Free convective boundary-layer flow in a heat-generating porous medium: similarity solutions

The free convection boundary-layer flow on a vertical surfacein a porous medium with local heat generation proportional to(T – T)^p, where T is the local temperature and T is theambient temperature, is considered when there are power-lawvariations in either the wall temperature or the wall heat fluxwhich enables the equations to be reduced to similarity form.When the wall temperature is prescribed, solutions are foundfor p 2 and p p_c (p_c = 10.673) with a saddle-node bifurcationat p = p_c and two solution branches for p > p_c. When thewall heat flux is prescribed, solutions are found only for p< 2. The special case p = 2 is considered and the limitingforms as p 2 and p are obtained and compared with the solutionsobtained from solving the similarity equations numerically     

Wave propagation in distributed media

The problem of chemical reaction-diffusion wave propagation through a random, heterogeneous medium is considered using a model based on cubic autocatalysis with decay. The autocatalyst is taken to diffuse and react through a reactant loaded at constant initial concentration in a reaction domain except that there may be gaps of arbitrary width in which the reactant concentration is zero. We first study the propagation of a permanent-form wave across a single gap and determine the critical width of the gap in terms of the kinetic parameters in the system. The numerical results are compared with an analytical estimate. Next, the critical conditions for propagation across two gaps separated by a domain are determined numerically, and this is extended to a series of three gaps. From these results, a series of "rules" is established to allow us to predict whether a wave will pass through an arbitrary random array of gaps of a given size subject to some imposed total void fraction for the material. (c) 2001 American Institute of Physics.     

Mixed Convection Boundary-Layer Flow Over a Vertical Surface Embedded in a Porous Material Subject to a Convective Boundary Condition

The mixed convection boundary-layer flow on one face of a semi-infinite vertical surface embedded in a fluid-saturated porous medium is considered when the other face is taken to be in contact with a hot or cooled fluid maintaining that surface at a constant temperature $T_\mathrm{{f}}$ . The governing system of partial differential equations is transformed into a system of ordinary differential equations through an appropriate similarity transformation. These equations are solved numerically in terms of a dimensionless mixed convection parameter $\epsilon $ and a surface heat transfer parameter $\gamma $ . The results indicate that dual solutions exist for opposing flow, $\epsilon <0$ , with the dependence of the critical values $\epsilon _\mathrm{{c}}$ on $\gamma $ being determined, whereas for the assisting flow $\epsilon >0$ , the solution is unique. Limiting asymptotic forms for both $\gamma $ small and large and $\epsilon $ large are also discussed.     

Mixed Convection Boundary-Layer Flow Along a Vertical Cylinder Embedded in a Porous Medium Filled by a Nanofluid

The steady mixed convection boundary-layer flow on a vertical circular cylinder embedded in a porous medium filled by a nanofluid is studied for both cases of a heated and a cooled cylinder. The governing system of partial differential equations is reduced to ordinary differential equations by assuming that the surface temperature of the cylinder and the velocity of the external (inviscid) flow vary linearly with the axial distance x measured from the leading edge. Solutions of the resulting ordinary differential equations for the flow and heat transfer characteristics are evaluated numerically for various values of the governing parameters, namely the nanoparticle volume fraction ${\phi}$ , the mixed convection or buoyancy parameter ?? and the curvature parameter ??. Results are presented for the specific case of copper nanoparticles. A critical value ?? _c of ?? with ?? _c <?0 is found, with the values of | ?? _c| increasing as the curvature parameter ?? or nanoparticle volume fraction ${\phi}$ is increased. Dual solutions are seen for all values of ?? >??? _c for both aiding, ?? >?0 and opposing, ?? <?0, flows. Asymptotic solutions are also determined for both the free convection limit ${(\lambda \gg 1)}$ and for large curvature parameter ${(\gamma \gg 1)}$ .     

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.     

