The effect of pressure upon natural convection in air

Abstract

Dimensional considerations show, on certain assumptions, that natural convection depends upon the dimensionless numbers M = ag θ l 3 sρ 2 / μk , and N, = μ s / k , where l is a representative linear dimension, θ a representative temperature difference, a the coefficient of expansion of the fluid, s the specific heat per unit mass at constant pressure, ρ the density, μ the viscosity, and k the conductivity. If H denotes the rate of heat flow across unit area of any given surface within the fluid, it also follows that P, = H l / k θ, is a function of M and N. The assumptions made are discussed in an Appendix. For gases N varies little between wide limits of pressure and temperature, and may in general be omitted, P therefore depending only upon M. For a given gas, M is proportional to θ l 3 , and increases with the pressure p , being nearly proportional to p 2 . The variation of P with M can be found by experiments in which either θ, l , or p is varied, but the range of M to be got by varying θ is relatively small, not only because of the different indices in M, but also because for large values of θ the assumption made in the dimensional analysis, that the constants of the gas do not vary with temperature, is inadmissible. By varying the pressure, M can be varied over a wide range for a single value of l ; thus only one experimental apparatus need be constructed, and it may be of reasonable size, large surfaces being difficult to heat uniformly and the surrounding conditions difficult to control.