J. H. Merkin

On dual solutions occurring in mixed convection in a porous medium

SummaryThe dual solutions to an equation, which arose previously in mixed convection in a porous medium, occuring for the parameter α in the range 0 < α < α0 are considered. It is shown that the lower branch of solutions terminates at α=0 with an essential singularity. It is also shown that both branches of solutions bifurcate out of the single solution at α=0 with an amplitude proportional to (α0-α)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 α=α0 being equivalent to the bifurcation at that point.

Natural-convection boundary-layer flow on a vertical surface with Newtonian heating

Abstract The natural-convection boundary-layer flow on a vertical surface generated by Newtonian heating in which the heat transfer from the surface is proportional to the local surface temperature is discussed. Solutions valid near the leading edge and valid far downstream are obtained and are joined by a numerical solution of the governing equations. The solution far downstream gives rise to a novel similarity system that is analyzed in detail, with solutions being obtained for large and small values of the Prandtl number.

Mixed convection from a horizontal circular cylinder

Abstract The combined convection boundary layer on a horizontal circular cylinder in a stream flowing vertically upwards is studied in both the cases of a heated and cooled cylinder. It is found that heating the cylinder delays separation and can, if the cylinder is warm enough, suppress it completely. Cooling the cylinder brings the separation point nearer to the lower stagnation point and for a sufficiently cold cylinder there will not be a boundary layer on the cylinder.

Mixed convection boundary layer flow on a vertical surface in a saturated porous medium

SummaryThe 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.

A simple isothermal model for homogeneous-heterogeneous reactions in boundary-layer flow. I Equal diffusivities

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.

A model for isothermal homogeneous-heterogeneous reactions in boundary-layer flow

A model for homogeneous-heterogeneous reactions in boundary-layer flow is presented in which the homogeneous reaction is represented by cubic autocatalysis and the heterogeneous reaction by a first-order process. The flow is of a uniform stream over a flat surface (Blasius solution). It is shown that the surface reaction is the dominant mechanism near the leading edge. Numerical solutions of the governing equations reveal that the homogeneous reaction dominates downstream with this reaction taking place in a narrow region located well away from the surface. An asymptotic analysis for this reaction region is obtained.

Mechanism reduction for the oscillatory oxidation of hydrogen; Sensitivity and quasi-steady-state analyses

In this paper, a strategy for reducing complex chemical reaction mechanisms is developed and illustrated with reference to the oscillatory H[sub 2] + O[sub 2] system in a CSTR in the region of the second explosion limit. The approach involves the identification of redundant species via rate sensitivity analysis and of redundant reactions by the principal component analysis of the rate sensitivity matrix. Temperature sensitivity analysis is also employed and the application of the quasi-steady-state approximation is discussed briefly and used n the final stages of the reduction. The above procedures are shown to assist the understanding of the underlying mechanisms of the reaction for the chosen conditions and the competition between branching steps during oscillatory ignitions is discussed. The reduced mechanism is compared with models discussed elsewhere.

Free convection with blowing and suction

Abstract The effects of uniform blowing and suction on the free convection boundary layer on a vertical plate are considered. A numerical solution of the full boundary layer equations is obtained in both cases. In the case of suction the asymptotic solution is found to be a boundary layer of constant thickness. The approach to this solution is also discussed. When fluid is blown through the plate, it is found that, at large distances from the leading edge, the boundary layer has an inner inviscid region made up of fluid that has been blown through the plate, and an outer viscous region where the fluid attains the ambient conditions.

Mixed convection boundary layer similarity solutions: prescribed wall heat flux

The similarity solutions for mixed convection boundary-layer flow when the wall heat flux is prescribed are analysed in detail in terms of a buoyancy parameterα andm the exponent of the free stream flow. It is shown that forα〉0 the solution approaches the free convection limit, and forα〈0, there is a range ofα,αs〈α〈0, over which dual solutions exist. The nature of the bifurcation atα=αs, and how the lower branch of solutions behaves asα→0− are also considered. It is established that the solution becomes singular asm→1/5 and the nature of this singularity is also discussed, where it is shown that two separate cases have to be treated, namely whenα is of 0(1) and whenα is small. Finally it is shown that form large the solution approaches that corresponding to exponential forms for the free stream and prescribed wall heat flux. Taken all together this information enables a complete description of how the solution behaves over all possible ranges of the parametersα andm to be deduced.

Conjugate free convection on a vertical surface

Abstract It is shown that the equations governing the conjugate free convection boundary-layer flow on a vertical plate can be made dimensionless so as to involve only the Prandtl number. An efficient finite-difference scheme is developed to solve these equations and results are given for Pr = 0.72, 0.733 and 7.0, respectively. It is seen that an asymptotic expansion gives reliable results even at moderate values of x (dimensionless distance along the plate).