The dual solutions to an equation, which arose previously in mixed convection in a porous medium, occurring for the parameter a in the range 0 < a < a 0 are considered. It is shown that the lower branch of solutions terminates at a = 0 with an essential singularity. It is also shown that both branches of solutions bifurcate out of the single solution at a= a o with an amplitude proportional to (a o -a) 1/2. Then, by considering a simple time-dependent problem, it is shown that the upper branch of solutions is stable and the lower branch unstable, with the change in temporal stability at a = a o being equivalent to the bifurcation at that point.

A simple model for homogeneous-heterogeneous reactions in stagnation-point boundary-layer flow is constructed in which the homogeneous (bulk) reaction is assumed to be given by isothermal cubic autocatalator kinetics and the heterogeneous (surface) reaction by first order kinetics. The possible steady states of this system are analysed in detail in the case when the diffusion coefficients of both reactant and autocatalyst are equal. Hysteresis bifurcations leading to multiple solutions are found. The temporal stability of these steady states is then discussed.

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The flow of a uniform stream past an impermeable vertical surface embedded in a saturated porous medium and which is supplying heat to the porous medium at a constant rate is considered. The cases when the flow and the buoyancy forces are in the same direction and when they are in opposite direction are discussed. In the former case, the flow develops from mainly forced convection near the leading edge to mainly free convection far downstream. Series solutions are derived in both cases and a numerical solution of the equations is used to describe the flow in the intermediate region. In the latter case, the numerical solution indicates that the flow separates downstream of the leading edge and the nature of the solution near this separation point is discussed.

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Numerical results are presented for free convection boundary layers over horizontal cylinders of elliptic cross section when the major axis is both horizontal and vertical and when the cylinder is isothermal and has constant heat flux. The particular case of a circular cylinder is considered and these results are compared with the various series expansions suggested for solving the equations.