The flow rate of water passing through a heating coil of an air handler is controlled by the:

The flow rate of water passing through a heating coil of an air handler is primarily controlled by the balancing valve on the heating loop. A balancing valve is designed to regulate and control the flow of water to ensure even distribution throughout the heating system. It does this by adjusting resistance in the flow, allowing for the optimal amount of hot water to circulate through the heating coils, which in turn maintains consistent air temperature and comfort levels.

In typical HVAC applications, precise control of water flow is crucial for efficient heating performance. The balancing valve helps prevent issues such as excessive flow, which can lead to energy waste and comfort control problems, or insufficient flow, which can result in inadequate heating.

The other options pertain to different components or contexts. An aquastat is used for temperature regulation in water heaters and does not directly control flow. Mixing valves in the heating loop regulate the mixture of hot and cold water for temperature control rather than directly managing flow rates through heating coils. Lastly, a mixing valve on the domestic hot water system is focused on managing water temperatures for domestic use, rather than for space heating purposes. These factors clarify why the balancing valve is the correct choice in this scenario.