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Thermodynamics: Heat Exchangers & Mixing Chambers

Mixing chamber are devices that mix two streams of fluid to cause a temperature change that is somewhere between the temperature of the two streams. The temperature alteration is highly dependent on the mass flow of the two streams in comparison to each other.

When solving for these types of problems the conservation of mass must be taken into consideration. The reason why is because the mass of fluid that is entering this device must equal the mass of fluid that leaves this device. In addition to the conservation of mass, if the device is well insulated, heat transfer in and out of the device can be considered negligible. Finally, changes in potential energy, kinetic energy, and work can be considered negligible. Taking these facts into consideration a basic equation for energy balance can be derived, refer to equation 1. Equation 1 is derived for the image seen below, if the device that you are analyzing is different, then you may have to modify equation 1. You can also modify this equation to fit other terms as needed.

energy balance of a mixing chamber equation (1)

Mixing Chamber Diagram

Heat exchangers on the other hand are similar to mixing chambers except they do not allow the two streams of fluid to mix. Since the streams of fluid does not mix the mass flow entering and leaving each of the pipes will remain constant. Also, just like with mixing chambers, if the heat exchanger is well insulated the heat transfer can be considered negligible. The kinetic energy, work, and potential energy can also be considered negligible. Taking this into consideration an energy balance equation can be derived for a heat exchanger; equation 2. Equation 2 is derived for the heat exchanger below. If the heat exchange you are trying to analyze is different you may have to modify this equation. You can also modify this equation to fit other terms as needed.

energy balance of a heat exchanger equation (2)

Heat Exchanger Diagram

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