Question

What is the heat capacity rate? What can you say about the temperature changes of the hot and cold fluids in a heat exchanger if both fluids have the same capacity rate? What does a heat capacity of infinity for a fluid in a heat exchanger mean?

Short answer

Answer: When hot and cold fluids in a heat exchanger have the same capacity rate, their temperature changes will be equal and opposite. For example, if the hot fluid temperature decreases by 10 degrees Celsius, the cold fluid temperature will increase by the same amount. A heat capacity of infinity for a fluid means that the fluid can absorb or release an infinite amount of heat without any change in its temperature, although no real fluid has an infinite heat capacity. In a heat exchanger, a fluid with a large heat capacity (compared to other fluids) might resemble a fluid with an infinite heat capacity, where its temperature changes negligibly during the heat exchange process.

Step-by-step solution

1. Heat Capacity Rate Definition

The heat capacity rate is the capability of a material or fluid to store heat energy. It is the product of the mass flow rate (m_dot) and the specific heat capacity (C_p) of the fluid. The heat capacity rate (C) can be defined as: C = m_dot * C_p

2. Temperature Changes in a Heat Exchanger with Same Capacity Rates

If both the hot and cold fluids in a heat exchanger have the same capacity rate, then their temperature changes will be equal and opposite. This is because the heat exchanged between the fluids equals the product of their capacity rates and temperature difference. Mathematically, Q = C_hot * (T_hot_in - T_hot_out) = C_cold * (T_cold_out - T_cold_in) Since C_hot = C_cold, we can write: (T_hot_in - T_hot_out) = (T_cold_out - T_cold_in) Therefore, the temperature change of the hot fluid will be equal to the temperature change of the cold fluid but in the opposite direction. For example, if the hot fluid temperature decreases by 10 degrees Celsius, the cold fluid temperature will increase by the same amount (10 degrees Celsius).

3. Meaning of Heat Capacity of Infinity for a Fluid in a Heat Exchanger

A heat capacity of infinity for a fluid means that the fluid can absorb or release an infinite amount of heat without any change in its temperature. In a heat exchanger, this would imply that the fluid with the infinite heat capacity could exchange heat indefinitely with other fluids without its temperature ever changing, regardless of the amount of heat transferred. In practice, no real fluid has an infinite heat capacity. However, a situation with a large heat capacity (compared to other fluids) might resemble the behavior of a fluid with an infinite heat capacity, where its temperature changes negligibly during the heat exchange process.