MT: Diffusion with a MT: Diffusion with a homogeneous chemical homogeneous chemical

reactionreaction

Instructor :Instructor : Dr. Nurul HasanDr. Nurul Hasan

Date :Date : 15/04/0915/04/09

Universiti Teknologi PETRONASUniversiti Teknologi PETRONAS

Shell balance of mass transfer Application of Fick’s Law Reaction Model for mass transfer

What we will learn today? What we will learn today?

Conservation of mass in the shell

onAccumalati

production

mass of rate

out mass

of Rate

in mass

of Rate

0|| 1 zSckSNSN AzzAzzAz

Divide/ Taking Limit

Divide by and taking the limit of zS 0z

01 AAz ckdz

dN

Apply Fick’s Law

Molar flux to the concentration gradient

dz

dcDN AABAz

Apply Fick’s Law (cont..)

Molar flux to the concentration gradient

The BCs:

012

2

AA

AB ckdz

cdD

0,,

,0, 0

Az

AA

NLzat

cczat

Taking Integration

Taking integration

Where the various parameters are:

022

2

dd

AB

AA

DLk

Lz

cc

/21

0

Apply B.C., concentration

Using the BC:

sinhcos 21 CC

cosh

sinhsinhcoshcosh

cosh

1cosh

Application of concentration

Average concentration:

tanh

0

0 0

0

,

L

L

AA

A

avgA

dz

dzcc

c

c

Final solution

Molar flux at the interface:

tanh0

00

L

Dc

dz

dcDN ABA

z

AABzAz

What we learnt todayWhat we learnt today

•Shell balance of mass transfer

•Application of Fick’s Law

•Reaction Model for mass transfer