Question

In a dairy operation, milk at a flow rate of 250 L/h and a cow-body temperature of 38.6 oC must be chilled to a safe-to-store temperature of 13 oC or less. Ground water at 10 oC is available at a flow rate of 0.72 m3/h. The density and specific heat of milk are 1030 kg/m3 and 3860 J/kg∙K, respectively.

a) What is the UA product of a counterflow heat exchanger required for the chilling process?

a) 0.043 W/°C

b) 0.057 W/°C

c) 0.065 W/°C

d) 0.072 W/°C

Answer 1

To find the UA product of the counterflow heat exchanger, the heat transfer rate Q must be calculated based on the flow rates, temperature differences, density, and specific heat of milk, then applied to the LMTD for a counterflow heat exchanger.

Step-by-step explanation:

The challenge posed by this question is to determine the UA product of a counterflow heat exchanger needed to chill milk from a cow-body temperature of 38.6 ℃ to a safe storage temperature of 13 ℃ using ground water at 10 ℃. The flow rate of milk is 250 L/h, and the flow rate of water is 0.72 m3/h. Given the density and specific heat of milk as 1030 kg/m3 and 3860 J/kg·K, respectively, the necessary heat transfer can be calculated, and from there, the required UA value can be found considering the logarithmic mean temperature difference (LMTD) for a counterflow heat exchanger. This involves using the formula Q = UA×LMTD where Q is the heat transfer rate.