Free and forced convection of heat in gases and liquids

THE general problem of heat transfer requires a knowledge of the laws of conduction, radiation and convection. In 1822, Fourier gave us the first thoroughly scientific definition of conductivity and reduced the problem of heat conduction to an exact science, with a power and completeness which left little room for extension or improvement even to the present day. The law of radiation was first suggested by Stefan in 1879 as a result of an analysis of some experiments made by Tyndall. In 1884 Boltzman deduced the law theoretically from the principles of thermo-dynamics and electromagnetics. Thus the laws of conduction and radiation have been accurately known for a long time, while the problem of convection has received relatively little study. This fact is surprising when we consider the important part played by convection in almost all cases of heat transfer. A complete mathematical solution of a convection problem would require a knowledge of the hydrodynamic laws of viscous fluids for stream line and turbulent motion, combined with the Fourier equations of heat conduction in a moving medium. At present our lack of the hydrodynamic laws for turbulent motion renders a rigorous solution impossible. Therefore in most of the theoretical work so far attempted the simplifying assumption of an in-viscid fluid has been found necessary. The theoretical results obtained when viscosity is neglected are in general far from the experimental facts. Langmuir's study of the problem showed that the viscosity is a factor of first importance which cannot be neglected. He therefore adopted a film theory as an approximation. The reason for the existence of a film around a hot body may be seen as follows: Consider a horizontal wire maintained at a given temperature in a fluid, the fluid adjacent to the wire will become heated and rise while the cooler fluid of greater density will flow into its place. Thus a convection current is set up by the difference in density between the hot and cold fluid. This condition is usually referred to as free convection. At the surface of the wire the fluid is stationary due to viscosity. As we proceed from the surface of the wire the velocity of the convection currents increase until a distance is reached at which the critical velocity conditions in the fluid are exceeded and the stream line flows bursts into turbulent motion. The discontinuity between the stream line and turbulent motion constitutes the outer boundary of the film. At the inner boundary the fluid has the temperature of the hot surface and at the outer boundary the temperature of the ambient fluid. The actual configuration of the outer boundary is unknown. As an approximation we might assume that it was an eccentric ellipse or cylinder, etc., and determine the size and eccentricity so as to best fit the experimental results. For ease of calculation Langmuir adopted the simplest approximation and assumed that the outer boundary of the relatively stagnant film was a cylinder concentric with the wire. He thus reduced the hopelessly complex problem of convection to one of conduction in the steady state.