heat transfer and fluid flow over a plate

8/7/2019 Heat Transfer and Fluid Flow Over a Plate

1/17

Heat Transfer and FluidHeat Transfer and Fluid

Flow Over a Flat PlateFlow Over a Flat Plate

MANE 4020

Fall 2005


2/17

H(x)

U0

U(y)

Ug

xo

U(x,0)=0

Boundary layer thickness: H!y U(y)/ Ug=0.99

Fluid Problem: Friction andFluid Problem: Friction and

Boundary layerBoundary layer

Xs ! Q xuxy

y!0

Shearstress


3/17

Measurement of the Velocity ProfileMeasurement of the Velocity Profile

ptotal p static !1

2V U

2

U


4/17

Laminar flow

Turbulent flow

Skin Friction CoefficientSkin Friction Coefficient

Cf |Xs

1

2VU

g

2

Cf

2!0.332

Rex1/2

Cf

2

!0.0296

Rex1/ 5

Re x U x! g R

Skin Friction Correlations

Skin Friction Measurement

Xs ! Q xu

xy y!From: (difficult to get u near to wall)


5/17

Boundary layer modelsBoundary layer models

71

!

g H

y

U

u

u! y

u! 1

Olny

B

y yu u u u | |X X

R ; u X |Xs

V

y+ u30

y+ e5

1/7th PowerLaw

More exact expression


6/17

Boundary layer modelsBoundary layer models


7/17

Convection Heat TransferConvection Heat Transfer

It quantifies the energy transfer between a

fluid at one temperature flowing over a

soli

dobject at a

differe

nt tem

perat

ure.

h !ddq

(T!

q

A(T- qis the heat flux (J/s m2 = W/m2)

(T is the difference between fluid temperature (in the

freestream) and the solidwall temperature

-A is the surface area of the solid.

-q is the total heat transfer from a surface (Watts).


8/17

Two common questions of anyTwo common questions of any

convective heat transfer problemconvective heat transfer problem Given the distribution ofsurface temperature asafunction

ofposition alongasurface, what is the distribution oflocal

heatflu ? Given the distribution oflocalsurface heatflu asa

function ofposition alongasurface, what is the

distribution ofsurface temperature?

Tfluid

Tsolid


9/17

Fluid flow and heat transfer overFluid flow and heat transfer over

flat plateflat plate -- A complex problemA complex problem

H(x)

U0, T0

U(x,y) Tw (x)

Tg (x)Ug (x)

H8(x)

T(x,y)

xo qw qw qw qw

U(x,0)=0 Tw>Tinf

Rex=Ug *x/Ris the criterion for the Turbulent/Laminar

Rex>105 for the flat plate flow

Red>2300, for the pipe flow


10/17

Stx !h

VcpUg! func

Ugx

R,RE

h is the propertyof flow

Pris the propertyof fluid

Stx! 0.453Re

x

0.5Pr

2/ 3

Stx ! 0.0307Rex0.2

Pr0.

Laminar flow can be derived

Turbulent flow - experimental

Dimensionless heat transferDimensionless heat transfer

coefficient (S

tanton #)coefficient (S

tanton #)


11/17

St decreases with the increase of Re.

St increases when the flow becomes turbulent flow.


12/17

Measurement of heat transferMeasurement of heat transfer

coefficient (I)coefficient (I)

Q0

QconvectionQradiation

Qconduction

Qo !Qconvection QbacksideQradiation


13/17

Tblack

TgTg

Tplate

Rcond


coefficient (II)coefficient (II)


14/17

Theplate is constructedof four layers of materials:

Four, 2 in. wide Ni-Chrome heating strips which are embedded in

fiberglass and epoxy resin;

3/8 in. balsa wood;

5/8 in. plywood; 1/8 in. plywood.


15/17

Qo !Qconvection QbacksideQradiation

Qo = VI

Qco ecti o ! T TRco

! T T

Qbackside !Ts Tback

Rplate

44 surrSradiation TTAQ ! IW

Tblack

TgTg

Tplate

cov

rad

co d

h


coefficient (III)coefficient (III)


16/17

Structure of Wind TunnelS

tructure of Wind Tunnel

Wind supply: Blower /Fan (quantity supply);

Settling chamber (quality supply)

Honeycomb, Mesh Screen To reduce turbulence


17/17

heat transfer and fluid flow over a plate

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