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Question: one proposed technique to treat cancerous tissue is by heating...

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One proposed technique to treat cancerous tissue is by heating it to a lethal temperature. For this purpose, metallic spherical particles (radius 1 mm, thermal conductivity 10 W/mK) are embedded at precise locations within the cancer tumor, and then the metallic spheres are heated up by absorbing infrared radiation, whose wavelength is fine tuned so that no heat is generated in the tissue. Assume 1 W of heat is generated uniformly within one particle. The temperature far from the particle is the body temperature, Tb-37°C. The tissue has thermal conductivity of 0.5 W/mK and is assumed to be in perfect thermal contact with the particle.

(a) Write down the general solutions of the temperature distributions inside the particle and in the tissue region, respectively. What are the proper boundary conditions?

(b) Derive the temperature distribution in both regions, and determine the maximum temperature obtained. If the lethal temperature for the tissue is 50 °C, how much of the cancer tissue would be "killed" this way?

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