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

Assuming the cancerous skin tissue to be a semi infinite medium with k_c = 0.20 W/m · K and T_c = 37°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 K, V_e = 20 m/s.

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Spent gas H Ts -Cryogenic probe Do Cancerous tissue