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

ratio of the average convection heat transfer = 2

Step-by-step 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=(1)/(5L)\int\limits^5_0 {h_(x) } \, dx` (2)

subsitute
`H_(x=5L)=C5L^(0.5)` in equation 2

`H=(C)/(5L)\int\limits^5_0 {x^(-0.5)  } \, dx`

`H=(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 = (H)/(H_(x) )`

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

`r=(10CL^(-0.5))/(5CL^(-0.5) )`

`r=2`