%0 Journal Article
%A
%A
%T Heat transfer at low temperatures between tube walls and gases in turbulent flow
%D 1947
%R 10.1098/rspa.1947.0099
%J Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
%P 6-21
%V 191
%N 1024
%X An apparatus was designed on the counter-flow system to study heat transfer between tube walls and gases at low temperatures in a region in which careful measurements had not previously been made. Oxygen, nitrogen and carbon dioxide were used, covering a temperature range from + 45° to –167° C, pressures up to 11 atm., and Reynolds numbers from 3000 to 60,000. Results were correlated by the use of dimensionless groups and a general equation obtained, independent of the nature of the gas and applicable over the whole range of experiments. With Reynolds numbers evaluated at mean film temperatures, the coefficient in the equation was found to be 5% lower than that obtained from measurements made at normal and high temperatures. This is regarded as justifying the extension of the ordinary equation to low-temperature regions. Determinations on friction accompanying heat transfer with gases in turbulent flow at low temperatures showed that the effect of heat transfer on the friction factor was small. Nomenclature C constant in Sutherland equation. D diameter of tube; equivalent diameter of annulus, i. e. internal diameter of outer tube minus external diameter of inner tube. F frictional force per lb. of fluid. L length of tube. T absolute temperature, ° K. V linear velocity of gas, as calculated from mass flow per unit time per unit of cross sectional area, divided by the mean density of the fluid. c specific heat of fluid at constant pressure. f friction factor, or coefficient of proportionality in pressure drop equation. g acceleration due to gravity. h coefficient of heat transfer between fluid and surface. k thermal conductivity of fluid. r, s constants (used as exponents). α, β constants. ϕ(x) function of x. μ absolute viscosity of fluid. ρ absolute density of fluid. Δp pressure drop in pipe. Subscripts a refers to annulus. i refers to inner tube. f refers to properties evaluated at film temperatures. Film temperature is taken as the arithmetic mean of the bulk fluid temperature and the tube-wall temperature.
%U http://rspa.royalsocietypublishing.org/content/royprsa/191/1024/6.full.pdf