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

What does it mean when a heat capacity of infinity is mentioned for a fluid in a heat exchanger? Answer: Heat capacity rate (C) refers to the rate at which a substance can absorb or release heat as its temperature changes, and it is calculated using the formula C = m * cp, where m is the mass flow rate (kg/s), and cp is the fluid's specific heat capacity (J/(kg·K)). In a heat exchanger with equal heat capacity rates for both the hot and cold fluids, the fluids will experience equal and opposite temperature changes, as their temperature differences will be equal. A heat capacity of infinity implies a hypothetical situation where a fluid has an unlimited capacity to absorb or release heat without experiencing any significant change in temperature, and it is used for approximate calculations when there is a vast difference in heat capacity rates between two fluids.

Step-by-step solution

Define Heat Capacity Rate

Heat capacity rate, denoted as C (also known as 'heat capacity flow rate'), is a property that defines the rate at which a substance can absorb or release heat as its temperature changes. It is a product of the mass flow rate (m) and the specific heat capacity (cp) of a fluid. The formula to find the heat capacity rate is: C = m * cp where C is the heat capacity rate, m is the mass flow rate (kg/s), and cp is the specific heat capacity of the fluid (J/(kg·K)). Heat capacity rate determines how fast a fluid's temperature changes with respect to the heat transfer rate (Q). Higher heat capacity rate indicates that the fluid can absorb or release larger amounts of heat with relatively smaller changes in temperature.

Temperature Changes in a Heat Exchanger with Equal Heat Capacity Rates

In a heat exchanger, heat is transferred between two fluids with different temperatures. One fluid is the hot fluid, which cools down while transferring its heat, and the other fluid is the cold fluid, which heats up by receiving the heat from the hot fluid. If both the hot and the cold fluids have the same heat capacity rate then they will experience equal and opposite temperature changes. This occurs because the heat transfer rate (Q) is constant throughout the exchanger, and since the heat capacity rates are the same, their temperature differences will be equal. This can be expressed mathematically as: ΔTh = -ΔTc where ΔTh is the temperature change of the hot fluid, and ΔTc is the temperature change of the cold fluid.

Heat Capacity of Infinity in a Heat Exchanger

A heat capacity of infinity for a fluid in a heat exchanger implies that the fluid has an unlimited capacity to absorb or release heat without experiencing any significant change in temperature. This is a hypothetical situation and is not practically possible. In reality, every fluid has a finite heat capacity. However, such scenarios can be used for approximate calculations when there is a vast difference in heat capacity rates between the two fluids. In this case, the fluid with a much greater heat capacity rate can be assumed to have infinite heat capacity. The temperature of this fluid will remain practically constant throughout the heat exchanger, while the other fluid will experience significant temperature changes.

Key concepts

Heat Exchanger

A heat exchanger is a device used to transfer heat from one fluid to another.
These two fluids can be either liquids or gases, and they flow through the heat exchanger, usually in separate pipes or channels.
This is done to ensure that the fluids do not mix, although they may exchange heat between them.

• The hot fluid, which has a higher temperature, releases its heat.
• The cold fluid, which starts at a lower temperature, absorbs this heat.

In a heat exchanger, the amount of heat exchanged depends on several factors including temperature difference, area of heat exchange, and the properties of the fluids involved.
Understanding the behavior of fluids in heat exchangers is crucial in many engineering applications, such as cooling systems, air conditioning units, and industrial processes.

Specific Heat Capacity

Specific heat capacity is a property that tells us how much heat is needed to change the temperature of a substance.
More technically, it is the amount of heat per unit mass required to raise the temperature by one degree Celsius (or one Kelvin).

• It is specific to the type of substance. For example, water has a high specific heat capacity compared to many other fluids.
• The unit of specific heat capacity is Joules per kilogram per Kelvin (J/(kg·K)).

A higher specific heat capacity means the substance takes more heat to change its temperature. Consider this similar to having a fuel tank; a larger tank (higher specific heat) means needing more fuel (heat) to fill it to the next mark (temperature change).
In heat exchangers, knowing the specific heat capacity helps determine how a fluid will behave as it receives or releases heat.

Mass Flow Rate

Mass flow rate is the amount of mass flowing through a given surface per unit time.
In heat exchangers, this is an essential concept, as it helps decide how much heat the fluid can exchange in a given time.

• The mass flow rate is usually measured in kilograms per second (kg/s).
• It directly affects the heat capacity rate, as the heat capacity rate is a product of the mass flow rate and specific heat capacity.

In the context of heat exchangers, managing the mass flow rate can help control the efficiency of heat exchange. A higher mass flow rate means more fluid is passing through, thus potentially carrying more heat.
Designing heat exchangers requires careful consideration of mass flow rate to optimize energy transfer and ensure system efficiency.