Question

2.2 Consider a plate fuel element of thickness 2L for a gas-cooled nuclear reactor. The energy generation in the fuel element can be approximated by a cosine distribution q-q0 cosx. Where x is the coordinate measured from the plate center. Thermal conductivity of the plate material is assumed constant. The out side surfaces of the plates at x-tL are at constant temperature Tw. Find the (T.D.E). and the maximum temperature value and location

Answer 1

| Assumption: | cis steady state conduction (ii) Thermal conductivity of the material is constance (K) Given Boundary condition owl , r Tw IT(&= I1l = Toll an to the 3-0 c) TDE: The generalise heat conduction equation through a plate under steady state with constant thermal conductivity K is given as i given: : %s (4121 get 13 Locos .. 2012 = x Integrating: OT -20 (+ sina) za - tci

SO! Integrating! I -q otros x) 34C, 8+ C2 TE go cosa K +GX+ C2 Now, from Boundary condition: 3=L, TE TW Two po cost tc, L+ cz K I Get Gz = Tw-Pocost also! 2. -b, TatW Tw= Pc cose-L) -, + (2 . - 0; 1-ccd Cz = Tw-qocosul from o f@: E,L +C2 = -6,6+ (z 20,220 [co] M. So, from o co lcg: Tur To cosa Sai temperature distribution becomes: Te qo Cosse : e vo cost Kt Tas que T-TW a quo (cosx- co5L) CSL -3 Now' at the point of mase temperature er - Tosinseco to [60

sui so. From temperature distribution ean (3) Tmox - Tous le closco) - co5l) Tmax= two (1-6052) @ 730 or poster
Do rate,Thanks.