Question

In a heat exchanger with 1 body - 4 pipes and 104 pipes per passage (each with a diameter of 2.6 cm, 4 m per passage), water enters at 8 kg/h and 350 K, while air enters at 15°C with a mass flow of 18 kg/s. The pollution factor of the sediment is 0.0026 m²K/W. Inner and outer surface transport coefficients are 450 and 200 W/m²K. Using specific temperatures at 25°C for air and water:

a. Draw the shape of the problem to show the heat exchanger effectiveness.
b. Calculate the heat transfer rate (kW).
c. Calculate the outlet temperatures (°C) of the water and air and show the temperatures in the (T_L) diagram.

Answer 1

To solve this problem, we can use the equations for heat transfer rate and effectiveness of a heat exchanger. The problem involves a counter-flow heat exchanger with specific temperatures for air and water. The heat transfer rate and outlet temperatures can be calculated using the given information.

Step-by-step explanation:

The shape of the problem can be represented as a counter-flow heat exchanger, where the hot water and cold air flow in opposite directions. To calculate the heat transfer rate, we can use the equation:

Q = U * A * ΔT

where Q is the heat transfer rate, U is the overall heat transfer coefficient, A is the surface area, and ΔT is the temperature difference. To calculate the outlet temperatures of the water and air, we can use the effectiveness of the heat exchanger:

ε = (T₁ - T₂) / (T₁ - T₃)

where ε is the effectiveness, T₁ is the initial temperature, T₂ is the outlet temperature of the hot fluid, and T₃ is the temperature of the cold fluid.

Using specific temperatures at 25°C for air and water:

a. The shape of the problem is a counter-flow heat exchanger.

b. The heat transfer rate can be calculated using the equation mentioned above.

c. The outlet temperatures of the water and air can be calculated using the effectiveness equation and the given initial temperatures.