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AME 60634
Int. Heat Trans.
Flow and Thermal Considerations
When a moving fluid comes into contact with a surface at some temperature
difference (e.g. heated surface, cold fluid) the fluid will
• transfer heat to/from the surface in a process analogous to
conduction (random motion of the fluid)
• advect heat away from the point of contact by its motion (bulk motion
of the fluid)
The combined effect of these two phenomena is called convection, which is
described by Newton’s Law of Cooling
q"= h(Ts - T¥ )
heat flux
[W/m2]
heat transfer coefficient
[W/m2-K]
fluid temperature
[K]
surface temperature
[K]
Implications:
• the “direction” of heat flux can be considered normal to the surface
• the heat transfer coefficient is related of the nature of the fluid flow
• in order to study convection heat transfer we must also study fluid dynamics
D. B. Go
AME 60634
Int. Heat Trans.
Convection Coefficients
• There are local and average heat transfer coefficients
– because flow conditions vary along a surface both the local heat flux
(q”) and local heat transfer coefficient (h or hx) vary along the surface
• The local heat transfer coefficient is defined as
h=
q"
q¢x¢
or hx =
(Ts - T¥ )
(Ts,x - T¥ )
• The average heat transfer coefficient is defined as
q=
ò q"dA = ò h(T - T )dA
s
As
D. B. Go
s
As
¥
s
= h As (Ts - T¥ )
1
h=
hdAs
ò
As A s
AME 60634
Int. Heat Trans.
Fluid Dynamics: Boundary Layers
• Velocity Boundary Layer (External Flow)
– consequence of viscous effects associated with relative motion between a
fluid and a surface
– region of the flow characterized by shear stresses and velocity gradients
– region between the surface and free stream whose thickness δ increases
in the flow direction
– manifested by a surface shear stress τs that generates a drag force FD.
approximate boundary
layer thickness
spherical
μ is the dynamic viscosity of the fluid
D. B. Go
shear stress for
du
ts = m
dy y= 0 Newtonian fluids
FD =
ò t dA
s
As
s
drag force over surface
area
AME 60634
Int. Heat Trans.
Fluid Dynamics: Boundary Layers
• Thermal Boundary Layer (External Flow)
– consequence of heat transfer between the surface and fluid
– region of the flow characterized by heat fluxes and temperature
gradients
– region between the surface and free stream whose thickness δt
increases in the flow direction
– manifested by a surface heat flux, q”s that provides a convection heat
transfer coefficient, h.
approximate
boundary layer
thickness
q¢s¢ = -k f
spherical
h=
D. B. Go
kf is the thermal conductivity of the fluid
dT
dy
y= 0
-k f dT dy y=0
Ts - T¥
heat flux at the
surface
heat transfer
coefficient
AME 60634
Int. Heat Trans.
Fluid Dynamics: Boundary Layers
• Boundary Layer Equations
– 2D, steady, incompressible flow
– negligible body forces
– constant & uniform fluid properties (μ,C,k)
• Apply conservation of mass, momentum, and energy to
differential control volume (dxdy)
D. B. Go