Question

Consider a heat exchanger in which both fluids have the same specific heats but different mass flow rates. Which fluid will experience a larger temperature change: the one with the lower or higher mass flow rate?

Short answer

Answer: The fluid with a lower mass flow rate will experience a larger temperature change.

Step-by-step solution

Review heat transfer relations for a heat exchanger

The heat transfer between two fluids in a heat exchanger can be described using the following equation: Q = m1 * c1 * (T1_out - T1_in) = m2 * c2 * (T2_out - T2_in), where Q is the heat transfer, m1 and m2 are the mass flow rates of each fluid, c1 and c2 are the specific heats of each fluid, and T1_out, T1_in, T2_out, T2_in are the inlet and outlet temperatures of each fluid. Since both fluids have the same specific heats, we can simplify the equation as: Q = m1 * c * (T1_out - T1_in) = m2 * c * (T2_out - T2_in).

Determine the temperature change for each fluid

Now we will determine which fluid will experience a larger temperature change depending on their mass flow rates. To do so, we'll examine how the temperature difference in each fluid relates to their mass flow rates. Divide both sides of the equation by their respective mass flow rates and specific heats: (T1_out - T1_in) / m1 = (T2_out - T2_in) / m2. Let ΔT1 = T1_out - T1_in and ΔT2 = T2_out - T2_in be the temperature changes of each fluid. Then we have: ΔT1 / m1 = ΔT2 / m2.

Analyze the relationship between mass flow rates and temperature changes

Since we are given that the fluids have different mass flow rates (m1 ≠ m2), we now study the relationship between the mass flow rates and the corresponding temperature changes. From the equation we derived in Step 2, suppose m1 > m2, then from ΔT1 / m1 = ΔT2 / m2, it follows that ΔT1 < ΔT2. This means that if Fluid 1 has a higher mass flow rate, it will experience a smaller temperature change compared to Fluid 2. On the other hand, if m1 < m2, then from the same equation, we would have ΔT1 > ΔT2. This means that if Fluid 1 has a lower mass flow rate, it will experience a larger temperature change compared to Fluid 2.

Conclusion

The fluid with a lower mass flow rate will experience a larger temperature change in the heat exchanger, while the fluid with a higher mass flow rate will experience a smaller temperature change.

Key concepts

Specific Heat

In the world of heat exchangers, understanding specific heat is essential. Specific heat (\( c \)) is a property of a material that measures the amount of heat needed to change its temperature. Think of it as the thermal capacity of a fluid. In a heat exchanger scenario, if two fluids have the same specific heat, they can absorb and release heat at the same rate per unit mass. This property helps balance out heat dynamics between the fluids. Specific heat is typically measured in joules per gram per degree Celsius (J/g°C).
A higher specific heat means more energy is needed to change the temperature, while a lower specific heat requires less energy.
When both fluids have the same specific heat, like in our exercise, it simplifies the problem as this factor cancels out when analyzing the heat exchange process.

Mass Flow Rate

Mass flow rate (\( m \)) is all about how much fluid moves through the heat exchanger in a given period of time. It's like the 'speed' of the fluid in the heat exchange process and is generally expressed in kilograms per second (kg/s).
The mass flow rate is crucial in determining how effectively a heat exchanger can transfer heat between two fluids. In our exercise, two fluids with differing mass flow rates can experience different temperature changes even when they have the same specific heat.

• A higher mass flow rate means more fluid is moving through, keeping the temperature change smaller.
• A lower mass flow rate results in a larger temperature change, as less fluid can absorb or release the heat energy.

This property of mass flow rate is central to solving which fluid experiences a greater temperature change.

Temperature Change

The temperature change (\( \Delta T \)) is the difference in temperature before and after the fluid passes through the heat exchanger. Defined mathematically as \( \Delta T = T_{out} - T_{in} \), it tells us how much heat is absorbed or released by the fluid.
In the exercise scenario, temperature change is directly influenced by the mass flow rate of the fluid. When two fluids have the same specific heat but different mass flow rates, the one with the lower mass flow rate will have a larger temperature change. This happens because less mass means less heat capacity, leading to a more significant change in temperature as it absorbs or loses heat.
Understanding the temperature change is vital as it highlights the effectiveness of heat transfer and the operational efficiency of the heat exchanger.

Heat Transfer Equation

The heat transfer equation is fundamental for calculating heat exchange between two fluids. It's a tool that ties together specific heat, mass flow rate, and temperature change. The equation is expressed as:
\[ Q = m \cdot c \cdot \Delta T \]Where \( Q \) is the heat transfer, \( m \) is the mass flow rate, \( c \) is the specific heat, and \( \Delta T \) is the temperature change.
In our specific heat exchanger scenario, since both fluids have the same specific heat, the equation simplifies and highlights the relationship between mass flow rate and temperature change without the influence of specific heat differences.
This equation shows us that by manipulating factors like mass flow rate, we can predict and control temperature changes, effectively managing the heat transfer process within a heat exchanger. Understanding this balance is crucial for designing efficient systems to maintain desired thermal conditions.