Fawzal number

The Fawzal number (Fa) is a dimensionless quantity that describes the ratio of convective heat transfer or cooling capacity over its power consumption to drive the coolant medium. The number was introduced earlier as Rotor Cooling Performance Index. for assessing rotor cooling design of YASA machine then later change to Cooling Performance Index as it can be used in a broader cooling application. It is defined as:

[math]\displaystyle{ Fa={Convective HT \over Power Consumption} }[/math]

The number is used to assist in determining the cooling performance when a design or parameter changes especially in conducting parametric studies. In general, the higher Fawzal number means better cooling performance because it shows that the convective heat transfer is dominated over the power required to drive the coolant

Definition

The Fawzal number was first introduced in assessing the rotor cooling design of an axial flux permanent magnet machine for automotive hybridisation or electrification application, However, it can be shared with other similar cooling principles such as rotating machinery or rotating component (i.e. electrical machine, automotive disc brake, turbine etc).

For this application, it is defined as:

[math]\displaystyle{ Fa={Convective HT \over Windage Losses}={\dot{Q} \over E{\scriptstyle\text{w}}}={hA(T_a - T_b) \over \tau\omega} }[/math]

where

[math]\displaystyle{ \dot{Q} }[/math] is the convective heat transfer [W]

[math]\displaystyle{ h }[/math]s the heat transfer coefficient [W/(m²•K)]

[math]\displaystyle{ A }[/math]is the area [m²]

T_a is the solid surface temperature [K]

T_b is the fluid temperature [K]

[math]\displaystyle{ E{\scriptstyle\text{w}} }[/math]is the windage losses [W]

[math]\displaystyle{ \tau }[/math]is the torque [Nm]

[math]\displaystyle{ \omega }[/math]is the rotational speed [rad/s]

Other applications

It was proposed that the Fawzal number can also be expressed in other terms for different applications yet verification required in the future.