Question

Water is heated by hot air in a heat exchanger. The flow rate of the water is 12 kg/s and that of the air is 2 kg/s. The water enters at 40⁰C, and the air enters at 460⁰C. The overall heat transfer coefficient of the heat exchanger is 275 W/m² K based on a surface area of 14 m². Determine the effectiveness of the heat exchanger if it is:

(A) A parallel-flow type
(B) A crossflow type (both fluids unmixed). Then calculate the heat transfer rate for the two types of heat exchangers described and the outlet temperatures of the hot and cold fluids for the conditions given.

Answer 1

The effectiveness of a heat exchanger is analyzed by calculating the heat transfer rate and outlet temperatures using the flow rates, inlet temperatures, specific heat capacities, heat transfer coefficient, surface area, and the exchanger type. Different flow arrangements in parallel-flow and cross-flow heat exchangers affect the temperature difference that drives the heat transfer.

Step-by-step explanation:

The effectiveness of a heat exchanger is a measure of its ability to transfer thermal energy between the hot and cold fluids as compared to an ideal heat exchanger that would achieve the maximum possible heat transfer.

The heat transfer rate and outlet temperatures of the hot and cold fluids in a heat exchanger can be calculated with knowledge of the flow rates, inlet temperatures, specific heats of the fluids, heat transfer coefficient, surface area, and the type of heat exchanger (parallel-flow or crossflow).

To calculate the heat transfer rate and the effectiveness of the heat exchanger, the following steps can be performed:

1. Use the relevant heat transfer equations to establish relationships between the heat transfer rates, temperatures, and flow rates of the cold and hot fluids.
2. Determine the temperature difference driving the heat transfer, based on the inlet temperatures and the type of heat exchanger.
3. Calculate the actual heat transfer rate by applying the overall heat transfer coefficient to the temperature difference and the surface area.
4. With the heat transfer rate known, the outlet temperatures of the fluids can be calculated using energy balance principles and the specific heat capacities of the fluids.
5. Compare the actual heat transfer rate to the maximum possible rate to determine the effectiveness of the heat exchanger.

For both a parallel-flow and a cross-flow heat exchanger, the principles remain the same, but the temperature difference driving the heat transfer may vary due to the different flow arrangements.