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Introduction To Convection

This document introduces convection and describes methods for determining the convective coefficient h. The local convective coefficient h is defined as the ratio of local heat flux to temperature difference between the surface and free stream. For a flat plate, the averaged convective coefficient is used. The boundary layer equations are presented and Reynolds and Prandtl numbers are important parameters. Dimensionless variables are introduced. The Nusselt number relates the convective coefficient to thermal conductivity and characteristic length. Boundary layer analogy means systems with the same parameters will have the same heat convection coefficients.

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46 views1 page

Introduction To Convection

This document introduces convection and describes methods for determining the convective coefficient h. The local convective coefficient h is defined as the ratio of local heat flux to temperature difference between the surface and free stream. For a flat plate, the averaged convective coefficient is used. The boundary layer equations are presented and Reynolds and Prandtl numbers are important parameters. Dimensionless variables are introduced. The Nusselt number relates the convective coefficient to thermal conductivity and characteristic length. Boundary layer analogy means systems with the same parameters will have the same heat convection coefficients.

Uploaded by

tahapak
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
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INTRODUCTION TO CONVECTION

6.2

Objective : determine convective coefficient h

CONVECTION COEFFICIENT
=
qconv

free stream
T

q =

= h (Ts T )
qconv

function of
a location

conv

=
A

A


A (Ts T ) = h A ( Ts T )

dAs

h dA

averaged
convective
coefficient

h =

total heat rate

free stream
T

= h (Ts T )
qconv

q = h (Ts T ) A

flat plate

Ts = const

VELOCITY

THERMAL

BOUNDARY LAYER

BOUNDARY LAYER

velocity
profile

free
stream

velocity
boundary
layer

hL =

temperature
profile

thermal
boundary
layer

u = 0.99u

h dx

convective
coefficient
for flat plate

free
stream

averaged

6.1

(Ts T ) h dA

h dA

u
Ts = const

dA = h (Ts T )dA =

local convective
h=
coefficient

Ts T
= 0.99
Ts T




T

( x)

qs

t ( x )

conductivity
of fluid k f

flat plate

friction
coefficient

Cf =

s =

shear
stress

u 2

kg

dynamic
viscosity

surface

N s


= 2
m
sm

u
y

local convective coefficient:


qs local heat flux

T
k f
y

BOUNDARY LAYER EQUATIONS

6.3 6.4

Rex =
v

La min ar

Transition

k f



y =0

m2

kinematic
viscosity

= h (Ts T )

h =

y =0

u x
u x
=

Reynolds
Number

Turbulent
The Convection Equations ( Appendix D 1 5 )

u
Boundar Layer Approximations ( 6.25 ) :

2u
2u
<< 2
x 2
y

6.5

xc

Recr =

u xc

= 5 10 5

PARAMETERS

Reynolds

ReL =

VL

Boundary Layer Equations (dinesionless)

( flat plate )

p
u = f x , y ,ReL ,
x

Pr =

p
T = f x , y ,ReL ,Pr,
x

Nusselt

Nu =

hL
k

Nu = f ( x ,ReL ,Pr )

hL
k

____

Nu =

2T
2T
<< 2
x 2
y

Boundary Layer Equations (Laminar)

Prandtl

____


x
Ts

Nu = f ( ReL ,Pr )

(6.26 6.30 )
( 6.35 6.36 )

T
y

y =0

Ts T

dimensionless
variables ( 6.31 33 ) :

x =

x
L

y =

y
L

u =

u
V

v =

v
V

T =

T Ts
T Ts

Boundary Layer Analogy:


the systems with the same parameters
have the same heat convection coefficients

Convective coefficient h
will be determined from Nu:
h=

Nu k
L

Ludwig Prandtl ( 1875 1953 )

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