# Conveccão - aula 1

```Transfer&ecirc;ncia de Calor por Convec&ccedil;&atilde;o
Profa. Fl&aacute;via Zinani
PPGENGMEC
[email protected] – sala 6A-234
Introduction
Introdu&ccedil;&atilde;o
Introduction
Introdu&ccedil;&atilde;o
Introdu&ccedil;&atilde;o
Introduction
Introduction
Introdu&ccedil;&atilde;o
Local and Average Coefficients
Distin&ccedil;&atilde;o entre Coeficiente de Transfer&ecirc;ncia de
Calor Local e M&eacute;dio
•
Coeficiente e Fluxo de Calor Local:
qs  h Ts  T 
Fluxo de Calor M&eacute;dio e Coeficiente para Temperatura Uniforme na
Superf&iacute;cie
•
q  hAs Ts  T 
q  As qdAs  Ts  T  A hdAs
s
1
h  As hdAs
As
Boundary Layer Features
Boundary Layers: Physical Features
Boundary Layer Features
Boundary Layers: Physical Features
• Velocity Boundary Layer
– A consequence of viscous effects
associated with relative motion
between a fluid and a surface.
– A region of the flow characterized by
– A region between the surface
and the free stream whose
thickness  increases in
the flow direction.
– Why does  increase in the flow direction?
– Manifested by a surface shear
stress  s that provides a drag
force, FD .
– How does  s vary in the flow
direction? Why?

u  y
u
u
s  
y
 0.99
y 0
FD    s dAs
As
Boundary Layer Features (cont.)
• Thermal Boundary Layer
– A consequence of heat transfer
between the surface and fluid.
– A region of the flow characterized
fluxes.
– A region between the surface and
the free stream whose thickness t
increases in the flow direction.
– Why does  t increase in the
flow direction?
– Manifested by a surface heat
flux q s and a convection heat
transfer coefficient h .
– If Ts  T  is constant, how do q s and
h vary in the flow direction?
t 
Ts  T  y 
Ts  T
T
qs  k f
y
h
 0.99
y 0
 k f T / y
Ts  T
y 0
Transition
Boundary Layer Transition
• How would you characterize conditions in the laminar region of boundary layer
development? In the turbulent region?
• What conditions are associated with transition from laminar to turbulent flow?
• Why is the Reynolds number an appropriate parameter for quantifying transition
from laminar to turbulent flow?
• Transition criterion for a flat plate in parallel flow:
u x
Re x ,c   c  critical Reynolds number

xc  location at which transition to turbulence begins
105  Re x ,c  3 x 106
~
~
Transition (cont.)
What may be said about transition if ReL &lt; Rex,c? If ReL &gt; Rex,c?
Transition (cont.)
• Effect of transition on boundary layer thickness and local convection coefficient:
Why does transition provide a significant increase in the boundary layer thickness?
Why does the convection coefficient decay in the laminar region? Why does it increase
significantly with transition to turbulence, despite the increase in the boundary layer
thickness? Why does the convection coefficient decay in the turbulent region?
Do que depende o Coeficiente de Transfer&ecirc;ncia de
Calor por Convec&ccedil;&atilde;o?
h  h(Ts ,T ,  ,  , k , c p , u, x,geometria, dimens&otilde;es)
Utilizando o teorema dos Pi de Buckingham e tornando o problema
•
Nu  Nu ( x*,Re,Pr )
hL
Nu 
k
Nu  Nu (Re,Pr )
VL

Re 
Pr 


• N&uacute;mero de Reynolds
• N&uacute;mero de Prandtl: raz&atilde;o entre a difusividade de
Est&aacute; relacionado ao crescimento relativo entre as
• Pr&lt;&lt;1: metais l&iacute;quidos, difus&atilde;o t&eacute;rmica mais eficiente
que difus&atilde;o de momentum, t&gt;&gt;.
• Pr1: gases, t.
• Pr&gt;&gt;1: &oacute;leos, difus&atilde;o de momentum mais eficiente
que difus&atilde;o t&eacute;rmica, t&lt;&lt;.
• N&uacute;mero de Nusselt: representa o gradiente de
a transfer&ecirc;ncia de calor por convec&ccedil;&atilde;o que
ocorre nesta superf&iacute;cie.
(provar)
Boundary Layer Equations
The Boundary Layer Equations
• Consider concurrent velocity and thermal boundary layer development for
incompressible flow with constant fluid properties   , c p , k  .
• Conserva&ccedil;&atilde;o da Massa: Equa&ccedil;&atilde;o da Continuidade
div u  0
u v w
 
0
x y z
ui
 ui ,i   iui  0
xi
• Equa&ccedil;&atilde;o de Navier-Stokes
Du
2

 p   u  g
Dt
u
1
 [u]u   p    2u  g
t

What is the physical significance of each term in the foregoing equation?
Refer&ecirc;ncia para a dedu&ccedil;&atilde;o das equa&ccedil;&otilde;es de Navier-Stokes e da continuidade:
Bejan, Adrian - Convective Heat Transfer
Fox, McDonald e Pritchard – Introdu&ccedil;&atilde;o &agrave; Mec&acirc;nica dos Fluidos
```