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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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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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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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