Question

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/mº. (a)Heat is generated uniformly in the rod with q'"' = 2 x 10 W/m. The rod is first cooled in oil with constant temperature Tu= 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 T.= 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.kw. Now with initial temperature To= Ts, calculate again the time required for the surface of the rod to reach 500K. Case 1 Case 2 Teh T. h 111 Rod Rod Tube

Answer 1

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De 40 mm, 2 when applying energy balance o Q al I g = 800k L= 1 m, k = 1 W/m-k, (=160051 Egk,f-booksling Qu= 2x100w w/m3 R=20mm = 을 heat is is generated uniformy Heat generated in roda Heat tromsportada by fluid (oil) hX (ADL) x (T-To) W = Volumetric heat generation rate, h = 50 W/m²K Toe surface temp. of rod, To = Shuid Pemp = 400k solving we get in @ When qin - The problem becomes that of transsient heat cond"> Bi= Biot No- Lt kt R.² SCR? for surface temp to be I T-Too се Jo (3) "T= 500k, Tg = 800k , Do = 400k G = 1.2071, 3= 1.2558 & Jols) = 0.6456 { from interpolation? get 0.7184 kt ってこ 0.7184 t = 183.98 SCRE h Ro then 197= 2 To - To we Soling it

When Ree - 0.1 miklu 1 The-1-23 h TD Bi heff Ro 010 246 – 4 = 1.00625, 130-22175 Do (9) = 01987303 from interpolation again applying same procedure 2=28.06 t=718340 A Kt Il R² 28.06.