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A scheme to compute the friction and heat-transfer coefficients for a fluid flow with polymer admixtures to reduce friction, based on the mixing-path-length representation, is proposed. The influence of the molecular Prandtl number, the Reynolds number, and the magnitude of friction reduction by polymer molecules on the regularities of heat transfer is analyzed. Formulas are obtained to determine the heat-exchange coefficients. The results of computations by means of the scheme proposed are in satisfactory agreement with experimental results.

Experimental investigations show that the presence in a fluid of fibers and rigid asymmetric particles leads to a greater stability of flow in tubes and lowers the turbulent frictional resistance in a certain range of Reynolds numbers [1]. In the present paper, the anisotropic structure of a fluid with additives is described by Ericksen's rheological model [2]. The parameters of the model are particularized in accordance with the paper [3] of Pilipenko, Kalinichenko, and Lemak, and in the limiting case of weak Brownian motion allowance is made for the effect of the predominant orientation of the particles and the influence of additives on the longitudinal and shear viscosity. The stability of the Poiseuille flow is considered in the linear formulation. In an anisotropic viscous fluid, an equation of Orr-Sommerfeld type has a singular point. A rule for choosing the path of integration avoiding the singular point is obtained on the basis of a generalization of the method of Dikii [4] proposed in an investigation of the stability of the flow of an ideal fluid. The results of numerical calculations of the neutral stability curve for two-dimensional perturbations are given.

A formula for turbulent viscosity which allows a simple analytic expression to be obtained for the distribution of the averaged velocity of turbulent liquid flow at a rough surface is proposed.

One of the methods of reducing the frictional resistance of bodies moving in water is the discharge of a water-soluble polymer admixture into the turbulent boundary layer on the surface of the body. For dilute polymer solutions having constant concentration, existing semiempirical methods of calculation which use information on the effect of long molecules on the rearrangement of the flow in the boundary layer enable one to calculate the resistance of smooth and rough tubes [1] with sufficient accuracy and to analyze effects of the redistribution of local tangential stresses on the surface of plane plates [2]. Methods of calculating the drag of plates that have been developed up to the present time are also suitable for predicting the reduction of turbulent friction of elongated bodies by polymer admixtures. It is of interest to generalize these methods to the case of variable concentration. Below we consider the problem of calculating the turbulent boundary layer on a plane plate when a polymer solution is injected near its leading edge. For its solution we use the simplifying assumption that it is possible to replace the actual distribution of the concentration of polymer admixtures along a normal to the surface of the plate with an effective uniform distribution. This assumption enables us to estimate the discharge rate of the polymer that is required to obtain a given reduction in the frictional resistance.

The steady attention of investigators to the problem of turbulent drag reduction by polymer additives is connected both with the search of reasonable answers to the question, why insignificant quantities of a polymer (at concentrations about 10−6 – 10−4 g/sm3) are capable of changing the structure of wall turbulence efficiently, and also with practical supplements, the number of which is permanently increased.