The motion of a fluid due to a moving source of heat at the boundary

Abstract

Experiments performed by Fultz et al. (1959) and Stern (1959) indicate that if a flame is rotated around the bottom exterior of a pan or of a circular cylindrical annulus containing water then the fluid acquires a net vertical component of angular momentum in a direction opposite to that of the flame's motion. Stern gave an analysis showing how fluid, bounded by two horizontal plates subjected to small two-dimensional sinusoidal travelling temperature perturbations, could acquire and maintain such momentum. An assumption in Stern's analysis was that the density variations were constant between the plates. Here we shall examine the importance of the relaxation of this assumption. Also, another model, in which the upper surface of the fluid is free, is analysed, because this model conforms more closely with the experiments of Fultz et al. and Stern.For the problem of flow between two plates we shall show that there is a net flux of momentum in the direction opposite to the motion of the thermal field for all frequencies thereof. The same result holds in the case with a free surface when conditions are comparable with those in the experiments.In both problems the phase lag of the thermal expansion wave with height produces a skewed thermal field. This field is the most important mechanism in producing velocity correlations. It is due to these correlations and the associated Reynolds stress that the fluid acquires its momentum.