Dr r nagarajan professor dept of chemical engineering iit madras
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Advanced Transport Phenomena Module 6 Lecture 29. Mass Transport: Illustrative Problems. Dr. R. Nagarajan Professor Dept of Chemical Engineering IIT Madras. Mass Transport: Illustrative Problems. SOLUTION TO THE PROBLEM. SOLUTION. Catalytic Converter. SOLUTION.

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Dr. R. Nagarajan Professor Dept of Chemical Engineering IIT Madras

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Dr r nagarajan professor dept of chemical engineering iit madras

Advanced Transport Phenomena

Module 6 Lecture 29

Mass Transport: Illustrative Problems

Dr. R. Nagarajan

Professor

Dept of Chemical Engineering

IIT Madras


Dr r nagarajan professor dept of chemical engineering iit madras

Mass Transport: Illustrative Problems


Solution to the problem

SOLUTION TO THE PROBLEM


Solution

SOLUTION

Catalytic Converter


Solution1

SOLUTION

  • Mechanism of CO(g) transport to the wall

    If Re < 2100 (see below),transport to the wall is by Fick diffusion of CO(g) through the prevailing mixture.


Solution2

SOLUTION

Therefore

Analogous heat transfer diffusivity is for gas

mixture

b. Discuss whether the Mass transfer Analogy Conditions(M A C) and Heat transfer Analogy Conditions (H A C) are met; implications ?

  • Since Mmix and Mco are close hence we will assume


Solution3

SOLUTION

c. Sc for the mixture :

Now:

and:


Solution4

SOLUTION

therefore

therefore


Solution5

SOLUTION

d. L=? We will need Re

Now:

therefore (laminar-flow regime)


Solution6

SOLUTION

For a square channel

and (used below).

If then the mass-transfer analogy is:


Solution7

SOLUTION

where

We estimate at which

If

then


Solution8

SOLUTION

therefore

Tentatively, assume F (entrance =1).Then:

that is,

(at which F (entrance) is indeed ). Solving for L gives: L =8.3 cm ( needed to give 95 % CO-Conversion).


Solution9

SOLUTION

e. Discuss underlying assumptions, e.g.,

fully developed flow?

nearly constant thermo physical properties?

no homogeneous chemical reaction?

“ diffusion-controlled” surface reaction?

f. If the catalyst were “ poisoned,” it would not be able to maintain . This would cause to exceed 8.3 cm. If catalyst were completely deactivated, then and, of course,


Solution10

SOLUTION

g. If the heat of combustion is 67.8 kcal/mole CO, how much heat is delivered to the catalyst channel per unit time? Overall CO balance gives the CO-consumption rate/channel:

where


Solution11

SOLUTION

Moreover,

hence,

and


Solution12

SOLUTION

Therefore

  • The “sensible” heat transfer required to keep the wall at 500 K can be calculated from a heat balance on the 8.3 cm-long duct- i.e., once we calculate , we have :


Solution13

SOLUTION

where

Mixing cup avg temp at duct outlet ?


Solution14

SOLUTION

Again, we see that

Moreover,


Solution15

SOLUTION

therefore

and


Solution16

SOLUTION

Therefore,


Solution17

SOLUTION

h. “Quasi-Steady” Application of These Results?

Note that:

and

hence, if the characteristic period of the unsteadiness >> 8.2 ms, the previous results can be used at each flow condition.


Solution18

SOLUTION

  • Pressure Drop

  • We have:

  • Therefore


Solution19

SOLUTION

But

Therefore


Solution20

SOLUTION

From overall momentum balance:


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