# GATE Mechanical 2014 Set 1 | Question: 46

The non-dimensional fluid temperature profile near the surface of a convectively cooled flat plate is given by $\dfrac{T_W-T}{T_W-T_\infty }=a+b\dfrac{y}{L}+c \left (\dfrac{y}{L} \right)^2$ , where $y$ is measured perpendicular to the plate, $L$ is the plate length, and $a$, $b$ and $c$ are arbitrary constants. $T_W$ and $T_\infty$ are wall and ambient temperatures, respectively. If the thermal conductivity of the fluid is $k$ and the wall heat flux is ${q}''$  , the Nusselt number $Nu=\dfrac{{q}''}{T_W-T_\infty }\dfrac{L}{k}$  is equal to

1. $a$
2. $b$
3. $2c$
4. $(b+2c)$

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