|
Download a Printable Version Here (Adobe Acrobat Format) Correlations for Convective Heat Transfer
In many cases it's convenient to have simple equations for estimation of heat transfer coefficients. Below is a collection of recommended correlations for single-phase
1 Forced Convection Flow Inside a Circular Tube
|
|
Dh = Do - Di
All properties at fluid bulk mean temperature (arithmetic mean of inlet and outlet temperature). |
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)
Equations for circular tube with hydraulic diameter
D = cylinder diameter, um = free-stream velocity, all properties at fluid bulk mean temperature. Correction for temperature dependent fluid properties see section 4-4.
4-1 Smooth circular cylinder
(Gnielinski)
where
Valid over the ranges 10 < Rel < 107 and 0.6 < Pr < 1000
4-2 Tube bundle
Transverse pitch ratio
Longitudinal pitch ratio
Void ratio for b > 1
for b < 1
Nu0,bundle = fANul,0 (Gnielinski)
Nul,0 according to section 4-1 with instead of Rel.
Arrangement factor fA depends on tube bundle arrangement.
In-line arrangement:
Staggered arrangement:
4-3 Finned tube bundle
In-line tube bundle arrangement:
(Paikert)
Staggered tube bundle arrangement:
(Paikert)
4-4 Effects of property variation with temperature
Liquids:
Subscript w: at wall temperature, without subscript: at mean fluid temperature.
Gases:
Temperatures in Kelvin.
|
All properties at mean film temperature
Laminar boundary layer, constant wall temperature:
(Pohlhausen)
valid for ReL < 2·105, 0.6 < Pr < 10
Turbulent boundary layer along the whole plate, constant wall temperature:
(Petukhov)
Boundary layer with laminar-turbulent transition:
(Gnielinski)
All properties at
L = characteristic length (see below)
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 < 4·1014,
0.022 < Pr < 7640, and constant wall temperature
All properties without subscript are for condensate at the mean temperature
Exception: = vapor density at saturation temperature Ts
7-1 Laminar film condensation
Vertical wall or tube:
(Nusselt)
Tw = mean wall temperature
Horizontal cylinder:
(Nusselt)
Tw = const.
7-2 Turbulent film condensation
For vertical wall
Re = C Am
Recrit = 350
turbulent film: (Grigull)
Tw = temperature of heating surface
Ts = saturation temperature
Heat transfer at ambient pressure:
(Stephan and Preußer)
' saturated liquid
'' saturated vapor
Bubble departure diameter
Angle | = rad for water |
= 0.0175 rad for low-boiling liquids | |
= 0.611 rad for other liquids |
For water in the range of 0.5 bar < p < 20 bar and 104 W/m2
< <
106 W/m2
the following equation may be applied:
(Fritz)
cp | specific heat capacity at constant pressure |
D, d | diameter |
g | gravitational acceleration |
h | mean heat transfer coefficient |
enthalpy of evaporation | |
H | height |
k | thermal conductivity |
L | length |
heat flux | |
T | temperature |
u | flow velocity |
thermal diffusivity | |
coefficient of thermal expansion | |
dynamic viscosity | |
kinematic viscosity | |
density | |
surface tension |
Subscripts
h | hydraulic |
i | inside |
m | mean |
o | outside |
s | saturation |
w | wall |
Dimensionless numbers
Gr | Grashof number |
Nu | mean Nusselt number |
Pr | Prandtl number |
Re | Reynolds number |
By: Dr. Bernhard Spang, Associate Content Writer (read the author's Profile)
b.spang@gmx.net
ChE Plus Subscriber - Click Here for a Printable Version
Send this Page to a Friend