Question

Water at 340 K and a flow rate of 5 kg/s enters a black, thin‐walled tube, which passes through a large furnace whose walls and air are at a temperature of 700 K. The diameter and length of the tube are 0.25 m and 8 m, respectively. Convection coefficients associated with water flow through the tube and airflow over the tube are 300 W/m2·K and 50 W/m2·K, respectively.

Write an expression for the linearized radiation coefficient corresponding to radiation exchange between the outer surface of the pipe and the furnace walls. Determine how to calculate this coefficient if the surface temperature of the tube is represented by the arithmetic mean of its inlet and outlet values. Use these expressions to determine the outlet temperature of the water, T m , o , in K.

Water at 340 K and a flow rate of 5 kg/s enters a black, thin-walled tube, which passes through a large furnace whose walls and air are at a temperature of 700 K. The diameter and length of the tube are 0.25 m and 8 m, respectively. Convection coefficients associated with water flow through the tube and airflow over the tube are 300 W/m2.K and 50 W/m2.K, respectively. Tube, D = 0.25 m L = 8 m, k = 1 Air T. - 700 K Water m = 5 kg/s - -Furnace, Ttur = 700 K Write an expression for the linearized radiation coefficient corresponding to radiation exchange between the outer surface of the pipe and the furnace walls. Determine how to calculate this coefficient if the surface temperature of the tube is represented by the arithmetic mean of its inlet and outlet values. Use these expressions to determine the outlet temperature of the water, Tm,o,in K.

Answer 1

Tube, D = 0.25 m L = 8 m, E = 1 Air T = 700 K Water m = 5 kgis 1 T. = 300 K Furnace. Tu = 700 K

KNOWN: Water at prescribed temperature and flow rate enters a 0.25 m diameter, black thin-walled tube of 8- m length, which passes through a large furnace whose walls and air are at a temperature of Tfur = T.. = 700 K The convection coefficients for the internal water flow and external furnace air are 300 W/m K and 50 W/ mK respectively FIND: (a) An expression for the linearized radiation coefficient for the radiation exchange process between the outer surface of the pipe and the furnace walls, represent the tube by an average temperature and explain how to calculate this value, and (b) determine the outlet temperature of the water. To SCHEMATIC: To = 700K h = 50 W/m2K Air То Tfur =T. 4cv, Grad Tfur = 700K Revo Read Water Revil m = 5 kg/s D-0.25 m, L = 8 m,€-1 Tmi = 300 K h = 300 W/m2K Tmo T = (Tm/+Tm,N2 ASSUMPTIONS: (1) Steady-state conditions; (2) Tube is small object with large, isothermal surroundings: (3) Furnace air and walls are at the same temperature, and (3) Tube is thin-walled with black surface. PROPERTIES: Table A-6, Water (Tm = (Tmi + Im,o)/2 = 331 K). (p = 4192 Jkg K ANALYSIS: (a) The linearized radiation coefficient follows from Eq. 1.9 with e = 1, head =ơ (T+ Tru (TTT) where To represents the average tube wall surface temperature, which can be evaluated from an energy balance on the tube as represented by the thermal circuit above.

Im =(Tm,i +Imo)/2 1 Rtot = Revi+ 1/Revo +1/R rad Im - 7 It - Tfur Revi 1/Rev.o +1/Rrad The thermal resistances, with As =PL = TDL, are Rcv,i =1/h;A Rev,o=1/h24 Rrad = 1/ hrad (b) The outlet temperature can be calculated using the energy balance relation. Eq. 8.46b, with Tfur = T. T. -Tm.o = expl 1..-Tmi where Cp is evaluated at Tm Using IHT the following results were obtained. Rev.: = 6.631x10 - K/W Rev.0 =3.978x10+ K/W Rrad = 4.724x10*K/W Im = 331 K īp = 418 K Tm,o = 362 K COMMENTS: Since Tos=Tfur it was possible to use Eq. 8.45b with Rtot. How would you write the energy balance relation ifT.. Tur? mop tot
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