A spherical, cryosurgical probe may be imbedded in diseased tissue for the purpose of freezing, and thereby destroying, the tissue. Consider a probe of 3-mm diameter whose surface is maintained at 30°C when imbedded in tissue that is at 37°C. A spherical layer of frozen tissue forms around the probe, with a temperature of 0°C existing at the phase front (interface) between the frozen and normal tissue. If the thermal conductivity of frozen tissue is approximately 1.5 W/m K and heat transfer at the phase front may be characterized by an effective convection coefficient of 50 W/m2 ∙ K, what is the thickness of the layer of frozen tissue (assuming negligible perfusion)?
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