Question

NE Steel tubes (k =35 W/m2.K) of 400-mm inner diameter and 30-mm wall thickness are used to route superheated steam from the boller to the turbine in a power plant. Safety and economic concerns make it practical to add a 200-mm layer of Insulation (k =0.1 W/mK) to each tube, which is wrapped in a thin sheet of aluminum with an emissivity e =0.15. The air (with a convective coefficient h =5 W/m2K) and wail temperatures of the plant are 27°C. If the inner surface temperature of the tube corresponds to the steam temperature, find the highest temperature, in °C, of the steam so the temperature of the aluminum does not exceed 50°C. What is the corresponding heat loss per unit tube length, in W/m? 4 W/m T =

Answer 1

Sol mm - 200 mm 1 Given dato:- steel tubes k: 35 Wm'k Inner diameter Cd; ] = 400 mm wall thickness (t) = 30 mm layer of insulation convective heat transfer coefficient Cho = 5 wlm-x Emmissivityce ) = -0.15 temperature of the plant = temperature of aluminium should not Exceed 50°C insulation ck) :01 wlm-k = 27°C 400 - 200 mm lar 72 = 200+30 - 230 mm Aluminium T5,0 550°c E-2.15 TSUY = 27°C Toogo ,: Insulation thickness ksteel - 35 wmk Kinsl = 0.1 w/m-k = 83-82 200 - 13 - 230 -Y3 = 4 30 mm a'yach Energy balance Equation q'- q'conr + >(1) heat Shese due to convection ( 9 conv] - 27183 hoC 75,0 - Two] q' conv

heat flere due to radiation 27183 &o [T5,0" To q'rad 1 Tsi - Ts, o q R'cond * r cond. ins in [2/3,) st R'cond.st 21 kgt R'condins in [83/02 Qu kins an iz ho [Ts,o - TO]+2 1Yger[T5,09 - Techno Tsi - Ts, o in [22] [33] + 21 kst 2 kins Where 79,0 = 50 = 50+273 = 323 k ورصدد 27 = 27+273 - 300 k 21 [15, i - 323] In[430] en [230 20% 430 5 (323-300] +0:1585-67x108 (398*-3001) 1000 + 35 2011 ( Tsi - 323] 374.688 6. 2609 2T CT, i- 323) 2345.885

i Ts, i 696.359 K .: highest steam temperature Ts, i = 423.359°C .. Therefore, heat rate qu' (Tg, i - Tso] In C3 in [83] - at kst at kins 21 (423.359 - 323) In (280) 230 200 In 430 230 + 35 0 1 100.716 W/m ..q' 100-716 W/m heat lose per unit tube length, in Wim q' 100 . 716 wlm