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

2

Step-by-step 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 =(1)/(x) \int\limit^x_0 h_x dx\\\bar{h}_x = (c)/(x) \int\limit^x_0 (1)/(√(x))dx\\\bar{h}_x = (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