Biomedical Engineering Reference
In-Depth Information
excess charges? Consider that the charged element has a diameter of 5 nm and is centered
within the channel, is a half radius from the wall and a quarter radius from the wall.
7.10
Knowing that there are channels that restrict the movement of ions based on charge and
size, propose a formulation that can represent this phenomenon.
ð
P
c
i
χ
7.11
Calculate the Debye length for a 120 mM sodium ion
2
i
5
5
μ
m
2
3
Þ
that is being trans-
ported through the interstitial space (where
ε
l
is 60; this is a relative number with no
units), at body temperature.
7.12
Calculate the surface tension and the force associated with the surface tension for a red
blood cell moving through blood. Assume that the radius of curvature for the red blood
cell is 4
m and the radius of curvature for the blood is 1 cm. The pressure difference
across the cell and blood is 25 mmHg. Assume that a red blood cell is a perfect sphere
when estimating contact area.
μ
7.13
Determine the velocity of interstitial fluid through the extracellular matrix where the pres-
sure gradient in the fluid direction is equal to
0.10 mmHg/cm. Assume that the porosity
of the media is 60%, the surface area to volume ratio is 8/cm and the shape factor is 2.
2
*7.14
Solve for the velocity profile of a pressure driven flow, through a small porous channel, in
which the hydraulic conductivity can be represented as
K
5
k
μ
, where
k
is a measure of the
permeability of the media.
Blood is flowing through the aorta at a temperature of 37
C. The aortic wall can be consid-
ered isothermal with a temperature of 30
C (on a cool day). The aorta has a diameter of
24 mm. If blood enters the aorta at 75 cm/s and leaves the 0.5-m section of the aorta at
33
C, determine the average heat transfer coefficient between the blood and the aorta.
Assume that the specific heat for blood is 3.8 kJ/kg
C.
7.15
7.16
The trachea is 0.25 m long and 12 mm in diameter and is used to heat air that enters at
25
C(
v
5
0.4 m/s). A uniform heat flux is maintained by the body so that the air enters the
lungs at a temperature of 35
C. Assume that the average properties of the air to be
ρ
5
1000 kg/m
3
, and
c
p
5
4000 J/kgK, and determine the required surface heat flux.
*7.17
Consider the velocity and temperature profiles for blood flow in a vessel with a diameter
of 100
μ
m can be expressed as
2
r
R
uðrÞ
5
0
:
35 1
2
2
2
3
r
R
r
R
TðrÞ
5
2
:
1 150
35
65
1
with units in
m/s and
K
, respectively. Determine the average velocity and the mean tem-
perature from the given profiles.
μ
References
[1] A.O. Frank, C.J. Chuong, R.L. Johnson, A finite-element model of oxygen diffusion in the pulmonary capillar-
ies, J. Appl. Physiol. 82 (1997) 2036.
[2] J.D. Hellums, P.K. Nair, N.S. Huang, N. Ohshima, Simulation of intraluminal gas transport processes in the
microcirculation, Ann. Biomed. Eng. 24 (1996) 1.
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