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 density of heat flux to the wall

Integral relations are derived for the calculation of the Nusselt number and coefficients of hydraulic drag and friction drag under conditions of pipe flow of dropping liquid and gas of temperature-dependent physical properties. In the limiting case of steady-state flow of liquid of constant properties, the expression for the Nusselt number transforms to the well-known Lyon integral. The results of calculation of heat transfer and drag by an integral method are compared with more exact results obtained using the numerical solution of the set of differential equations of convective heat transfer. An inference is made about the conditions under which integral methods may be employed. An algorithm is developed for the calculation by an integral method of heat transfer and drag under conditions of quasi-steady-state pulsating flow. It is demonstrated that the flow rate oscillations superposed on the flow in the pipe enhance the effect of the variability of the properties on heat transfer, and for gas on friction drag. For a dropping liquid under conditions of pulsating flow, the friction drag depends less significantly on the variability of the properties (viscosity) than in the case of steady-state flow. The degree of manifestation of the effects identified above is the higher, the higher the oscillation amplitude and the lower the value of the Reynolds number of averaged flow.