(15 pts) Fused deposition modeling (FDM) 3D printers often have finned tube on the hot end to prevent the plastic filament from melting prematurely and causing jams. Consider the assembly shown below with annular fins extending from a central tube. Adiabatic Spider Raf Rat Rt TH 3 mm h,T The central tube has inner diameter Rit k = 180 W m K- = 2 mm, Rot 4 mm, Lt = 40 mm, and Annular fins on the tube have Ro,f= 15 mm, thickness tf = 1 mm. The fins are spaced by center- to-center distance 3 mm. The fins also have k = 180 W m K Cooling air at T = 30C. provides a convective heat transfer coefficient of h=70 W m K on the fins. The hot-end at the bottom (x = 0) is at TH = 230C. The cold-end at the top (x = L) can be modeled as adiabatic. (5 pts) Calculate the overall resistance for the convectively cooled array of fins on the outside of the tube. The net effect of the fins can also be interpreted as a higher equivalent heat transfer coefficient on the outside surface of the tube of radius Ro,t: 1 Aext,tube heff Ro,fins Determine this heff value. (5 pts) Now, the tube itself can be modeled like a fin extending from the fixed base temperature TH to the adiabatic cold end at z = Lt with convection coefficient heff on its outside surface. Calculate the cold end temperature T(z = Lt) and the total heat removed by the finned tube. (Hint: See notes from classes 10-11 and textbook Table 3.4) (5 pts) Real FDM 3D printer hot ends also have a short unfinned tube section called a "heat break". Explain the purpose of the heat break. Cold-End Teflon liner Heatsink Cooling fan Hot-End Heat break Heater block thermistor cartridge Nozzle