Chapter 3, Problem 3.69P

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 $1.5\text{W/m}\cdot \text{K}$ and heat transfer at the phase front may be characterized by an effective convection coefficient of $50{\text{W/m}}^{\text{2}}\cdot \text{K,}$ what is the thickness of the layer of frozen tissue (assuming negligible perfusion)?