The possibility of instability arising as overstability in the magnetohydrodynamic Bénard problem is discussed. Results are derived for large Hartmann numbers when the regions outside the fluid layer are conducting or insulating, the interfaces being rigid or free.

If we neglect the viscous dissipation, the temperature distribution in an incompressible fluid flowing in the annulus between two coaxial cylinders with radii r1 and r2 (> r1) is determined by the equation

Initial conditions

Boundary conditions

where ∂Q/∂t is a function of time alone representing the rate of heat generation per unit volume per unit time in the fluid.

A system of equations is derived for determining the elastic fields in an inclusion and its surrounding finite matrix when the inclusion suffers a physical change and, if not constrained by the matrix, would undergo a deformation . A method for obtaining the exact solution of these equations, when the matrix and inclusion have the same elastic constants, is described and the particular problem of the square inclusion in an infinite matrix solved.

A theory is presented for small deformations of a plate which is initially stressed, the state of initial stress not necessarily being obtained by elastic deformation from some other unstressed state. The method used is an asymptotic integration of the full three-dimensional equations. The usual Kirchhoff boundary conditions for stretching and bending are deduced from the analysis.

The two-dimensional incompressible fluid flow problem along an infinite flat plate with no heat transfer between the fluid and the plate is discussed when the suction velocity normal to the plate, as well as the external flow velocity, varies periodically with time. Expressions for the velocity and temperature fields in the boundary layer have been obtained in a non-dimensional form. It has been found that the effect of increasing the suction velocity fluctuations is that the amplitude of the skin-friction fluctuations is increased while the phase is decreased and it may be negative for very small values of the frequency. Also the plate temperature decreases with increasing the suction velocity fluctuations for small values of the frequency while there is no effect for very large frequencies.