1- Determine the velocity distribution in the velocity boundary layer assuming second degree polynomial: u=C, +C,y+C,y²

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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ChapterMA: Math Assessment
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Introduction to heat convection
Solved problems
HW-10-
1- Determine the velocity distribution in the velocity boundary layer assuming second degree polynomial:
u =C, +C,y+C,y?
Answer: The boundary conditions are:
du
.. u = 0
at y = 0; u = u, ;
at y = 6;
= 0
at y = 8
dy
2
y
This gives:
يجب حفظ الشروط الحدية اذا كان الامتحان حضوري
2- Determine the velocity distribution in the velocity boundary layer assuming third degree polynomial:
u = C, +C,y+C,y' +C,y'
Answer: The boundary conditions are:
.. u = 0
at y = 0
= 0
dy?
at y = 0
du
= 0
u = u,
at y = 8
at y = 8
dy
3 y 1y
This gives:
28 28
يجب حفظ الشروط الحدية اذا كان الامتحان حضوري
3- Determine the velocity distribution in the velocity boundary layer assuming fourth degree polynomial:
2
u = a, +a, y+a,y +a,y' +a,y
Answer: The boundary conditions are:
. u = 0
= 0
dy?
at y = 0
at y = 0
du
= 0
dy
d'u
at y = 6 ;
dy?
u = u,
at y = 6
at y = 6
4.
This gives:
= 2
يجب حفظ الشروط الحدية اذا كان الامتحان حضوري
4- For flow over a slightly curved surface, the local shear stress is given by the relation:
0.5
T,(x) = 0.3
ULS
From this dimensional equation, obtain non-dimensional relations for the local and average friction
coefficients.
Answer::
0.6
1.2
Re
Re
Transcribed Image Text:Introduction to heat convection Solved problems HW-10- 1- Determine the velocity distribution in the velocity boundary layer assuming second degree polynomial: u =C, +C,y+C,y? Answer: The boundary conditions are: du .. u = 0 at y = 0; u = u, ; at y = 6; = 0 at y = 8 dy 2 y This gives: يجب حفظ الشروط الحدية اذا كان الامتحان حضوري 2- Determine the velocity distribution in the velocity boundary layer assuming third degree polynomial: u = C, +C,y+C,y' +C,y' Answer: The boundary conditions are: .. u = 0 at y = 0 = 0 dy? at y = 0 du = 0 u = u, at y = 8 at y = 8 dy 3 y 1y This gives: 28 28 يجب حفظ الشروط الحدية اذا كان الامتحان حضوري 3- Determine the velocity distribution in the velocity boundary layer assuming fourth degree polynomial: 2 u = a, +a, y+a,y +a,y' +a,y Answer: The boundary conditions are: . u = 0 = 0 dy? at y = 0 at y = 0 du = 0 dy d'u at y = 6 ; dy? u = u, at y = 6 at y = 6 4. This gives: = 2 يجب حفظ الشروط الحدية اذا كان الامتحان حضوري 4- For flow over a slightly curved surface, the local shear stress is given by the relation: 0.5 T,(x) = 0.3 ULS From this dimensional equation, obtain non-dimensional relations for the local and average friction coefficients. Answer:: 0.6 1.2 Re Re
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