Predictions are presented of the concentration fluctuations in the turbulent mixing of two steady, coaxial jets of equal density issuing into a circular, concentric duct. The range of the jet-velocity ratio considered includes cases in which recirculation occurs. The root-mean-square fluctuating concentration is calculated from an elliptic differential equation which has the same form as the equations for the time-mean concentration, the stream function, the vorticity, the kinetic energy of turbulent motion and the rate of dissipation of turbulent kinetic energy. The equations are solved simultaneously by the method of Gosman et al. The predictions are compared with previously published experimental data. Satisfactory agreement is obtained.

Turbulent diffusion flames in a small, axisymmetrical cylindrical furnace are studied, using town gas. Results are reported, of the measurements made by an ionization probe of the probability of reaction at many locations inside the furnace. Predictions are also obtained for the experimental, conditions by numerical solution of a set of six simultaneous, elliptic, partial differential equations. The time-mean hydrodynamic characteristics are described by the four variables: stream function, vorticity, turbulence kinetic energy and the rate, of dissipation of turbulence energy; the reaction is described by the time-mean mixture fraction, f, and the mean-squared fluctuations of the mixture fraction, g. Instantaneous values of the mass fractions and the temperature are evaluated from the assumption that the variation with time of the instantaneous values of f is described by a random wave form which has a suitably clipped Gaussian distribution of the probability density. Effects on the time-mean density of the concentration and temperature fluctuations are accounted for. A method is suggested for calculating the probability of chemical reaction at points in the flow field. Computed results agree fairly well with measurements.

Fifteen methods for predicting laminar heat transfer coefficients are analysed and classified. Then each is applied to the problem of calculating the distribution of Nusselt number around the leading half of a circular cylinder in laminar flow. Large differences are shown to exist beween the predictions of the theories.

In this paper, the authors introduce and investigate the general solution and generalized Hyers-Ulam stability of n-dimensional non-quadratic functional equation of the form f∑i=1nxi=∑1⩽i