Biomedical Engineering Reference
In-Depth Information
The movement of the hot air by differences in fluid density is a prime example of unforced
convection. Normally, free convection is much smaller in magnitude than forced convection,
since the movement of fluid via density differences is often far smaller than the movement of
fluid via pressure gradients. Hot air rises but at a rate far smaller than forced hot air from a
heat pump through vents or via windchill from a strong wind.
Convective heat loss can generally be approximated by a convective heat loss coefficient
used in the generalized equation
Q
c
¼
h
c
A
D
T
where
Q
c
¼
convection heat transfer rate
h
c
¼
convective heat transfer coefficient
A
¼
area over which heat transfer occurs
D
T
¼
temperature gradient between the surface and the environment
Typically, the convective heat transfer coefficient is a function of fluid velocity for forced
convective heat transfer. There are several versions of the equation relating the convective
heat transfer coefficient to fluid velocity. One such example is
6v
0:67
h
c
¼
5
:
where v is in m/sec and h
c
is in kcal/m
2
-hr-
o
C.
As the fluid velocity increases, so does the convection heat transfer, which increases the
convective heat transfer rate. Thus, as the wind velocity increases, so does the windchill,
which is an example of convection cooling. The convection heat transfer rate for free (natu-
ral) convection is normally a constant at about 2-2.3. If one equates the free convective coef-
ficient with the forced coefficient equation, then the air velocity required for the forced term
to exceed the free term is
6v
0:67
with v
0:67
2
:
3
¼
5
:
¼
2
:
3
=
5
:
6
¼
0
:
4107
and therefore
v
¼
0
:
263 m
=
sec or v
¼
0
:
588 mph
Thus, any wind speed over about a half mile per hour would exceed the free convective
heat loss.
However, the more accurate method of computing the forced convective heat loss is to
use the Reynolds number (indicative of laminar vs. turbulent flow), the Prandtl number
(relating viscous effects to thermal effects/conduction), and the Nusselt number (convective
heat transfer to thermal effects/conduction). This allows for the specific calculation of the
convection heat transfer rate for laminar or turbulent flow. Because these two types of fluid
flow are very different in terms of velocities and velocity profile, it is not surprising that the
heat transfers associated with these two types of fluid flow are quite different.
In general, the Nusselt number (Nu)
h
c
D/k, where D is the tube diameter or represen-
tative length, k is the thermal conductivity, and h
c
is the convective heat transfer coefficient.
¼
