Question

A circular plate of 500-mm diameter is maintained at T1 = 600 K and is positioned coaxial to a circular top plate. The back side of the top plate is well insulated and thus it acts as reradiating surface q2=0. These two plates whose surfaces are black, are located in a large, evacuated enclosure whose walls are at 300 K. Surroundings make a side surface of the Insulated enclosure. Assume view factors: back side F12= F21=0.172; F13=F23=0.828. T2 (a) What is the temperature of the conical surface, T2? Surroundings Tsur = 300 K (Check number: 413K) L = 500 mm D = 500 mm (b) What is the electrical power that T1 = = 600 K would be required to maintain the lower circular plate at T1=600 K? (Check number: qı=1312W) Plate with electrical heater

Answer 1

Solefon: Given, D: 500 mm - 0.5m T = book Tsur = Book T3 L 500 mm Fiz F21 -0.172 = 0.82% Fiz =F23 (a) Here, there is no conical Surface but a top plate is well insulated general equation for heat transfer due to Since, we have a radiation between & Black bodies Eb, Eb2 the As there Considering are 3 Surfaces involved, So we hence to solve resistance netwoork of below by kirchoft's network law. means of where, q2 = 0 [given Jz Ebz Ebi ة - There are 1- & &A & Az ) A 1 A₂ F23 Pifa &=&=1 E63 = 33 Since, for black bodies And for Surrounding eta Then the resistance network is modified to

Ebg=Jz ara 67 26 + Since A = P2 E53 -3, the heat traus for due to radiation between plate with insulted (ะ) (5) A F23 Now, we have ข,ะ 31 Ebi - En (AF) (5) then 7,ฯ - ยาง , 8, รา- 6 () 7 FC 1-121) + (1) ) 0 Substitute values 4 85 XL6 • Temperature of the Conical Surfall backside plate and plate with electrical heater E6% บ> (รฯ - 1 ) () () อง13 (601ฯ) + 0.42t (sec (2) รอ 1 - 0 10 15 M12:46 k 913 F |7, - 41zk (6) Fabi R

quis . R 2 Heat transfer of insulated backende plate and surroundings Em - Eb T(7,4 -14) Caris) The electical power that would be required to maintain the tower Circular plate at T = book is a = 9 12 + UB OR [(T ,"_T2") X Fort (74–194) x F1z] = (5«?%B5°) ( "10.5") {lcowy Goy-4139)0.42) + (600-3001) (0.47e] - 1311, 78 - 1312 w 19. a = 1312k Thank you