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The Quarterly Journal of Mechanics and Applied Mathematics 1970 23(2):163-170; doi:10.1093/qjmam/23.2.163
© 1970 by Oxford University Press
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SINGULAR PERTURBATION SOLUTIONS OF SOME HOT WIRE CONDUCTION PROBLEMS

AEMER D. ANDERSON

( Department of Energy Engineering, University of Illinois at Chicago Circle Chicago, Illinois )

Solutions are presented for the temperature profile along a hot wire anemometer immersed in a steady constant-property flow of parabolic velocity profile. A King-type heat transfer coefficient is assumed. The solutions are obtained using singular perturbation techniques. These methods are particularly suitable since there are thin conduction boundary layers near each end of the wire. The effects of the linear coefficient of resistivity of the wire and the curvature of the velocity profile are taken into account as perturbations to the solution for a linear velocity profile. These results could well be useful in the design of a device to measure wall shear stresses in turbulent flows.


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