For laminar flow over a flat plate, the local heat transfer coefficien

Donald Johnson 2021-12-16 Answered
For laminar flow over a flat plate, the local heat transfer coefficient hx is known to vary as x12, 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?
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Expert Answer

Laura Worden
Answered 2021-12-17 Author has 45 answers

We are given following data:
hxx12
=Kx12
Required:
×hhx
Using the relation (6.14) of average coefficient:
h=1x0xhxdx
=1x0xKx12dx
=1x×K[x12+112+1]0x
=Kx[2x12]
h=2Kx12
Calculating ratio of average coefficient between the leading edge and some locaion x on the plate to the local coefficient at x
hhx=2Kx12Kx12
hhx=2

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Barbara Meeker
Answered 2021-12-18 Author has 38 answers
Solution: We have for laminar heat flow over a flat plate the local heat transfer coefficient hx,
varies as hx,Cx12, where hx, is the coefficient at a distance x from the leading edge of the surface and the quantity C,
which depends on the fluid properties, is independent of x. Here, we
assume that hx,=Cx12.
The average heat transfer coefficient between the leading edge to some location x (say at point P) is piven by

hx=0xhxdx0xdx
=1x0xCx12dx
=2Cx[x12]0x=2Cx12=2hx
Hence,hxhx=2

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nick1337
Answered 2021-12-27 Author has 575 answers

Step1
The average heat transfer coefficient is given by as follow:-
hxo= average heat transfer coefficient
hx=x=local heat transfer coefficient
hx=0=1x0xhxdx
hx=0=1x0xCx1/2dx
hx=0=1x0xCx1/2+11/2+1dx
hx=0=1x0xCx1/21/2dx
hx=0=2x(Cx1/2)0x
Step2
after normal integration,
we get,
hx=0=2Cx1/2
hx=0=2×C×hx
hence the final result shows that the average heat transfer coefficient is twice of local heat transfer coefficient.
Therefor the ratio of average and local heat transfer coefficient = 2

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