Question

Hot water (cph=4188 J/kg-K) with mass flow rate of 2.5 kg/s at 100 C enters a thinwalled concentric tube counter-flow heat exchanger with a surface area of 23 m² and an overall heat transfer coefficient of 1000 W/m²-K. Cold water (cpc=4178 J/kg-K) with mass flow rate of 5 kg/s enters the heat exchanger at 20 C , determine

(a) the heat transfer rate for the heat exchanger

Answer 1

To calculate the heat transfer rate for the heat exchanger, use the equation Q = mcΔT. For the hot water, Qh = mh * cph * ΔTh, and for the cold water, Qc = mc * cpc * ΔTc. The heat transfer rate for the heat exchanger is the difference between the heat transferred to the hot water and the heat transferred to the cold water, Q = Qh - Qc.

Step-by-step explanation:

To calculate the heat transfer rate for the heat exchanger, we can use the equation:

Q = mcΔT

where Q is the heat transfer rate, m is the mass flow rate, c is the specific heat, and ΔT is the temperature difference.

For the hot water:

Qh = mh * cph * ΔTh = (2.5 kg/s) * (4188 J/kg-K) * (100 °C - 20 °C) = 804,600 J/s = 804.6 kW

For the cold water:

Qc = mc * cpc * ΔTc = (5 kg/s) * (4178 J/kg-K) * (100 °C - 20 °C) = 1,050,600 J/s = 1.05 MW

The heat transfer rate for the heat exchanger is the difference between the heat transferred to the hot water and the heat transferred to the cold water:

Q = Qh - Qc = (804.6 kW - 1.05 MW) = -245.4 kW