A hot-wire anemometer is used to determine the boundary layer velocity profile in the air flow over a scale model of an automobile. The hot-wire is held in a traversing mechanism that moves the wire in a direction normal to the surface of the model. The hot-wire is operated at constant temperature. The boundary layer thickness is to be defined as the distance from the model surface at which the velocity is 90% of the free stream velocity. If the probe current is I0, when the hot-wire is held in the free stream velocity, U?, what current indicates the edge of the boundary layer? Neglect radiation heat transfer from the hot-wire and conduction from the ends of the wire.

Question

GIVEN
• Thin, electrically-heated constant-temperature wire in air flow near an automobile model
• Boundary layer thickness ° point when velocity (Uy) = 90% free stream velocity Vo
• Probe current at U? = Io FIND
• Probe current at edge of the boundary layer (Ib)
ASSUMPTIONS
• Radiation is negligible
• Conduction from the ends of the hot-wire is negligible
• Reynolds number is small

Answer 1

Restating the desire result: What is the current of V = 0.9 V? in terms of the current Io at Vo? Since the diameter of the wire will be very small, the Reynolds number will be small. For 1 < Re < 40 the Nusselt number,



Uy is the air velocity at a distance y from the model surface. The rate of electrical energy dissipation must equal the rate of convective heat transfer. The electrical resistance of the wire (ReI) is a function of the wire temperature only and is therefore constant in this case.



The current will be 0.979 Io at the edge of the boundary layer.