Homework 1
CH EN 4903 - Projects Lab I
Ring
1.)
Using non-linear least squares determine the Arrhenius pre-exonential and
activation energy for the data given below for the surface reaction rate
constant for oxidation of carbon particles
C(s)+O2  CO2
With the surface reaction rate given by:
Rate (Moles/cm2/s) = k CO2
with CO2 given in moles per liter.
T
Rate Constant, k
Kelvin
546.3
556.3
566.3
576.3
586.3
596.3
606.3
616.3
626.3
636.3
646.3
656.3
666.3
676.3
686.3
696.3
706.3
716.3
726.3
736.3
746.3
2.)
cm/s
4.80E-07
7.12E-07
2.01E-06
2.08E-06
1.48E-06
2.98E-05
4.51E-05
1.79E-04
1.71E-03
6.98E-04
1.40E-03
2.03E-03
3.46E-03
4.40E-03
1.35E-03
6.35E-03
4.71E-03
0.026
0.019
0.02
0.028
Perform an error analysis on the Nusselt Number determined with a diameter
of 0.010±0.001 m, velocity of 1.0±0.2 m/s and water temperature of
358.0±2.5 K using the fit equation
1
NNu
a1
a  NRe  NPr
0
3
with the unknowns a0 and a1 and the definitions for the Reynolds and Prandlt
numbers given by:
NRe
( T)  V D
 ( T)
Cp   ( T)
NPr
k( T)
.
Using the following data to calculate the values of the unknowns a0 and a1, you
can then perform the error analysis needed.
The data listed below was collected for an experimental program for heat transfer
in a pipe with a 0.0200±0.0005 m diameter pipe operating with water at a
temperature of 301.36±1.25 K
Water flow Velocity
Nusselt Number.
m/s
Dimensionless
3.249
0.525
3.082
3.328
3.039
2.292
1.898
2.632
2.498
1.659
1.095
39.693
9.589
39.653
40.514
38.574
29.674
25.621
33.567
34.249
23.742
16.497
For physical properties of water at various temperatures please use the
tabulated values.
k( T)  
0.0015
 K
 T  0.1689  
 m K
 1.1538 10 7
( T)  


watt
4
K
4
T 
1.6538E-04
3
K
3
T 
9.1327E-02
2
K
2
T 
22.333
K
 kg
 m3

 T  1014.6  
J
Cp  4200
kg  K
3.34e-10 4 4.57e-07 3 2.36e-4 2 0.054
T 
T 
T 
 T  4.67   Pa s


4
3
2
K
K
K
 K

For simplification of the partial derivatives you can use the term which is first
order in temperature to evaluate the partial derivative of the various properties
with respect to temperature.
 ( T)  
3.)
If you chose to do problem 3 using a spread sheet or partial derivatives redo it
using the opposite method.