Heat Transfer
DM23815
Chapter 6. Introduction to convection
Eunseop Yeom
esyeom@pusan.ac.kr
School of Mechanical Engineering, Pusan National University
6. Convection
Heat transfer due to a superposition of energy transport by the random motion
of the molecules (diffusion), and by the bulk motion of the fluid
(advection).
(The term convection refers to heat transfer that will occur between a solid surface and the adjacent
fluid when they are at different temperatures.)
Newton's law of cooling
Convective heat flux
  hTs  T 
qconv
Ts and T∞ : Temperatures at surface and fluid [K].
h : Convection heat transfer coefficient [W/m2·K].
 Example of convection
Cooling of boiled-egg
Fluid motion forced by fan or buoyancy forces cool
boiled-egg down.
2
6. Convection
Cooling fan
 Forced convection
Fluid motion is forced by external means, such as
a fan, a pump, or the wind.
Hot air balloon
 Natural (or free) convection
Fluid motion is set up by buoyancy effects resulting
from density difference caused by temperature
difference in the field.
 Convection with phase change
A latent heat exchange is associated with phase change between liquid and vapor states of the
liquid. Two special cases are boiling and condensation.
 Convection heat transfer coefficient
Process
h depends on conditions in the
boundary layer, which are influenced by
① Surface geometry
② The nature of the fluid motion
③ An assortment of fluid thermodynamic properties
h (W/m2·K)
Free convection
Gases
2 - 25
Liquids
50 - 1,000
Forced convection
Gases
25 - 250
Liquids
100 - 20,000
Convection with phase change
3
Boiling and condensation
2,500 - 100,000
6. Convection
 Dimensionless Parameters
Reynolds number
Re 
inertia force
viscous force
A criterion to determine the change from laminar to turbulent flow.
Prandtl number
Pr 
molecular diffusivity of momentum
molecular diffusivity of heat
A measure of relative effectiveness of momentum and energy
transport by diffusion in the velocity and thermal boundary layers.
Nusselt number
Nu 
4
heat transfer by convection
heat transfer by conduction
When convection and conduction have similar magnitude,
Nusselt number closes to one.
Continue
6. Convection
Stanton number
St 
heat flux to the fluid
h
ρC p u

thermal capacity of fluid flow
Stanton number arises in the consideration of the geometric similarity of
the momentum boundary layer and the thermal boundary layer.
Eckert number
Ec 
kinetic energy of flow
boundary layer enthalpy difference
The magnitude of the Eckert number becomes the criterion in
deciding whether the viscous-energy-dissipation effects should be
considered in the heat transfer analysis.
Grashof number
Gr L 
5
buoyancy force
viscous force

g  T x - T  L c

2
3
β: the coefficient of thermal expansion
It is important parameter in the study of natural convection.
6.1.1 Velocity Boundary Layer
 Velocity boundary layer δ (x)
- A consequence of viscous effects associated with relative motion between a fluid and
a surface.
- For external flow, the distance from the surface of the plate where the velocity
becomes 99% of the free-stream value.
On the flat plate
In a circular tube
Critical Re
Hydrodynamic entry length
6
6.1.1 Velocity Boundary Layer
 Surface Shear Stress
When a viscous fluid is stirred, the force resisting the relative motion of solid surfaces occurs.
Friction force per unit area, τ
τs  μ
u
y
y 0
[N/m2]
μ : viscosity
A measure of resistance to flow, and a strong function of temperature
A more practical approach in external flows relate τs to the upstream velocity u∞ as
Cf 
τs
u 2 /2
where Cf is the dimensionless friction coefficient(마찰계수), whose value in most cases is
determined experimentally. Thus, the friction force (Ff) over the entire surface (As) is
determined from
u 2
F f  C f As
2
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6.1.1 Thermal boundary layer
 Thermal boundary layer δt(x)
- As velocity boundary layer develops, a thermal boundary layer also develops. When
there is temperature difference between the fluid and surface.
- A consequence of heat transfer between the surface and fluid.
- The distance from the surface at which the temperature difference equals 99% of
temperature difference between fluid and surface.
δt 
8
Ts  T  y 
 0.99
T s  T
As thermal boundary layer develops along streamwise direction, thermal gradient at
surface is varied.
6.2 Local and Average Convection Coefficients
Considering condition that fluid flows over a surface of arbitrary shape and area,
surface heat flux and convection heat transfer coefficients vary along surface.
 Total heat flux based on local heat flux
q   qdAs  Ts  T   hdAs
As
As
 Total heat flux based on
 Average convection coefficient h
h
9
1
As
 hdA
s
As
w
6.3 Laminar and Turbulent Flow
Velocity boundary layer development on a flat plate
- Velocity distribution determines advection component
of thermal energy transfer.
- Similar to velocity boundary layer, thermal boundary
layer grows along streamwise direction.
- Turbulent mixing promotes increase in heat transfer.
- Difference in velocity and thermal boundary layers is
much smaller in turbulent flow than in laminar flow.
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Variation of boundary layer(δ) and heat transfer
coefficient(h) for isothermal flat plate
6.4 boundary Layer Equations
 Continuity equation (연속 방정식)
This is essentially the equation for the conservation of mass.
Differential control volume
ρv 

 ρv dy
y
dy
ρu 
ρu

 ρu dx
x
Net rate at which
Rate of increase of
mass enters the
= mass stored within
control vol.
the control vol.
y
x
x, y 
dx
ρv
dz  1
 ρu dy   ρu 

11

 ρu dx dy   ρv dx   ρv    ρv dy dx  0
x
y


