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/m3. The rod is first cooled in oil with constant temperature To= 400 K and average heat transfer coefficient h=50 W/m2K. 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 To= 400 K and h =50 W/m2K. 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 Th To h 111 E Rod Rod Tube

Answer 1

GIVEN DATA D = 40mm = 0,04m L Im C = I wlmk 1600J/kg.k 400kg/m3 Р (a) 2x100 w/m3 १५ Heat generated TA чоо к h 50 wlm²K Ts = ? Surface temperature Qinput Ogenerated Clourpon - Astored a Basic equation Ogen Coupur qg. voim = h As I Is-Tool MR²L 9g. = h. anRL.las-Tal 2x 106 x H x (0.02)2 x 1 50 x 28 x 0.02x1 (Ts - 400) 219s-400) Ps - 400 800 You To - 800k S

( 7 = 1s 1 2 case 1: time required to T-sook – GIUGN reach "sook" 7 - Too - ht Sclc e V To - To La = 50xt As TIR?L 400x1600X 0.02 5oo 400 TIRL e IS 800 40o = R 3.90 6x 10 3 t 0.25 e t = 354.91 seconds