Optimum length of tubes for heat transfer in turbulent flow at constant wall temperature

Maximum heat transfer per cross-sectional area of a tube with smooth wall in turbulent flow at constant wall temperature is determined for a given pressure loss. The dimensionless tube length is determined dependent on the pressure Reynolds number, Prandtl number and inlet local pressure loss coefficient. Limiting cases for short and long tubes are separately investigated. Semi-empirical equations are derived for both optimum dimensionless tube length and dimensionless maximum heat flow per cross-sectional area using numerically obtained values with a maximum deviation of ±6.6% and with a RMSE of 3.5%. The results can also be applied to the channels with non-circular cross-sectional area.