Question

1. In a counterflow heat exchanger, the heat loss to the environment is to be included in the mathematical model. Considering the case of the hot fluid on the outside and the colder fluid on the inside, as shown in Figure below, sketch qualitatively the change that the inclusion of this consideration will have on the temperature distribution in the heat exchanger. Also, give the energy equation taking this loss into account. Hot Cold Energy loss

Answer 1

1. Given vigurie Hot cold Energy loss. 1 1 fig. with the energ 1OSS T Lose Lex Cymmetry Fig: wimout Energy At any given condition.. 6 cold Onet - Rate of energy Loss 12.5 15.5 12.8 15.0 10.0 geti' where Given that kg/hr 19.8 22.0 P (atm) 20.0 25.0 30.0 we know mat me Ap. Taking log on both the sides we les m Inm th in (0) y : mate y = lncmi coin (A). y and a wing the formula above and line wing matlab labove, we obrain, na0.9867 CE1.4221 = ln (A) 1,4221 - 4,1456 m 5.4.1458 p(0.4846) ] Calculating the R2: 0.96961 we find fit a Ace we get value of R2

If we hit a we get This line ar line having aboua / Matlab, m: 0:45 40A+,8.4400) gets an R² value of 0.9981 a better fir wina line of the can get Therefore linear form 6000 kg /m² ь . T(t) - Tlf) Ti - Tf -3 2.8x106m Q3 Given that Sid2cm. density Specific heat - 300 J/kg*, TA 220°C Ti = dool has -bt ce Step let 14) -14) shx2.4 VID a 6000 x 300 + Ti-Tf - 1:67 10-4 h 4 [+=(2x102)? e In a = -1.67x10-4 ht hx2.9x103 in 600 x 300 x 3210-6 Ч x m y = ma b = 1,67 x 10-45 lets Ait a line wing ontre smallab and we get y. -0,32 512 -- 0.0005 y ~ -0.325) x . -0.32513 -1.67 X10-4h n=1946.6 W/m2K R? value is 0.9960.

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