1

h = effective heat transfer @ 5 J

c_p = specific heat @ 3 J kg^-1 K^-1

v = vapor @ 7 Celsius / .15 seconds during mixing

a = specific exchange superficial area between gas and particles @ .22 m^-1

p = particle

b = bubble phase @ 22.5 C room temp

m = moisture

Thanks!