XII. On the convection of heat from small cylinders in a stream of fluid: Determination of the convection constants of small platinum wires with applications to hot-wire anemometry

Abstract

The general problem of the convection of heat from bodies immersed in moving media has recently received considerable attention both from the theoretical and experimental point of view. The equation of the conduction of heat in a moving fluid was stated by Fourier as long ago as 1820,( 1 ) and a few years later was expressed by Poisson( 2 ) and Ostrogradsky( 3 ) in the familiar form c D θ /D t = ∂/∂ x ( k ∂ θ /∂ x ) + ∂/ ∂ y ( k ∂ θ /∂ y ) + ∂/∂ z ( k ∂ θ /∂ z ), . . . . . (1) where θ is the temperature of the fluid at any point ( x, y, z ), c the heat capacity of the fluid per unit volume, k its thermal conductivity, and D/D t the “mobile operator” D/D t = ∂/∂ t + u ∂/∂ x + v ∂/∂ y + w ∂/∂ z of the hydrodynamical equations. In 1901 the problem was taken up by Boussinesq,( 4 ) whose memoir on the subject in 1905 contains a great number of successful calculations of heat losses from bodies of various shapes immersed in a stream of fluid.