Question

A tank with 2 m3 capacity initially contains 1 m3 liquid at 50 °C. There are two inlet streams to the tank and one outlet stream. The first inlet stream is steady at 0.2 m3 /min with T= 50 °C. Second inlet stream has a temperature of 100 °C and surges on a 2 min cycle. During the first minute the flow rate is steady at 0.2 m3 /min and during the second minute its flow stops completely, then the cycle repeats itself. The flow rate of the outlet stream is constant at 0.3 m3 /min. What will be the temperature in the tank at the end of the 4 minutes from the start of the operation (List the assumptions used)?

Answer 1

Doudm? Inin looc: © Sd Consider System as some Shown in which stream o enters at flowrete ord m/min (Lonste) n Strom ② enteret Vt (m/min) which I | 0-3 moyoni Chonges with tre & stiem I exits with Constant flow Rote 0.3m/ min Let t h e density of entering Lexing Stream which . is assumed to be constat ! C (pe specipe Heat Copclition of enting & exiting fluid e is essumed Constato Behovoro of it con be visulised as. tt 4 Applying moss Bdonce on tenk. P02 + Vpp - 0:3p- of lev) 00D + VH 0.3=hy ve volume of liquid in tok at time to Vt-o-1-dur dra (Ut-0-1)dt. Betneen -1 min. VH=0.9 mln. Savo I'60-) - 0-13-14 Na 001() [v=lol.ms

T-63.74 + cé 0.36€ At to , T=50c. 50-60 pceo. C=3-44 : T= 6 7 g +87-14 e 036t At t=lmin , AS292127588 6 66 T = 63-11-13:lle. To untreat T = 53.960) 1-13011203611)

Vto, dv=-0.1 m Now, between t = 1- I min . Valmo From a -0-317-50) -01 -011 dt d1+0=27=15 dt Test feest osat+C. Teoost 75 e tc. T= 75+ ce ost] At t=1 min, T=53.96. 53-96=75+C10818). re=-95.70°C Vallmy m at T=75-85.72 € ost. At t=2 min T-75-75-12 éa(s) T= 57.75°C) now betreen t=2-3 min Vt=0-2 mm, dv-olm Solution will be some as for t co-i min) - T= 63.11+cē.36t At t= dmin, T=57:75°C. 57.75 = 63:11 +(8 09617). 57-75-63111- - IC --11:03 00406 - T= 63.11 & 11:02 e 0.36t. At t = 3 min T=63011-11-02 ē 0-36(3). T = 59.36°C)

wom between ta3-4mm Veo, dv 1 2 0 m from min at (1-2 min ) v=lm? Solution will be some es betree T= 75+ceast At t= 3mn T-59:36°C 59.36-75=cé 02 (3) C=59:36-75=1-88.5°C 0:549 T=75-28-seat At t= 4min. toat: T= 75-78-5e0aly) TI = 62.19°C Temp after I min.

using given conditions at inlet at assuming no time delay and constant fluid properties we can find the temeprature at end of 4 min

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