1. Thermal Analysis of short bake out jacket version 1 12-Nov-2013

2. Bake out jacket without outer cover and cooling lines PTFE frame with stainless heater support with 3 heater rods on a side

3. Simplified model of bake out jacket for thermal analysis outer stainless jacket with fixed temperature cooling ribs/tubes insulation layer stainless heater supports naked Be beam pipe naked Aluminum beam pipe 6 mm dead air layer between heater support tube and beam pipe The beam pipe wall thickness and outer stainless shell have been scaled up by a factor of 5 and the thermal conductivities have been scaled down by a factor of 5 to compensate. This was to facilitate meshing and reduce solving time.

4.  The analysis was done by adjusting the heater power input to raise the beam pipe temperature to approximately 250 deg at the center.  The ambient temperature was adjusted to give approximately zero power into the air. That is the heat into the air by convection from hotter elements is equal to the heat out by convection to the cooled surface.  Two cases were run with different conditions. Case 1 did not have radiative heat transfer between the beam pipe and the heater jacket while Case 2 did. The convective parameter is a factor of 2 higher in Case 1 than Case 2. Case 2 has a higher temperature for the cooling tubes.

5. Boundary conditions and results for SolidWorks Thermal Simulation parameters & boundary conditionscase 1case 2 convection parameter20 W/(m^2 K)10 W/(m^2 K) cooling tube temperature22 deg. C32 deg. C beam pipe end temperature250 deg. C heater power150 W125 W radiative coupling between heater tube & beam pipeemissivity: 0emissivity: 0.9 conductivitiesW/(m K) Stainless18 Insulator0.082 Dead air layer0.027 Aluminum167 Beryllium216 Results beam pipe min (deg. C)168204 beam pipe max (deg. C)247258 beam pipe spread (deg. C)7954 stainless heater rod support min (deg. C)206208 stainless heater rod support max (deg. C)303276 ambient air temperature (deg. C)4150 convective heat loss from naked beam pipe sections90 W51 W

6. beam pipe temperature distribution Case 1 Case 2

7. Stainless heater support temperature distribution Case 1 Case 2

8. End region temperature distribution Case 1 Case 2

9. Outer jacket temperature distribution Case 1 Case 2

10. Power entering beam pipe ends from jacketed beam pipe sections set at 250 deg C Power slightly different for the two ends since one pipe is Beryllium and one is Aluminum. Also the wall thicknesses are not the same. Case 1 Total 72 W Case 2 Total 39 W

11. Case 1 Cooling ribs/tubes power transfer total for all ribs: 222 W

12. Case 2 Cooling ribs/tubes power transfer total for all ribs: 159 W

13. Convective heat loss from the naked sections of the beam pipe. Case 1 Total 90 W Case 2 Total 51 W

14. Summary of results and comments The spread in temperature on the beam pipe is 168 deg C to 247 deg C for 150 watts of heater power in case 1. For case 2 the input heater power is 125 watts with a spread in beam pipe temperature from 204 deg C to 258 deg C. The more uniform beam pipe temperature in case 2 is the result of choosing a reduced convection parameter thus reducing the convective heat loss from the naked portions of the beam pipe. The reduced temperature of the stainless heater in case 2 is because of the increased coupling of between beam pipe and heater that results from including radiative heat transfer. As these two cases demonstrate there is uncertainty in the heat loss from the naked portions of the beam pipe, since one can’t know in this limited model what the correct convective heat loss is. A factor of 2 uncertainty can be expected. In either case however there is significant heat transfer from the naked sections to the surrounding air. So it makes sense to arrange some exchange of air in the PST region, rather than trying to absorb all of the heat with the cooling jacket as has been done in this simulation.

15. The model does not include the PTFE (Teflon) ribs which have a factor 3 higher conductivity than the insulation, but the ribs are some what isolated from the hot stainless heater carrier. This is important because the stainless heater support tube reaches 280 deg C and the melting point of PTFE is 327 deg C. Decomposition sets in at a lower temperature. It is expected that the ambient air temperature will be somewhat lower that indicated in the simulation, because there will be additional heat loss to the PST walls which have not been included in this model.