Biomedical Engineering Reference
In-Depth Information
EXAMPLE PROBLEM 17.9
Consider the skin subjected to a constant temperature heating T. For exposure durations
30 minutes, find the critical temperature, T_c (in
C)
t
¼
1
m
s, t
¼
1ms,t
¼
1s, t
¼
60s, and t
¼
required to achieve thermal damage,
O ¼
1, during the exposure. Plot T_c versus exposure
duration.
Solution
Given that the exposure durations are 1
m
s, 1 ms, 1 s, 60 s, and 30 minutes, and R is the univer-
2 cal/gm-
C, then what is required for each case is for T_c (critical temperature
at which point omega
sal gas constant
¼
¼
1) to be calculated.
Assumptions
Values of ln A and E are approximated to pig tissue values of 102.72 and 74,000, respectively.
Equation
ð
t
Oð
z,
t
Þ¼
exp
ð
ln
A
E
=ð
RT
ð
z
,
t
ÞÞ
dt
0
ð
t
∴
1
¼
exp
ð
ln
A
E
=ð
RT c
ÞÞ
dt
ð
ex1
Þ
0
ð
t
1
¼
exp
ð
102
:
72
74000
=ð
2*
T c
ÞÞ
dt
∴
0
ð
t
1
¼
exp
ð
102
:
72
74000
=ð
2*
T c
ÞÞ
dt
ð
ex2
Þ
∴
0
1
¼
exp
ð
102
:
72
74000
=ð
2*
T c
ÞÞ
t
ð
ex3
Þ
∴
Solving Eq. (ex3) for all values of
t
, we can get
T_c
for those values. The tabulated values of
t
and
T_c
are as follows:
Exposure Time t (in s)
Critical Temperature T_c (in
C)
1 e-6
143.1548
1 e-3
113.153
1
87.2
60
74.56
1,800
72
17.5.6 Effect of Vaporization and Ablation Temperature
The coefficient
was introduced previously in relation to the heat of ablation as the
water fraction parameter. Another nonvaporization phenomenon that can affect this coeffi-
cient is ejection of material due to subsurface nucleation. As was discussed, chunks of the
material may be ejected without vaporization. Another factor that can affect the ablation
f
L
