Biomedical Engineering Reference
In-Depth Information
However, the Nusselt number is related to the Reynolds number (Re) and the Prandtl num-
ber (Pr) by the following representative equations:
322 Re 0:5 Pr 0:33
Nu
¼
0
:
for laminar flow
023 Re 0:8 Pr 0:33
Nu
¼
0
:
for turbulent flow
where
Re
¼ r
VD/
u
Pr
¼
c p u
/k
r ¼
density
u ¼
viscosity
specific heat
Since the Nusselt number is related to both the Reynolds number and the Prandtl
number, as well as to the convective (forced) heat transfer coefficient, by computing these
three parameters, one can determine the convective heat transfer for the appropriate type
of flow. Obviously, this is a more complex set of calculations than the simple form of
h c
c p ¼
5.6 v 0.67 , but it is more accurate, since the simplistic form does not designate the type
of fluid flow.
¼
14.3.4 Heat Exchangers
Heat exchangers are commonly used in medical settings as blood heaters/coolers for open
heart-lung machines or for patient heating/cooling for standard surgeries. The purpose of
cooling the patient during surgery is to reduce the metabolic load, which lowers the need
for larger blood flow rates or ventilation rates. The patient is then heated (or the blood
heated) toward the end of surgery. A typical type of heat exchanger for blood is the double
pipe heat exchanger, which consists of two concentric pipes with blood in one pipe and water
in the other. By using cold water, the blood is cooled, while using warm water heats the
blood. A double pipe heat exchanger combines convective heat transfer, as the fluids are
moving, along with heat conduction through the pipe walls. A typical double pipe heat
exchanger is shown in Figure 14.45. Because the blood and the water can either be moving
in the same direction (cocurrent flow) or in opposite directions (countercurrent flow), there
are two versions of the heat exchanger. The physical device is shown in Figure 14.46.
The design equations for a double pipe heat exchanger combine Fourier's law for heat
conduction through the wall of the inner pipe, together with the complex form of the con-
vective heat transfer coefficients with the Reynolds, Prandtl, and Nusselt numbers.
This equation is Q
T lm , where U is the overall heat transfer coefficient and is a
function of the thermal conductivity and the convective heat transfer coefficient, A is the
surface area of the pipe, and
¼
UA
D
T lm is the effective temperature difference between the two
fluids from one end of the exchanger to the other. This term is known as the log mean of
the temperature gradient. Since the surface area of the pipe could be the inner or outer sur-
face, then the overall heat transfer coefficient is synched with the surface area as U o and A o ,
or U i and A i . The temperature gradient is unaffected by inner or outer diameter but is
affected by whether the flow is cocurrent or countercurrent. In general, countercurrent flow
is more efficient for overall heat transfer.
D
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