One way to treat tumors that exist near the skin surface is to heat the tumor tissue, as the cellular viability of some tumor tissues is more sensitive to higher temperatures than the sur-rounding skin tissue. In the simplest method, a directed heat source is put in contact with the skin surface as shown in the figure. In the present treatment process shown, the tumor is approximately 3 mm (0.003m) below the skin surface and begins to respond to thermal treatment when its temperature reaches 45°C. The surface temperature is maintained at 55.5°C (132°F). After 2 min, the patient feels discomfort, and the device is turned off. Independent measurements showed that both the skin tissue and the tumor tissue had the following thermo-physical properties: thermal conductivity, k = 0.35 W/m €¢ K, heat capacity, = 3.8 kJ/kg €¢ K, and density p = 1005 kg/m3. The body temperature before treatment was uniform at 37°C.
a. What is the thermal diffusivity of the tissue?
b. How long was the active treatment time of the tumor-i.e., how long was the tumor at a minimum of 45°C within the 2.0 min treatment time?

Transcribed Image Text:

directed heat source T = 55.5°C %3D skin tissue 3.0 mm tumor-