1. Simple CFD Estimate of End Flange Tuner Finger Cooling

2. Estimated Dimensions 2cm 1cm 3cm 5cm 6mm 4cm 5cm

3. Estimated Heat Load FETS RFQ: 62 Wcm -2 at vane cut-back Assume less than half this on fingers? So 25 Wcm -2 is reasonable. IPHI RFQ end flange: 26 Wcm -2 on fingers (CW RFQ, though, so ours will have much less than this in reality, but 25 Wcm -2 will allow large safety margin)

4. 15°C Water in at 1 ms -1 flow rate Water out with temperature raised and at 0 Bar relative pressure 25 Wcm -2 heat flux load on finger High mesh density in region between finger and pipe Copper starting temperature = 22°C

5. Flow Estimates Total power, P, to be removed from each finger ≈ 160 W Water mass flow rate,, per pipe = 0.028 kgs -1 (assuming flow speed = 1 ms -1 = 1.7 l min -1 ) Estimated temperature rise, ΔT, of cooling water = 1.35 °C Pipe length, L, within copper = 10 cm Average water flow rate v av = 1 ms -1 Pipe diameter, D H = 6 mm Estimated pressure drop, Δp = 0.003 Bar Nusselt number, N u, of water flow = 55.03 Thermal conductivity of water, k = 0.6 Wm -1 K -1 Estimated heat transfer coefficient = 5500 Wm -2 K -1

6. Intersection of drilled pipes slightly disrupts smooth flow

7. Faster, disrupted flow round corner increases local HTC Average HTC ~ 6000 Wm -2 K -1 which agrees with estimate

8. Temperature rise of water ~ 2 °C which agrees with estimate

9. Pressure drop is slightly higher than estimate because the pipe doesn’t have a smooth bend at corner, but it’s still nice and low

10. Bulk copper in end flange is ~ 40 °C Finger gets pretty warm (100 °C) but that shouldn’t matter at all

11. Summary Majority of heat removed ok Indirect cooling means finger gets hot …but not enough to worry about Assumes 25 Wcm -2 heat load (OVERESTIMATE!) Will proceed with RF simulation to get better estimate of heat load on fingers Overall, this cooling strategy should be fine