Download - Heat Transfer and Fluid Flow Over a Plate
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Heat Transfer and FluidHeat Transfer and Fluid
Flow Over a Flat PlateFlow Over a Flat Plate
MANE 4020
Fall 2005
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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
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Measurement of the Velocity ProfileMeasurement of the Velocity Profile
ptotal p static !1
2V U
2
U
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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)
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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
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Boundary layer modelsBoundary layer models
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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).
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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
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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
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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 #)
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St decreases with the increase of Re.
St increases when the flow becomes turbulent flow.
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Measurement of heat transferMeasurement of heat transfer
coefficient (I)coefficient (I)
Q0
QconvectionQradiation
Qconduction
Qo !Qconvection QbacksideQradiation
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Tblack
TgTg
Tplate
Rcond
Measurement of heat transferMeasurement of heat transfer
coefficient (II)coefficient (II)
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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.
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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
Measurement of heat transferMeasurement of heat transfer
coefficient (III)coefficient (III)
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Structure of Wind TunnelS
tructure of Wind Tunnel
Wind supply: Blower /Fan (quantity supply);
Settling chamber (quality supply)
Honeycomb, Mesh Screen To reduce turbulence
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