Question

For laminar flow over a flat plate, the local heat transfer coefficient $h_x$ is known to vary as $x^{-1/2}$, where x is the distance from the leading edge of the plate The ratio of the average coefficient between the leading edge and some location x = L on the plate to the local coefficient at x = L , is

• A. 3/2
• B. 2
• C. 2/3
• D. 1/2

Answer 1

The correct option is B 2

$h_x\alpha x^{-1/2}$

$h_x=c{x}^{-1/2}$

Average heat transfer coefficient $\left(\overline{h}\right)=\frac{1}{L}{\int }_0^L{h}_{x}dx$

$=\frac{1}{L}{\int }_0^{L}c{x}^{-1/2}dx$

$=\frac{1}{L}c{\left(\frac{x^{-1/2+1}}{\frac{1}{2}}\right)}_0^L$

$=\frac{2c}{L}{\left[x^{1/2}\right]}_0^L$

$=\frac{2c}{L}[x^{1/2}-0]$

= $2c.L^{-1/2}$

At location 'L'

$\frac{\overline{h}}{h_{x=L}}=\frac{2c{L}^{-1/2}}{c{L}^{-1/2}}=2$

$\frac{\overline{h}}{h_x}=2$