Question

For laminar flow over a flat plate the local heat transfer coefficient varies as hx 5 Cx20.5, where x is measured from the leading edge of the plate and C is a constant. Determine the ratio of the average convection heat transfer coefficient over the entire plate of length L to the local convection heat transfer coefficient at the end of the plate (x 5 L).

Answer 1

Answer:

ratio of the average convection heat transfer = 2

Explanation:

local heat transfer expression can be written as

$H_{x}=Cx^{0.5}$       (1)

C= Constant

x=measured from the leading edge of the plate

We need to find local heat transfer coefficient at

 x=5L

so for equation 1 it can be written as

$H_{x=5L}=C5L^{0.5}$

we can find the average heat transfer over entire lenght of plate as

$H=\frac{1}{5L}\int\limits^5_0 {h_{x} } \, dx$  (2)

subsitute $H_{x=5L}=C5L^{0.5}$ in equation 2

$H=\frac{C}{5L}\int\limits^5_0 {x^{-0.5}  } \, dx$

$H=\frac{10C}{L}L^{-0.5}$

$h=10CL^{-0.5}$

for ratio of the average convection heat transfer coefficient over the entire plate of length L to the local convection heat transfer coefficient at the end of the plate is given as

$ratio = \frac{H}{H_{x} }$

Now putting values for H ,Hx and 5L for x

$r=\frac{10CL^{-0.5}}{5CL^{-0.5} }$

$r=2$