Module 3: Velocity Measurement
  Lecture 16: Validation of PIV with HWA
 

The term which contains the effects of fluid velocity, temperature of the wire and the fluid temperature is Nusselt number. The general expression for Nusselt number in forced convective heat transfer for incompressible flow is given by

(6)

where is the Reynolds number, is the effective cooling velocity, is the kinematic viscosity of fluid, is the fluid Prandtl number, is the specific heat of the fluid at constant pressure, is the angle between the free stream direction and the normal to wire, is Grash off number, Ma is Mach number, is the specific heat of fluid at constant volume, and is the temperature loading or overheat ratio. Further, are the thermal conductivities of the wire material and the fluid medium respectively. Fortunately, most applications permit a significant reduction in the number of parameters that must be included. The reasons are:

1 Forced convection parallel to the wire is small.

2. Prandtl number depends only on fluid properties.

3. Buoyancy effects can be neglected for This expression shows that for air velocities greater than about 5.2 cm/s, buoyancy effects can be neglected.

4. For near atmospheric conditions of pressure and temperature and low velocities, Mach number is negligibly small.

5. Over a suitable range of temperatures (where HWA is commonly employed) can be assumed to be constant.