Chapter 7, Problem 7.102P

A cryogenic probe is used to treat cancerous skin tissue. The probe consists of a single round jet of diameter $D_e=2\text{mm}$ that issues from a nozzle concentrically situated within a larger, enclosed cylindrical tube of outer diameter $D_o=15\text{mm}\text{.}$ The wall thickness of the AISI 302 stainless steel probe is $t=2\text{mm,}$ and the separation distance between the nozzle and the inner surface of the probe is $H=5\text{mm}\text{.}$

Assuming the cancerous skin tissue to be a semi-infinite medium with $k_c=0.20\text{W/m}\cdot \text{K}$ and $T_c=37°\text{C}$ far from the probe location, determine the surface temperature $T_s.$ Neglect the contact resistance between the probe and the tissue. Cold nitrogen exits the jet at $T_e=100\text{K,}{V}_e=20\text{m/s}\text{.}$ Hint: Due to the probe walls, the jet is confined and behaves as if it were one in an array such as in Figure 7.18c.