Question

For laminar flow over a flat plate, the local heat transfer coefficient hx is known to vary as x−1/2, where x is the distance from the leading edge (x = 0) of the plate. What is the ratio of the average coefficient between the leading edge and some location x on the plate to the local coefficient at x?

Answer 1

Answer:

2

Explanation:

So for solving this problem we need the local heat transfer coefficient at distance x,

$h_x=cx^{-1/2}$

We integrate between 0 to x for obtain the value of the coefficient, so$\bar{h}_x =\frac{1}{x} \int\limit^x_0 h_x dx\\\bar{h}_x = \frac{c}{x} \int\limit^x_0 \frac{1}{\sqrt{x}}dx\\\bar{h}_x = \frac{c}{c} (2x^{1/2})\\\bar{h}_x = 2cx^{-1/2}$

Substituing

$\bar{h}_x=2h_x\\\frac{\bar{h}_x}{h_X}=2$

The ratio of the average convection heat transfer coefficient over the entire length is 2