In a dairy operation, milk at a flow rate of 250 L/h and a cow-body temperature of 38.6 °C must be chilled to a safe-to-store temperature of 13 °C or less. Ground water at 10 °C 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 counterflow heat exchanger is used for this system. (a) Determine the effectiveness of the heat exchanger. (Ans: ε=0.895) (b) Determine the NTU of the heat exchanger (Ans: NTU=2.84) (c) Determine the UA product of a counterflow heat exchanger required for the chilling process. (Ans: 785 W/K) (d) Determine the length of the exchanger if the inner pipe has a 50-mm diameter and the overall heat transfer coefficient is U = 1000 W/m2-K. (Ans: 5.0 m) (e) Determine the outlet temperature of the water. (Ans: Tc. o=18.4 °C)

Aheat engine running backward is called a refrigerator if its purpose is to extract heat from a cold reservoir. the same engine running backward is called a heat pump if its purpose is to exhaust warm air into the hot reservoir. heat pumps are widely used for home heating. you can think of a heat pump as a refrigerator that is cooling the already cold outdoors and, with its exhaust heat qh, warming the indoors. perhaps this seems a little silly, but consider the following. electricity can be directly used to heat a home by passing an electric current through a heating coil. this is a direct, 100% conversion of work to heat. that is, 19.0 \rm kw of electric power (generated by doing work at the rate 19.0 kj/s at the power plant) produces heat energy inside the home at a rate of 19.0 kj/s. suppose that the neighbor's home has a heat pump with a coefficient of performance of 4.00, a realistic value. note: with a refrigerator, "what you get" is heat removed. but with a heat pump, "what you get" is heat delivered. so the coefficient of performance of a heat pump is k=qh/win. an average price for electricity is about 40 mj per dollar. a furnace or heat pump will run typically 200 hours per month during the winter. what does one month's heating cost in the home with a 16.0 kw electric heater? what does one month's heating cost in the home of a neighbor who uses a heat pump to provide the same amount of heating?