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The non-dimensional fluid temperature profile near the surface of a convectively cooled flat plate is given by
Tω - T = a + b y c + y ² Tω - T∞ L L
where y is measured perpendicular to the plate, L is the plate length, and a, b and c are arbitrary constants. Tw and T∞ are wall and ambient temperatures, respectively. If the thermal conductivity of the fluid is k and the wall heat flux is q', the Nusselt numberNu = q" L is equal to Tw - T∞ K
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- a
- b
- 2c
- (b + 2c)
Correct Option: B
= a + | c + | ![]() | ![]() | ² | |||
Tω - T∞ | L | L |
T = Tω + (T∞ - Tω) | ![]() | a + | + c | ![]() | ![]() | ² | ![]() | ||
L | L |
q" = -k | = -k(T∞ - Tω) | ![]() | + | ![]() | |||
dy | L | L² |
at y = 0
⇒ = | = b = Nu | |
(T∞ - Tω)k |
∴ Nu = b.