Mt: Diffusion With A Homogeneous Chemical Reaction

MT: Diffusion with a homogeneous chemical reaction Instructor Date

:Dr. Nurul Hasan :15/04/09

Universiti Teknologi PETRONAS

What we will learn today? ♦ Shell balance of mass transfer ♦ Application of Fick’s Law ♦ Reaction Model for mass transfer

Conservation of mass in the shell  Rate of   Rate of   rate of mass    −   +    mass in   mass out   production  = ( Accumalation )

SN Az |z − SN Az |z + ∆z − k1′′c′ A S∆z = 0

Divide/ Taking Limit Divide by

S∆z and taking the limit of ∆z → 0 dN Az + k1′′c′ A = 0 dz

Apply Fick’s Law Molar flux to the concentration gradient

N Az = − DAB

dc A dz

Apply Fick’s Law (cont..) Molar flux to the concentration gradient 2

DAB

d cA ′ ′ ′ − k c 1 A =0 2 dz

The BCs:

at , z = 0, c A = c A0 at , z = L, N Az = 0

Taking Integration Taking integration

d Γ 2 −φ Γ = 0 2 dζ 2

Where the various parameters are:

Γ = c A c A0

ζ =z L 2 ′ ′ ′ φ = k1L / DAB

Apply B.C., concentration Using the BC:

Γ = C1 cos φζ + C2 sinh φζ

cosh φ cosh φζ − sinh φ sinh φζ Γ= cosh φ cosh[φ (1 − ζ ) ] Γ= cosh φ

Application of concentration Average concentration:

c A,avg c A0

(c ∫ = ∫

c A0 ) dz

L

0

A L

0

dz

tanh φ = φ

Final solution Molar flux at the interface:

N Az

z =0

dc A = − DAB dz

z =0

 c A0 DAB  = φ tanh φ  L 

What we learnt today •Shell balance of mass transfer •Application of Fick’s Law •Reaction Model for mass transfer