1. (30 Pts) The NASA Multi-Mission Radioisotope Thermal Generator (MMRTG) uses a cylindrical radioisotope heater unit (RHU, plutonium oxide) as its heat source (radius R = 0.08 m). This ceramic cylinder has volumetric heat generation (q" = 1.5.105 W m). The outer surface of the RHU delivers heat via radiation to a surrounding enclosure that contains an array of thermoelectric generators. Some additional specifications are as follows: The RHU has thermal conductivity k = 2 W m K- The heat transfer between the outside of the RHU and the surrounding surface can be modeled as radiation in a large enclosure with effective emissivity = 0.8. The surrounding cylindrical surface is at temperature Tc = 1200 K. The top and bottom faces of the RHU are well insulated. Insulated q"" R Insulated a. (8 Pts) Set up the reduced conduction differential equation for heat transfer inside the RHU. Clearly indicate assumptions you are using the simplify the general differential equation for conduction. Also, define the boundary conditions for this situation. b. (8 Pts) Solve the conduction equation and boundary equations to obtain a solution for the temperature profile. Calculate the minimum and maximum temperatures in the RHU. c. (8 Pts) Plot the temperature profile through the thickness of the RHU. Indicate important values and features on the profile. d. (6 Pts) The maximum operating temperature for the RHU ceramic is 2,000 K. What is the maximum radius of the RHU that can be employed before this limit is reached?