Estimation of Convective Heat
Transfer Coefficient
Convective heat transfer coefficient
• Convective heat transfer coefficient (h) is predicted from
empirical correlations.
• The coefficient is influenced by such parameters as type
and velocity of fluid, physical properties of fluid,
temperature difference, and the geometrical shape of the
physical system underconsideration.
• Dimensional analysis is used to develop empirical
correlations that allow estimation of h.
• Following correlations apply to Newtonian fluids only. For
expression for non-Newtonian fluids, the textbook by
Heldman and Singh (1981) is recommended.
Force convection
Fluid is forced to move over an object by external
mechanical means
NNu = (NRe, NPr)
Where NNu = Nusselt number = hD/k
h
= convective heat-transfer coefficient
(W/ m2oC)
D
k
NRe
NPr
=
=
=
=
characteristic dimension (m)
thermal conductivity (W/moC)
Reynolds number = uD/
Prandtl number
= Cp/k
Laminar flow in horizontal pipes
When Reynolds number < 2100
For (NRe x NPr x D )
 100
For (NRe x NPr x D )
> 100
L
L
All physical properties are evaluated at bulk fluid temp. except w is
at surface temp of wall.
D = characteristic dimension = diameter of pipe
Example
• Water flowing at a rate of 0.02 kg/s is heated
from 20 to 60C in a horizontal pipe (inside
diameter = 2.5 cm). The inside pipe surface
temperature is 90C. Estimate h if the pipe is
1 m long.
Transition flow in horizontal pipes
When Reynolds number between 2100 and 10000
Turbulent flow in horizontal pipe
When Reynolds number > 10000
All physical properties are evaluated at bulk fluid temp. except w is
at surface temp of wall.
D = characteristic dimension = diameter of pipe
Example
• Water flowing at a rate of 0.2 kg/s is heated
from 20 to 60C in a horizontal pipe (inside
diameter = 2.5 cm). The inside pipe surface
temperature is 90C. Estimate h if the pipe is
1 m long.
Example
• What is the expected percent increase in
convective heat transfer coefficient if the
velocity of the fluid is doubled while all
other related parameters are kept the
same for turbulent flow in a pipe.
Convection in non-circular ducts
Equations for circular tube with hydraulic
diameter
Flow past immersed objects
• For flat plate
1/2
NNu = 0.664 NRe
1/3
NPr
• For cylinder
if fluid is gas
if fluid is liquid
NRe
0.4-4
4-40
40-4000
4000-40000
40000-400000
NNu
NNu
C
0.989
0.911
0.683
0.193
0.0266
=
=
C NRe
C NRenNPr1/3
n
0.330
0.385
0.466
0.618
0.805
Flow past immersed objects
Flow past immersed objects
• For single sphere
NNu =
2 + 0.60NRe0.5 X NPr1/3
where 1 < NRe < 70,000
0.6 < NPr < 400
Fluid properties are evaluated at film
temperature (Tf) where
Tf =
(Twall + Tmedium) / 2
Example
• Calculate
convective
heat
transfer
coefficient when air at 90C is passed
through a deep bed of green peas.
Assume surface temperature of a pea to
be 30C. The diameter of each pea is 0.5
cm. The velocity of air through the bed is
0.3 m/s.
Free convection
Free convection occurs due
to density differences in
fluids as they come into
contact with a heated
surface. The low density of
fluid at a higher temperature
causes buoyancy forces, and
as a result, heated fluid
moves upward and colder
fluid takes its place
NNu =
hD
k
= a (NGr NPr)m
where a, m = constants
NGr = Grashof number = D32gT/2
D = characteristic dimension (m)
 = coefficient of volumetric expansion (K-1)
T = Temperature difference between wall
and surrounding bulk (oC)
All physical properties are evaluated at film temperature
(Tf = (Tw+Tb)/2)
Use Figure A
Use Figure B
Figure A
Figure B
Example
Estimate the convective heat transfer coefficient
for convective heat loss from a horizontal 10 cm
diameter stem pipe. The surface temperature of
the uninsulated pipe is 130C, and the air
temperature is 30C
Other empirical equations for
h estimation
1. Forced Convection Flow Inside a
Circular Tube
• All properties at fluid bulk mean
temperature (arithmetic mean of
inlet and outlet temperature).
• Nusselt numbers Nu0 from
sections 1-1 to 1-3 have to be
corrected
for
temperaturedependent
fluid
properties
according to section 1-4.
1-1 Thermally developing, hydrodynamically
developed laminar flow (Re < 2300)
Constant wall temperature:
(Hausen)
Constant wall heat flux:
(Shah)
1-2 Simultaneously developing laminar flow (Re
< 2300)
Constant wall temperature:
(Stephan)
Constant wall heat flux:
which is valid over the range 0.7 < Pr < 7 or if Re
Pr D/L < 33 also for Pr > 7.
1-3 Fully developed turbulent and transition
flow (Re > 2300)
Constant wall heat flux:
(Petukhov,
Gnielinski)
where
Constant wall temperature:
For fluids with Pr > 0.7 correlation for constant wall
heat flux can be used with negligible error.
1-4 Effects of property variation with
temperature
Liquids, laminar and turbulent flow:
Subscript w: at wall temperature, without subscript:
at mean fluid temperature
Gases, laminar flow: Nu = Nu0
Gases, turbulent flow:
Temperatures in Kelvin
2. Forced Convection Flow Inside Concentric
Annular Ducts, Turbulent (Re > 2300)
All properties at fluid bulk mean
temperature (arithmetic mean of inlet
and outlet temperature).
Dh = Do - Di
Heat transfer at the inner wall, outer wall insulated:
(Petukhov and Roizen)
Heat transfer at the outer wall, inner wall insulated:
(Petukhov and Roizen)
Heat transfer at both walls, same wall temperatures:
(Stephan)
3. Forced Convection Flow Inside Non-Circular
Ducts, Turbulent (Re > 2300)
Equations for circular tube with hydraulic
diameter
4. Forced Convection Flow Across Single
Circular Cylinders
D = cylinder diameter, um = free-stream velocity,
all properties at fluid bulk mean temperature.
4-1 Smooth circular cylinder
Valid over the ranges 10 < Rel < 107 and
0.6 < Pr < 1000
(Gnielinski)
where
4-2 Effects of property variation
with temperature
Liquids:
Subscript w: at wall temperature,
without subscript: at mean fluid temperature.
Gases:
Temperatures in Kelvin.
5. Forced Convection Flow over a Flat Plate
All properties at mean film temperature
Laminar boundary layer, constant wall temperature:
(Pohlhausen)
valid for ReL < 2x105, 0.6 < Pr < 10
Turbulent boundary layer along the whole plate,
constant wall temperature:
(Petukhov)
Boundary layer with laminar-turbulent transition:
(Gnielinski)
6. Natural Convection
All properties at
L = characteristic length
Nu0
"Length" L
Vertical wall
0.67
H
Horizontal cylinder
0.36
D
Sphere
2.00
D
For ideal gases:
(temperature in K)
(Churchill, Thelen)
valid for 10-4 < Gr Pr < 4x1014,
0.022 < Pr < 7640, and constant wall temperature
Combined free and forced
convection
• From J.P. Holman (1992)
UWT = uniform wall temp., UHF = uniform heat flux
Aiding flow = forced and free convec. Are in the same direction while opposite flow
means they are in opposite direction.
=
=