Heat transfer at low temperatures between tube walls and gases in turbulent flow

Abstract

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.