Question

In an experiment, the local heat transfer over a flat plate were correlated in the form of local Nusselt number as expressed by the correlation Nux=0.035Rex^(0.8) Pr^(1/3) Determine the ratio of the average convection heat transfer coefficient (h) over the entire plate length to the local convection heat transfer coefficient (hx) (h/hx = L) at x = L.

Answer 1

Answer:

$\dfrac{\bar{h}}{h}=\dfrac{5}{4}$

Explanation:

Given that

$Nu_x=0.035Re_x^{0.8} Pr^{1/3}$

We know that

Rex=ρvx/μ

So

$Nu_x=0.035Re_x^{0.8} Pr^{1/3}$

$Nu_x=0.035\times\left(\dfrac{\rho vx}{\mu}\right)^{0.8}Pr^{1/3}$

All other quantities are constant only x is a variable in the above equation .so lets take all other quantities as a constant C

$Nu_x=C.x^{0.8}=C.x^{4/5}$

We also know that

Nux=hx/K

$C.x^{4/5}=\dfrac{hx}{k}$

m is the constant

$h=mx^{-1/5}$

This is local heat transfer coefficient

The average value of h given as

$\bar{h}=\dfrac{\int_{0}^{L}hdx}{L}$

$\bar{h}=\dfrac{5m}{4}\times\dfrac{L^{4/5}}{L}$

$\bar{h}=\dfrac{5m}{4}L^{-1/5}$             ---------1

The value of local heat transfer coefficient at x=L

$h=mx^{-1/5}$

$h=mL^{-1/5}$            -----------2

From 1 and 2 we can say that

$\dfrac{\bar{h}}{h}=\dfrac{5}{4}$