11.28 A shell-and-tube heat exchänger l and two tube passes is used as a regener

Question

11.28 A shell-and-tube heat exchänger l and two tube passes is used as a regenerator, to pre- heat milk before it is pasteurized. Cold milk enters the regenerator at Ta = 5°C, while hot milk, which has completed the pasteurization process, enters at Thu 700. After leaving the regenerator, the heated milk enters a second heat exchanger, which raises its tem- perature from To to 70°C Pasteurizer with secondary heat exchanger in, me, Thi Regenerator h,0 (a) A regenerator is to be used in a pasteurization process for which the flow rate of the milk is m, m, = 5 kg/s. For this flow rate, the manufac- turer of the regenerator specifies an overall heat transfer coefficient of 2000 W/m2 K. If the desired effectiveness of the regenerator is 0.5, what is the requisite heat transfer area? What are the corre- sponding rate of heat recovery and the fluid outlet temperatures? Refer to Problem 11.27 for the properties of milk. (b) If the hot fluid in the secondary heat exchanger derives its energy from the combustion of natural

Explanation / Answer

Solution:

U= 2000

a)

From given arrangement

we can say it is a counter flow arrangement.

here mc = mh = 5kg/s

Cp for milk is not given but both lines fluid is same therefore Ch = Ch = Cp

& assumping Cp = 1

therefore it is case of C=1 & Effectiveness is given as 0.5

0.5 = Thi-Tho/(Thi - Tci)

0.5 = (70-Tho)/(70-5)

Tho = 37.5

Heat transfer is given by

Q = mh Ch (Thi-Tho)

= 5 x 1x (70-37.5)

= 187.5 W

LMTD for such case with C=1 & counter flow is given by = temp difference at any side = Tho-Tci = 37.5-5

LMTD = 32.5 C

Q = U A LMTD

187.5 = 2000 (A) (32.5)

A =2.88 x 10^-3 m2 = 28.846 cm2

Temp outlet for hot fuild Tho 37.5 C

Temo outlet for cold fluid Tco = 37.5 C

b)

fuild entering the secondary regenerator is at temp = 37.5 C

final temp is 70

m = 5kg/s

Cp =1

Q = mC(T1-T2)

= 5 x 1 x (70-37.5)

= 162.5 W

this energy 162.5 J is consumed per sec

total energy in a year = 162.5 x 365x 24x60x60

= 5124.6 MJ

cost of natural gas is 0.02 /MJ

cost save for natural as is = 0.02 x 5124.6

= 102.492 dollars per year

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