Transferência de Calor Radiativo - Aquecimento de Pelota de Carvão em Forno a 1000C

PROBLEM 532 KNOWN Spherical coal pellet at 25C is heated by radiation while flowing through a furnace maintained at 1000C FIND Length of tube required to heat pellet to 600C SCHEMATIC ASSUMPTIONS 1 Pellet is suspended in air flow and subjected to only radiative exchange with furnace 2 Pellet is small compared to furnace surface area 3 Coal pellet has emissivity 1 PROPERTIES Table A3 Coal T 600 25 C2 585K however only 300K data available 1350 kgm3cp 1260 JkgK k 026 WmK ANALYSIS Considering the pellet as spatially isothermal use the lumped capacitance method of Section 53 to find the time required to heat the pellet from To 25C to TL 600C From an energy balance on the pellet in st E E where 4 4 in rad s sur s st p dT E q A T T E c dt giving 4 4 s sur s p dT A T T c dt Separating variables and integrating with limits shown the temperaturetime relation becomes T To t L s 4 4 p 0 sur A dT dt c T T The integrals are evaluated in Eq 518 giving p 1 1 sur sur i i 3 sur sur i sur sur s sur c T T T T T T t ln ln 2 tan tan T T T T T T 4A T Recognizing that As D2 and D36 or As 6D and substituting values 3 3 8 2 4 1350 kgm 0001 m 1260 Jkg K 1273 873 1273 298 t ln ln 1273 873 1273 298 24 567 10 Wm K 1273 K 1 1 873 298 2 tan tan 118s 1273 1273 Hence L Vt 3ms118s 354m The validity of the lumped capacitance method requires Bi h Ask 01 Using Eq 19 for h hr and As D6 find that when T 600C Bi 019 but when T 25C Bi 010 At early times when the pellet is cooler the assumption is reasonable but becomes less appropriate as the pellet heats