Integral methods of calculation of heat transfer and drag under conditions of turbulent pipe flow of liquid of variable properties: Steady-state and quasi-steady-state flows in a round pipe with constant temperature on the wall

An integral method is suggested for the calculation of heat transfer and drag under conditions of flow of dropping liquid and gas in a pipe with constant wall temperature. It is found that the kind of thermal conditions on the wall $(T_{\text{wall}} = \text{const}$ or $q_{\text{wall}} = \text{const})$ has insignificant effect on the Nusselt number and coefficient of friction drag for a steady-state flow of dropping liquid of variable viscosity. For a quasi-steady-state pulsating flow of dropping liquid, the thermal boundary conditions have an appreciable effect on the Nusselt number alone; in so doing, the degree of this effect increases with the oscillation amplitude and hardly depends on the temperature factor. For steady-state and quasi-steady-state flows of gas at high temperature factors, the values of heat transfer and drag at $T_{\text{wall}} = \text{const}$ differ significantly from those at $q_{\text{wall}} = \text{const}$.