Biomedical Engineering Reference
In-Depth Information
TABLE 1.1
Ranges of Typical Values for
h
as
Encountered for Various Combinations of Convective
Transport Process Characteristics
are very different, and therefore forced and free convection pro-
duce quite disparate heat transfer effects. Also, analysis of the
fluid flow characteristics in forced and free convection is unique
because of the differing patterns of motion. Usually the mag-
nitude of forced convection effects is much larger than for free
convection, as indicated in Table 1.1. Thus, although the poten-
tial for free convection will be present whenever a temperature
field exists in a fluid, if there is also an imposed forced source of
fluid motion, the free convection effects usually will be masked
since they are much smaller, and they can be neglected.
The convection process consists of the sum of two separate
effects. First, when there is a temperature gradient in a fluid,
heat conduction will occur consistent with the thermal con-
ductivity of the chemical species and its thermodynamic state.
The conduction effect can be very large as in a liquid metal or
very small as in a low density vapor. The conduction occurs via
microscopic scale interactions among atoms and molecules,
with no net translation of mass. Second, there will be transport
of energy associated with the bulk movement of a flowing fluid.
The component due to only bulk motion is referred to as
advec-
tion
. Convection involves a net aggregate motion of the fluid,
thereby carrying the energy of the molecules from one location
to another. These two effects are additive and superimposed.
A fundamental aspect of convection heat transfer is that the
processes involve both velocity and temperature boundary lay-
ers in the fluid adjacent to a solid interface. Illustrations of these
boundary layers are shown in Figure 1.4. The velocity boundary
Process Characteristics
Range of
h
(W/m
2
·K)
Free Convection
Va p o r s
3-25
Liquids
20-1000
Forced Convection—Internal/External
Va p o r s
10-500
Liquids
100-15,000
Phase Change
Between liquid and vapor
5,000-100,000
frequently a mechanical force to move the solid or to impose
a pressure gradient on the fluid. However, in the absence of an
external motivational force, the heat transfer process itself will
cause relative motion. Owing to the constitutive properties of
fluids, the existence of a temperature gradient produces a con-
comitant density gradient. When the fluid is in a force field such
as gravity or centrifugation, the density gradient causes inter-
nal motion within the fluid by buoyancy effects as the less dense
fluid rises and the more dense fluid falls under the action of the
force field. This phenomenon is called
free convection
since no
external energy source is applied to cause the motion directly.
Any time there is a temperature gradient in a fluid, there is the
potential for having free convection heat transfer. As can be
anticipated, the fluid flow patterns for forced and free convection
Free
∞
∞
Boundary
layer
y
(
y
)
δ
x
(a)
Free
T
∞
T
∞
Boundary
layer
y
T
(
y
)
δ
T
T
s
(
x
)
x
(b)
FIGURE 1.4
(a) Velocity boundary layer; (b) temperature boundary layer.