Simultaneous Determination of the Amplitude-Phase Structure of an Optical Signal and a Transfer Function with the Influence of the Medium Given by a Modulation Function

We consider a solution to the phase problem in optics as applied to registering and analyzing amplitude-phase structures of 1) d optical fields that form or transfer images and 2) transfer or spread functions of the medium where optically inhomogeneous fields propagate or those of the systems forming fields and producing distortions. The influence of the medium is characterized by the modulation function and is described by the operation of multiplication. In order to measure the amplitude and phase field characteristics and transfer or spread functions, we use an original development of the modulation-spectral method proposed earlier by the authors. There are two variants of optical schemes considered. They include identical parts designed to form the light field to be processed. Using the first optical system, one forms the spectrum of spatial frequencies and introduces the first additional space modulation in the plane of spatial frequencies. The second optical system is placed in the same plane to form the image of the investigated field in the input plane of the developing scheme after passing the transmitting medium. In the first variant, the second part of the scheme contains at the input the third optical system forming the spatial spectrum in the registration plane. At the input of this scheme, the second additional spatial modulation is introduced. In the second variant, the third optical system forms the image of the developing scheme input plane in the registration plane. The second additional spatial modulator is placed in the spatial frequency plane of the third optical system. In the output, in both cases four independent two-dimensional intensity distributions are registered, which allow one to solve the formulated problem.     

Convective Flows on Reactive Surfaces in Porous Media

A model for the convective flow in a fluidsaturated porous medium containing a reactive component is considered. This component undergoes an exothermic reaction (modelled by a first order mechanism) on an impermeable bounding surface, the resulting heat released driving the convective flow. Large Rayleigh number flow near a stagnation point is treated in detail by first considering the steady states. Multiple solution branches and critical points arising from a hysteresis bifurcation are identified. The form that these solution branches take depends on whether or not the effects of reactant consumption are included. An initialvalue problem is then discussed. This shows that both the lower (slow reaction) and upper (fast reaction) solution branches are stable (and the ultimate state of the system). When the parameter values are such that there is no steady state, the solution develops a finitetime singularity, the nature of which is analysed.     

Free convection boundary layers on a vertical surface in a heat-generating porous medium

The natural convection boundary-layer flow on a solid verticalsurface with heat generated within the boundary layer at a rateproportional to (T – T)^p (p 1) is considered. The surfaceis held at the ambient temperature T except near the leadingedge where it is held at a temperature above ambient. The behaviourof the flow as it develops from the leading edge is examinedand is seen to become independent of the initial heat input;however, it does depend strongly on the exponent p. For 1 p 2, the local heating eventually dominates at large distancesand there is a convective flow driven by this mechanism. Forp 4, the local heating does not have a significant effect,the fluid temperature remains relatively small throughout andthe heat transfer dies out through a wall jet flow. For 2 <p < 4, the local heating has a significant effect at relativelysmall distances, with a thermal runaway developing at a finitedistance along the surface.     

Kinetic description of the hydrogenation of nitrobenzene and nitrosobenzene on skeletal nickel in aqueous solutions of propan-2-ol of different compositions

The kinetics of the hydrogenation of nitrosobenzene and nitrobenzene is simulated taking into account accompanying processes and specific features of the conversion of reactive groups. The constants of the hypothetical reaction steps are calculated. The influence of sodium hydroxide and acetic acid on the kinetic parameters of the reactions is discussed.     

Effects of a constant electric field on the diffusional instability of cubic autocatalytic reaction fronts

An electric field applied in the direction of propagation of a chemical reaction-diffusion front can affect the stability of this front with regard to diffusive instabilities. The influence of an applied constant electric field is investigated by a linear stability analysis and by nonlinear simulations of a simple chemical system based on the cubic autocatalytic reaction A-+2B--->3B-. The diffusional stability of the front is seen to depend on the intensity E and sign of the applied field, and D, the ratio diffusion coefficients of the reactant species. Depending on E, the front can become more or less diffusively unstable for a given value of D. Above a critical value of E, which depends on D, electrophoretic separation of the two fronts is observed.