uchagawkar_modeling of chemical reactor xxii maple

7/25/2019 Uchagawkar_Modeling of Chemical Reactor XXII Maple

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Effect of Simultaneous Heat and Mass Transfer inside

and outside of pellet on reaction rate-II

- Anoop Uchagawkar

Mass & Enthalpy Balance

Considering First order reaction

A0B

T

MASS BALANCE:

Mass in - Mass out + rate of reaction = Rate of accumulation

Considering steady state system


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(11)(11)

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(13)(13)

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This is the Mass Balance equation

ENERGY BALANCE:

Heat in - Heat out + rate of heat generation due to chemical reaction = rate of heat accumulation


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is the average concentration and is defined by:


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Mass Balance in Dimensionless form:

Dimensionless Parameters :


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Boundary Conditions:

Energy Balance in Dimensionless form:


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SOLUTION OF GOVERNING EQUATIONS


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A) FIRST ORDER REACTION


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The above evaluation can also


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This can be written as

For the sake of brevity let us omit in following developments the subscript infinity so, Equation

E25 becomes,


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using above Eq z7 can be written as

Let

and

substituting a8 and a9 in z7 and transforming into


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(110)(110)

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Now,

The Effectiveness factor is defined by the relation


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This is the required relation between Effectiveness factor and thiele Modulus

GENERAL KINETICS:

where r(Y) is a power function rate or a hyperbolic rate for Langmuir-Hinshelwood kinetics.

Let introduce the substitution

isolate for diff(diff(Y(xi),xi),xi)


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add4*r*Y(xi) to both sides

multiply both sides by xi

From E25, it requires to compute the integral ,


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Integrating by parts and back substituion yields

substituting G11 in E25

We transform G1 by susbtituting


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Substituting this in Eq G13 and solving

GRAPHS:


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(142)(142)


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(149)(149)

(146)(146)

(143)(143)

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(147)(147)


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(151)(151)


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uchagawkar_modeling of chemical reactor xxii maple

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