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1. A cryoprobe at liquid N temp (-196°C) is used to destroy tissue in prostrate
cryosurgery. The silicone is used as an insulator to protect the surrounding tissu
from cryoinjury. Usually the treatment will last about 20 minutes including initial
process and final rewarming-up process. The physical model for heat transfer
process in the sillicone insulator can be descripted as in the following figure and
the mathematic model can be descripted as the following equation:
Prostate
Silicone insulator
Rectal tissue
$\frac{\partial T}{\partial t} + u \frac{\partial T}{\partial x} = \frac{k}{\rho c_p} \frac{\partial^2 T}{\partial x^2} + \frac{Q}{\rho c_p}$
(a) Simplify the above equation for initial starting-up of the treatment or the final
rewarming process and explain the reasons. (10 pts)
(b) For the steady state treatment, if the temperature in the interface of prostate
and silicone insulator is T? (liquid nitrogen temperature, -196°C,) and the
temperature in the interface of silicone insulator and surrounding tissue is T?
(body temperature, 35°C), express the temperature distribution within the silicone
insulator. What will be the temperature in the middle of silicone insulator? The
thickness of the silicone insulator is L. (20 pts)
