Prandtl Number Importance in Thermal Mass Flow Measurement

One of the RTDs is heated by an integrated circuit and functions as the flow sensor, while a second RTD acts as the reference sensor and determines the gas temperature. The circuitry maintains a continuous overheat between the flow sensor and reference sensor. As gas flows by the heated RTD, flowing gas molecules transport heat away from it, and as a result, the sensor cools, and the energy is lost. The circuit balance disrupts, and the temperature difference (ΔT) between the heated RTD and the reference RTD changes. Within a second, the circuit restores the lost energy by heating the flow sensor to adjust the overheat temperature. The electrical power required to sustain this overheat denotes the mass flow signal. The Prandtl number is defined as the ratio of momentum diffusivity to thermal diffusivity. Small values of the Prandtl number, Pr less than 1, mean the thermal diffusivity dominates. Whereas with large values, Pr more than 1, the momentum diffusivity dominates the behavior. For example, the typical value for liquid mercury, about 0.025, indicates that heat conduction is more significant than convection, so thermal diffusivity is dominant. The Prandtl number is a dimensionless number, named after its inventor, a German engineer Ludwig Prandtl. The Prandtl number is defined as the ratio of momentum diffusivity to thermal diffusivity. The momentum diffusivity, or as it is normally called, kinematic viscosity, tells us the material’s resistance to shear-flows (different layers of the flow travel with different velocities due to, e.g., different speeds of adjacent walls) in relation to density. In comparison to the Reynolds number, the Prandtl number is not dependent on the geometry of an object involved in the problem but is dependent solely on the fluid and the fluid state. Air at room temperature has a Prandtl number of 0.71, and for water, at 18°C, it is around 7.56, which means that the thermal diffusivity is more dominant for air than for water.

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