Transferência de Calor por Convecção
Profa. Flávia Zinani
PPGENGMEC
fzinani@unisinos.br – sala 6A-234
Introduction
Introdução
Introduction
Introdução
Introdução
Introduction
Introduction
Introdução
Local and Average Coefficients
Distinção entre Coeficiente de Transferência de
Calor Local e Médio
•
Coeficiente e Fluxo de Calor Local:
qs  h Ts  T 
Fluxo de Calor Médio e Coeficiente para Temperatura Uniforme na
Superfície
•
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
shear stresses and velocity gradients.
– 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
by temperature gradients and heat
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 < Rex,c? If ReL > 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 Transferência de
Calor por Convecção?
h  h(Ts ,T ,  ,  , k , c p , u, x,geometria, dimensões)
Utilizando o teorema dos Pi de Buckingham e tornando o problema
adimensional
•
Nu  Nu ( x*,Re,Pr )
hL
Nu 
k
Nu  Nu (Re,Pr )
VL

Re 
Pr 


Significado dos números adimensionais
• Número de Reynolds
Significado dos números adimensionais
• Número de Prandtl: razão entre a difusividade de
quantidade de movimento e a difusividade térmica.
Está relacionado ao crescimento relativo entre as
camadas-limite fluidodinâmica e térmica:
• Pr<<1: metais líquidos, difusão térmica mais eficiente
que difusão de momentum, t>>.
• Pr1: gases, t.
• Pr>>1: óleos, difusão de momentum mais eficiente
que difusão térmica, t<<.
Significado dos números adimensionais
• Número de Nusselt: representa o gradiente de
temperatura adimensional na superfície, mede
a transferência de calor por convecção que
ocorre nesta superfície.
(provar)
Significado dos números adimensionais
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  .
• Conservação da Massa: Equação da Continuidade
div u  0
u v w
 
0
x y z
ui
 ui ,i   iui  0
xi
• Equação 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?
Referência para a dedução das equações de Navier-Stokes e da continuidade:
Bejan, Adrian - Convective Heat Transfer
Fox, McDonald e Pritchard – Introdução à Mecânica dos Fluidos