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141.
John H. Merkin Ioan Pop Azizah Mohd Rohni Syakila Ahmad 《Transport in Porous Media》2012,95(2):373-375
The aim of this Letter is to show that a further exact solution of the problem on unsteady mixed convection boundary layer in a porous medium with temperature slip can be obtained in addition of that reported very recently by Fang et al. (2012). 相似文献
142.
Vocational College at the Leningradskii Metallicheskii Zavod Industrial Association. Translated from Prikladnaya Mekhanika, Vol. 26, No. 4, pp. 72–79, April, 1990. 相似文献
143.
The effects of a complexation reaction on travelling wave-fronts in a quadratic autocatalytic system
Needham D. J.; Leach J. A.; Merkin J. H. 《The Quarterly Journal of Mechanics and Applied Mathematics》2005,58(4):577-599
A model which describes the effect that a complexation reactioncan have on the propagation of reaction fronts in a quadraticautocatalytic system is considered. An initial-value problemis set up, which involves the (dimensionless) parameters K,the equilibrium constant for the complexation reaction, and, the initial concentration of the complexing agent. This initial-valueproblem is analysed, with global existence and uniqueness beingestablished. Numerical integrations indicate the formation ofpermanent-form travelling waves at large times. The equationsthat govern the travelling waves in the model are treated indetail. It is determined that there is a minimum propagationspeed vmin lying in the range v0 2/(1 + ) vmin 2, with thevalue v0 corresponding to the minimum speed derived from thelinearization of the travelling wave equations. The existenceof a curve is established, which divides the (K, ) parameter plane into two regions, one where vmin =v0 and one where vmin > v0 with waves propagating fasterthan their linearized speed in this region. The curve is determined numerically together with the dependenceof vmin on K and . 相似文献
144.
Mixed Convection on a Horizontal Surface Embedded in a Porous Medium: the Structure of a Singularity
The mixed convection boundary-layer flow on a horizontal impermeable surface embedded in a saturated porous medium and driven by a local heat source is considered. Similarity solutions are obtained for specific outer flow variations and these are shown to have a solution only for parameter values greater than some critical value. When this is not the case the solution develops a singularity at a finite distance from the leading edge. The nature of this singularity is also discussed. 相似文献
145.
A. A. Merkin T. V. Mironova T. T. Sultanov V. A. Zubov 《Journal of Russian Laser Research》2000,21(6):575-584
A solution to the phase problem in optics is considered within the context of the registration and analysis of the amplitude–phase structure of optical nonuniformities in stationary transmitting media or in investigated objects. To solve the problem, the object or the medium is tested by radiation with a known structure. For a certain selected direction of testing, the structural change due to the interaction with the object is registered. To obtain information on the amplitudes and phases of the testing light field, an original development of the modulationspectral method put forward by the authors is used. To solve the problem, the intensity distribution is detected in the image plane both for an unmodulated field and for that subjected to an additional twodimensional modulation specially formed in the plane of spatial frequencies. The modulation should provide a visualization of the phase information contained in the light field. The intensity distributions obtained make it possible to determine the twodimensional structure of the testing field at the output of the medium or the object. In the proposed variant of the method, the testing field should not be affected in the investigated plane. The interpretation of the results is easier, since it is the image that is registered. The two intensity distributions can be registered simultaneously, provided the light beam is divided into two channels after the optical system. It is significant that the method requires no iteration procedures in solving the problem. This allows one to expect speedingup of the processing of the information and analyzing it in almost real time. Two variants of optical schemes are considered in the paper. The first one deals with media or objects with a modulation effect described by multiplication by a complex function characterizing the effect. In the second case, the effect of the object leads to redistribution of the radiation in the investigated plane and is described by the operation of convolution of the testing signal and the function characterizing the effect. 相似文献
146.
The convective boundary-layer flow on an impermeable vertical surface in a fluid-saturated porous medium is considered where the flow results from the heat released by an exothermic catalytic reaction on the surface converting a reactive component within the convective fluid to an inert product. The reaction is modelled by first-order kinetics with an Arrhenius temperature dependence. Numerical solutions of the governing equations are obtained for a range of parameter values. These show, for large activation energies, that localized rapid changes in wall temperature and localized high reaction rates occur a little way from the leading edge. Asymptotic expansions, valid at large distances from the leading edge, are derived, the form that these expansions take is qualitatively different depending on whether or not reactant consumption is included in the model. 相似文献
147.
Merkin JH 《The Journal of chemical physics》2008,129(3):034507
A linear stability analysis of planar reaction fronts to transverse perturbations is considered for a system based on an autocatalytic reaction of general order p. Dispersion curves, plots of the growth rate sigma against a transverse wavenumber k, are obtained for a range of values of p and D, where D is the ratio of the diffusion coefficients of autocatalyst and substrate. A value D(0) of D, dependent on p, is found at which sigma(max), the maximum value of sigma in the unstable regime, is largest, with D(0) increasing as p is increased. An asymptotic analysis for small wavenumbers is derived, which enables the region in the (p, D) parameter space for instability to be determined. An analysis for D small is undertaken, which leads to upper bounds on the wavenumber for a possible instability. 相似文献