A dairy farm needs to chill the milk from 39°C (extraction temperature is the same as the cow's bodytemperature) to at least 12°C for storage by using an existing 4-m long concentric-tube heat exchanger.The inner tube of the heat exchanger is 4 cm in diameter. The milk (density: 1035 kg/m³, specific heat:3860 J/kg.K) flows into the heat exchanger at a rate of 270 liters per hour. On the cold side, there isa supply of water at 2°C at a rate of 0.23 kg/s. The estimated overall heat transfer coefficient of theheat exchanger is 1084.2 W/m².K. It was measured that the water comes out of the heat exchangerat 11°C. Is the milk indeed being cooled down to at least 12°C by heat exchanger as required by thefarm? Looking at the temperatures obtained from your calculation, put an argument whether the heatexchanger is a parallel-flow or a counter-flow heat exchanger. Approximate specific heat of water is4200 J/kg.K. Neglect radiation. Effectiveness and NTU relationships for common heat exchangersEffectiveness as a function of NTU and Cr:Parallel flow:Counter flow:One shell and 2, 4, ... tube passes":n shells and 2n, 4n, ... tube passes*:Cross-flow both unmixed:Cross-flow* Cmar on mixed side:Cross-flow* Cmin on mixed side:All heat exchangers with C, = 0:NTU as a function of e and Cr:Parallel flow:Counter flow:One shell and 2, 4, ... tube passest:n shells and 2n, 4n, ... tube passes¹:Cross-flow both unmixed:Cross-flow" Cmaz on mixed side:Cross-flow* Cmin on mixed side:€ =All heat exchangers with Cr = 0:€ ==1 - exp[-NTU (1 + Cr)]1+ Cr1- exp[-NTU (1 - Cr)]1 - C, exp[-NTU (1 — Cr)]'NTU1+ NTU'when C₂ = 1€1 = 21+ C₂ + (1+C²) ¹1/²€ =1€ == [(²₁₁ ²¹+ )" - ¹] [(²¹²¹)" - c]'1-€1€1Use ₁ and NTU₁ from Eqn. 4€ = 1- expFNTU=(1 - exp{-C, [1 - exp(-NTU)]})NTU=€ = 1 - exp[-C₂¹ (1 - exp[-CrNTU])]€ = 1- exp(- NTU)=[(+)₁ NTU0.22 [exp(-C, NTU0.78) - :1+ exp-NTU₁ (1+ -C²) ¹/21- exp -NTU₁ (1+C²) ¹/2]C₂²-1¹n (6--11),InCrIn [1 - € (1 + Cr)]1+ Cr1 when C₁ = 1€NTU₁ = (1 + C²)-¹/2 In€1 =when Cr < 1F-1F-CrSolve Eqn. 6 numericallyNTU - InNTU=-NTU = nx NTU₁, use NTU₁ is from Eqn. 13 with €₁ as1/n= (Cr-1) ¹/F =1Crln (1-ɛ)when Cr < 1(E = 1).- In [1 + / - In (1 - eCr)]E =2 − (1+Cr)(1+C2) ¹1/2In [Cr In (1 e) + 1](1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(16)NTU=(17)1: If it is only a one-shell heat exchanger, € = ₁ and NTU = NTU₁. If there are n shells, use the ₁ and NTU₁ calculated based on oneshell formulation and calculate final and NTU for the entire heat exchanger. Also note, number of tubes does not directly feature in theseequations, they come in via the total area calculation.*: Single pass crossflow heat exchangers(13)(14)(15)

Answered: Image /qna-images/answer/ec59b577-64de-44c7-9120-f1024f519d08.jpg

A dairy farm needs to chill the milk from 39°C (extraction temperature is the same as the cow's body temperature) to at least 12°C for storage by using an existing 4-m long concentric-tube heat exchanger. The inner tube of the heat exchanger is 4 cm in diameter. The milk (density: 1035 kg/m³, specific heat: 3860 J/kg.K) flows into the heat exchanger at a rate of 270 liters per hour. On the cold side, there is a supply of water at 2°C at a rate of 0.23 kg/s. The estimated overall heat transfer coefficient of the heat exchanger is 1084.2 W/m².K. It was measured that the water comes out of the heat exchanger at 11°C. Is the milk indeed being cooled down to at least 12°C by heat exchanger as required by the farm? Looking at the temperatures obtained from your calculation, put an argument whether the heat exchanger is a parallel-flow or a counter-flow heat exchanger. Approximate specific heat of water is 4200 J/kg.K. Neglect radiation.

A dairy farm needs to chill the milk from 39°C (extraction temperature is the same as the cow's body temperature) to at least 12°C for storage by using an existing 4-m long concentric-tube heat exchanger. The inner tube of the heat exchanger is 4 cm in diameter. The milk (density: 1035 kg/m³, specific heat: 3860 J/kg.K) flows into the heat exchanger at a rate of 270 liters per hour. On the cold side, there is a supply of water at 2°C at a rate of 0.23 kg/s. The estimated overall heat transfer coefficient of the heat exchanger is 1084.2 W/m².K. It was measured that the water comes out of the heat exchanger at 11°C. Is the milk indeed being cooled down to at least 12°C by heat exchanger as required by the farm? Looking at the temperatures obtained from your calculation, put an argument whether the heat exchanger is a parallel-flow or a counter-flow heat exchanger. Approximate specific heat of water is 4200 J/kg.K. Neglect radiation.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter10: Heat Exchangers

Section: Chapter Questions

Problem 10.32P

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