Question

1. Molten copper flows through a l m long alumina pipe that has an ID of 25 cm and a wall thickness of 5 cm. The molten copper has a temperature of 1,500 °C and the alumina pipe is surrounded by 25 °C air. The thermal conductivity of alumina is 46 W/m °C. The convection heat transfer coefficients are 500 W/m2 °C between the alumina pipe and ambient air and 200 W/m² °C between molten copper and the alumina pipe. (a) Draw the equivalent electric circuit of the thermal resistance for this heat transfer system. (5 points) (b) What is the total heat transfer rate? (10 points) (c) What is the temperature at the outer surface of the pipe? (5 points) (d) What is the overall heat transfer coefficient U, between copper and air? (5 points) (e) What is the overall heat transfer coefficient U, between the copper and air? (5 points)

Answer 1

tr Given that t T2= 2500 t=san (wall the ticknes). Di=25cm Ti=15ooc R *wall=46 W ma → ( blew , Alumina pire and Ambient mrc w ho= 500 E h; = 200 wire airs • (between moltes coppes and alumina Pires Do = Di +2 (+) = 25 +225) - 25 +10 10²m Do= -35 cul = 0.35 m Thickness is I lyn Di = 0.25m х added two sides t = 0.05 m. a) Resistance & Equivalant electric ciscuit 2 Ri R3 T min R2 Munna •To RJ Resistance due to moltan Copped and alumini Pike L Ray Resistance due to wall. R3 Resistance due to alumina pipe and ambient ais.

6)d). o 100 + Do in Ko 8 + ho rihi Do =0.35 bo = Q35 _ 0-17S Yi =0.25 = 0-125 Vo " 0 17 0. + 0.3S } 125 200 les + u6 0125 STO Vo 0.007 0) 28 +0.00 2 Vo = 3S 36 3 mroc e Ors | 111 니 ) hi lis 5 + + 여 ro ho ic 0.125 + in 0. A 1125 0.25 200. + 금 u6 0.5 SEO Ui OOOS + 0-000919 + 0.000043

E U; 16 5.09 mrc b) overall heat teavistes rate based to Q = VO A OT Q = Uo to DOL AT Q=35.36 W X TIX0 175 81 mx (1500-25)/ morod Q=28659.7 W @=28.6597 kW At steady state overall heat loss ů individual Heat loss. From convection heat loss Q = hoĄ (Ts-Too) 28.659.5 = SOO X TTX Do XL (Ts -25°) 28.6596 = Soo X 3.14X0:175(TS-20595 Ts=129.31 °C