The impulsively starting motion of a circular cylinder submerged horizontally below a free surface is studied analytically using a small-time expansion. The series expansion is taken as far as necessary to include the leading gravitational effects for two cases: constant velocity and constant acceleration, both commencing from rest. The hydrodynamic force on the cylinder and the surface elevation are calculated and expressed in terms of bipolar coordinates. Comparisons are also made with earlier theoretical and experimental work. The theory is valid for arbitrary value of submergence depth to cylinder radius.

In this paper a theoretical investigation of convection currents in anisotropic porous media is performed. The porous layer is homogeneous and bounded by two infinite, perfectly heatconducting horizontal planes. The criterion for the onset of convection is derived. The supercritical, steady two-dimensional motion, the heat transport and the s:tability of the Ill.Otion are investigated. The results may be applied in insulation technique.

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We investigate the onset of Rayleigh–Bénard convection in a horizontal porous layer with anisotropic permeability. The permeability is transversely isotropic, whereas the orientation of the longitudinal principal axes is arbitrary. This is sufficient to achieve qualitatively new flow patterns with a tilted plane of motion or tilted lateral cell walls. The critical Rayleigh number and wavenumber at marginal stability are calculated. There are two different types of convection cells (rolls): (i) the plane of motion is tilted, whereas the lateral cell walls are vertical; (ii) the plane of motion is vertical, whereas the lateral cell walls are tilted as well as curved. It turns out that type (i) occurs when the transverse permeability is larger than the longitudinal permeability, and for the converse case type (ii) is preferred.

The onset of Rayleigh–Bénard convection in a finite circular porous cylinder with vertical axis is investigated analytically. The cylinder is heated from below, and its top and bottom are assumed impermeable and perfectly heat-conducting. The impermeable sidewall of the cylinder is assumed to be heat-conducting so that the temperature perturbation there is zero. The eigenvalue problem is split into two different Helmholtz equations. The resulting eigenmode is expressed in terms of Bessel functions. The preferred mode at the onset of convection is found to be axisymmetric. The critical Rayleigh number is a smooth function of the aspect ratio of the cylinder, in contrast to the standard case of an insulating sidewall.