Combined Free and Forced Convection

​
plate diagram
Gr and Re versus velocity
​
length of plate (m)
5
velocity (m/s)
5
fluid temperature (K)
260
plate temperature (K)
430
The Grashof number
Gr
and the square of the Reynolds number
Re
are plotted as functions of the velocity of air as it passes over a flat plate. The yellow area represents the region where
2
Re
/Gr<0.2
and free convection dominates heat transfer. The blue area represents the region where
2
Re
/Gr>5
and forced convection dominates heat transfer. The dashed purple line represents the air velocity (select with slider), and the Nusselt number
Nu
is displayed above the plot for that velocity. The plate diagram is a representation of the system. You can vary the plate temperature, fluid temperature and plate length with sliders.

Details

This Demonstration shows parameters that lead to combined forced and free convection over a flat plate. The conventional range where free and forced convection are combined is
0.2>
2
Re
/Gr>5
. A combined equation was used to calculate the Nusselt number
Nu
for all velocities:
1/4
Nu
=
1/4
Nu
N
+
1/4
Nu
F
,
Nu
F
=(0.037
4/5
Re
-A)
1/3
Pr
,
Nu
N
=
2
0.825+
0.387
1/6
Ra
1+
8/27
(0.492
-9/16
Pr
)
,
where the subscripts
F
and
N
refer to forced and natural convection, and
A
is a constant determined by the critical Reynolds number.
The Reynolds number is:
Re=
uL
v
,
where
u
is the velocity of air,
L
is plate length and
v
is kinematic viscosity of air.
The Grashof
Gr
and Rayleigh
Ra
numbers are:
Gr=gβ
T
S
-T
3
L
2
v
,
Ra=GrPr
,
where
g
is acceleration due to gravity,
β
is the thermal expansion coefficient (approximated as
1/T
),
T
is the air temperature,
T
S
is plate temperature and
Pr
is the Prandtl number (
v
and
Pr
are approximated by fitting an equation to a range of known values of
v
and
Pr
at corresponding temperatures for air).

References

[1] T. L. Bergman, A. S. Lavine, F. P. Incropera and D. P. DeWitt, Introduction to Heat Transfer, 6th ed., Hoboken: John Wiley and Sons, 2011.

Permanent Citation

Mathew L. Williams, Rachael L. Baumann, John L. Falconer
​
​"Combined Free and Forced Convection"​
​http://demonstrations.wolfram.com/CombinedFreeAndForcedConvection/​
​Wolfram Demonstrations Project​
​Published: April 14, 2014