Question

2. A nuclear fuel rod with diameter of D=40 mm and length L=1m, has properties of k=1 W/mK, c=1600J/kg.K, and p=400 kg/m3. (a)Heat is generated uniformly in the rod with q'"' = 2 x 106 W/m?. The rod is first cooled in oil with constant temperature To= 400 K and average heat transfer coefficient h=50 W/m².K. Under steady state, determine the surface temperature of the rod Ts. (10 pts) (b)Now the heat generation in the rod is stopped, where q'" = 0 W/m². Assume the rod has an initial uniform temperature To= Ts as solved in (a) and is still cooled in oil with constant temperature Tw= 400 K and h =50 W/m2.K. Consider two different cases as following: (25 pts) In case 1, with initial temperature To= Ts, calculate the time required for the surface of the rod to reach 500K. In case 2, if the rod is bonded with a very thin tube for mechanical protection, and the bonding between the rod and the tube has a thermal contact resistance of Rt.c= 0.1 m K/W. Now with initial temperature To= Ts, calculate again the time required for the surface of the rod to reach 500K. Case 1 Case 2 Toh Th IIT: 0 Rod Rod Tube

Answer 1

conduction

Diameter Yomm Length Im (w/mk 1600J/kg k f = 400 log/m3 C- Head generation = 2x10 W/m² To look generation Its connection Under steady state cond" Heel generatie Conection Q =hADT PQ: ha CT- To q" = hlaup, O2 + rî RxL) (Ts - Too) AXL 6 hLD + TIDL) (Ts Tos) 4 2010 Ixo²XL 29 4 2x70 I x 1 x (0.0472 250.7 Is-400 Is = 6507k -50 (a bow'+ 96.04)*)(1-2)

♡ l=R-10mm q"=0 To=ts = 650k To=yook ñ = 50w/mik Brst no: Bia hl hel. Bi=0.5 Cose I Lumped parameter connot be applied 50xlo 1x1000 1 x = K fc 400 X 600 d²t = to offer JN² (Is-Toße (IST) t DR² ta 2 x 250x to (0.02) 460 Xitoy 2sid 170 sec