Oil Film Thickness Calculation On A
Flat Plate Withdrawn from Oil Bath
Numerical Analysis for Engineering
MEAE-4960
April 10, 2001
Jeff Bode
Oil Film Thickness Calculation On A
Flat Plate Withdrawn from Oil Bath
Problem was the determination of oil film thickness on plate
X
MEAE-4960
2
Jeff Bode
Oil Film Thickness Calculation On A
Flat Plate Withdrawn from Oil Bath
Third Order Differential Equation Was Analyzed
d d  3U 
 3U 
d

d  
d f
3
dx   
  
3
3
3U
•
is treated as a constant.

• df is not known, and needs to be solved for.
MEAE-4960
3
Jeff Bode
Oil Film Thickness Calculation On A
Flat Plate Withdrawn from Oil Bath
Runge-Kutta Method for Systems of Differential Equations Selected
• Third Order DE transformed into 3 First Order
Differential Equations.
f1 t , x1 , x2 , x3   x2
f 2 t , x1 , x2 , x3   x3
.00964604697321 x1  d F 
f 3 t , x1 , x2 , x3   
x1 3
MEAE-4960
4
Jeff Bode
Oil Film Thickness Calculation On A
Flat Plate Withdrawn from Oil Bath
Initial Conditions Are Required For Analysis
• Initial guess of df is required (iteration necessary).
• Equations not valid at x=0, therefore approximation
necessary.
• d(0.0001) is guessed for initial condition.
• d’(0.0001) and d’’(0.0001) are determined numerically.
 2 g 2 x 4 gx 2

1
2
4

d ' 
  2 g 2 x 4 gx 2

1  

 1
2

 4

MEAE-4960
gx 1  d '
d ''

5

3
2 2
Jeff Bode
Oil Film Thickness Calculation On A
Flat Plate Withdrawn from Oil Bath
Initial Conditions For d(x) Became Roadblock For Accurate Results
• Solution should have the following output
– d = df
– d’ = 0
– d’’ > 0
• Despite variation of initial conditions for
d(0.0001), no solution with all of above 3
conditions could be found.
• Closest estimate with d’ = 0 produced over
2000% error.
MEAE-4960
6
Jeff Bode