Heat Transfer and Fluid Heat Transfer and Fluid Flow Over a Flat PlateFlow Over a Flat Plate

MANE 4020Fall 2005

(x)

U0

U(y)

U

xo

U(x,0)=0

Boundary layer thickness: yU(y)/ U =0.99

Fluid Problem: Friction and Fluid Problem: Friction and Boundary layerBoundary layer

s u

yy0

Shear stress

Measurement of the Velocity ProfileMeasurement of the Velocity Profile

ptotal pstatic1

2 U2

U

Laminar flow

Turbulent flow

Skin Friction CoefficientSkin Friction Coefficient

C f s

12 U

2

C f

2

0.332

Rex1/ 2

C f

2

0.0296

Rex1/ 5

Re x U x

Skin Friction Correlations

Skin Friction Measurement

s u

yy0

From: (difficult to get u near to wall)

Boundary layer modelsBoundary layer models

71

y

U

u

u y

u 1

ln y B

y yu u u u ; u s

y+ 30

y+ 5

1/7th Power Law

More exact expression

Boundary layer modelsBoundary layer models

Convection Heat TransferConvection Heat Transfer

It quantifies the energy transfer between a fluid at one temperature flowing over a solid object at a different temperature.

h q

T

q

AT- q” is the heat flux (J/s m2 = W/m2)T is the difference between fluid temperature (in the freestream) and the solid wall temperature-A is the surface area of the solid. -q is the total heat transfer from a surface (Watts).

Two common questions of any Two common questions of any convective heat transfer problemconvective heat transfer problem

Given the distribution of surface temperature as a function of position along a surface, what is the distribution of local heat flux?

Given the distribution of local surface heat flux as a function of position along a surface, what is the

distribution of surface temperature? Tfluid

Tsolid

Fluid flow and heat transfer over Fluid flow and heat transfer over flat plate - A complex problemflat plate - A complex problem

(x)

U0 , T0

U(x,y) Tw (x)

T (x)U (x)

(x)

T(x,y)

xo qw qw qw qw

U(x,0)=0 Tw>Tinf

Rex= U *x/is the criterion for the Turbulent/LaminarRex>105 for the flat plate flowRed >2300, for the pipe flow

Stx h

cpUfunc

Ux

,

h is the property of flow Pr is the property of fluid

Stx 0.453Re x0.5 Pr 2/ 3

Stx 0.0307Re x0.2 Pr 0.4

Laminar flow – can be derived

Turbulent flow - experimental

Dimensionless heat transfer Dimensionless heat transfer coefficient (Stanton #)coefficient (Stanton #)

St decreases with the increase of Re.St increases when the flow becomes turbulent flow.

Measurement of heat transfer Measurement of heat transfer coefficient (I)coefficient (I)

Q0

QconvectionQradiation

Qconduction

Qo Qconvection Qbackside Qradiation

Tblack

TT

Tplate

Rconv

R rad

Rcond

Measurement of heat transfer Measurement of heat transfer coefficient (II)coefficient (II)

The plate is constructed of 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.

Qo Qconvection Qbackside Qradiation

Qo = VI Qconvection

Ts TR conv

hA(Ts T )

Qbackside Ts Tback

Rplate

44surrSradiation TTAQ

Tblack

TT

Tplate

Rconv R rad

Rcond

h

Measurement of heat transfer Measurement of heat transfer coefficient (III)coefficient (III)

Structure of Wind TunnelStructure of Wind Tunnel

Wind supply: Blower /Fan (quantity supply); Settling chamber (quality supply)

Honeycomb, Mesh Screen To reduce turbulence