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  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 1131-1141 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In this paper the axisymmetric flow of a viscous fluid through a porous annular pipe with constant and equal fluxes through each pipe wall is studied theoretically. A nondimensional parameter, δ, based on the radii of the walls of the pipe is defined and the equations and boundary conditions are written so that at δ=0 they coincide with the analogous two-dimensional problem. By numerical integration, the significant properties found previously for δ=0 are continued into the region 0〈δ〈1 corresponding to flow in an annular pipe. Of the steady, unsteady, periodic, quasiperiodic, and chaotic solutions found when δ=0, only steady, unsteady, and periodic solutions have been found when δ≠0.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 35 (1984), S. 72-80 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Résumé Nous considérons l'écoulement magneto-hydrodynamique impulsivement engendré à un point de stagnation arrière. On porte plus loin l'étude de Leibovich par la formulation du problème visqueux intérieur et en fournissant des solutions analytiques et numériques complètes correspondantes au champ entier du paramètre d'interaction. On montre que les résultats actuels sont en accord avec les solutions numériques, et de similitude et de non-similitude, déjà connues des équations stationnaires.
    Notes: Summary We consider the impulsively generated magnetohydrodynamic flow at a rear stagnation point. The work of Leibovich is carried further by formulating the inner viscous problem and providing analytical solutions and complete numerical solutions for the entire range of the interaction parameter. It is shown that the present results are consistent with previously obtained numerical solutions to the steady equations of both similarity and non-similarity form.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 37 (1986), S. 910-918 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Die thermische Stabilität von chemisch reagierenden Platten mit örtlich variierender Oberflächentemperatur wird untersucht. Es wird angenommen, daß die Temperaturunterschiede gering sind. Dann kann eine Perturbationsmethode angewendet werden. Die kritischen Bedingungen für periodische und aperiodische Verteilungen werden angegeben. Ebenso wird ein verwandtes Problem behandelt, bei dem der Verlauf des Plattenrandes leicht gestört, aber auf einer konstanten Temperatur gehalten wird.
    Notes: Summary The thermal stability of reacting slabs whose surface temperature is a function of position is investigated. It is assumed that the variation is not large so that a perturbation approach may be adopted. Conditions for criticality are sought both for periodic distributions and others. A related problem where the boundary is perturbed but maintained at constant temperature is also considered.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 38 (1987), S. 925-933 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary The work of Lin, Richardson & Eyring and Boddington, Feng & Gray on the theory of the initiation of thermal explosion by steady intense light is developed further. In the large activation energy limit analytic solution is possible and conditions for criticality are deduced for large and small values of light-intensity parameter. The disappearance of criticality is examined numerically for the full range of light-intensity parameter. Results are compared with those obtained by using a simple constant reaction-rate assumption.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of engineering mathematics 19 (1985), S. 247-249 
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Summary We show that the free-convective boundary-layer flow in a porous medium in the vicinity of a parameter value at which similarity solutions cease to exist is of semi-jet form.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Journal of engineering mathematics 21 (1987), S. 41-46 
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract We consider the free-convection boundary-layer flow in a saturated porous medium adjacent to an impermeable vertical surface. It is assumed that the surface is supplying heat to the porous medium in a prescribed way, which varies along the surface. The problem, which relates to the spatial stability of the known similarity solutions of the boundary-layer equations, is formulated and certain analytical results presented for special cases. For this special class of flows we are able to determine analytically the first eigenvalue for all relevant parameter values and thereby show that such flows are spatially stable.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Journal of engineering mathematics 25 (1991), S. 375-397 
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract We examine theoretically the two-dimensional free-convective flow in a parallel-walled cell with vertical walls at non-uniform temperature; this temperature variation is such that similarity solutions for the flow and temperature fields are possible. Both symmetric and asymmetric boundary conditions are considered. In the former case we find that in addition to a trivial symmetric solution, corresponding to stagnant flow, there are non-trivial steady symmetric solutions and also steady asymmetric solutions for certain ranges of Rayleigh number. The temporal stability of all these solutions is also investigated and the nature of the bifurcations examined; these include bifurcations of pitchfork, transcritical and Hopf types. The breaking of symmetry is studied and also the effect on the flow character of different Prandtl numbers.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Journal of engineering mathematics 8 (1974), S. 45-56 
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Summary Results are presented of a numerical study of the three-dimensional free convectional flow near a stagnation point of attachment on an isothermal surface when the Prandtl number is 0.72. The boundary layer flows that result are of both nodal and saddle point type. The results of the numerical integrations are presented graphically for various values ofc=b/a, whereb anda are the principal curvatures of the surface at the stagnation point. Two singularities are found to exist.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Journal of engineering mathematics 13 (1979), S. 193-212 
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Summary The boundary-layer growth near the equator of an impulsively rotated sphere is considered numerically and analytically. The numerical work is highly suggestive of the presence of a singularity at a finite time at which two of the velocity components and the swirl displacement thickness become infinite. Details of an analytic investigation are presented which is consistent with the gross features of the numerical results. Brief consideration is also given to the flow near the equators of impulsively rotated spheroids and it is shown that the relevant boundary-layer equations for this class of bodies can be written in the same form as those for the sphere.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Journal of engineering mathematics 6 (1972), S. 109-115 
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Summary This paper is concerned with the existence of a three-dimensional solution to the free convection boundary layer equations near a two-dimensional isothermal surface. The numerical solution is presented in detail, and it is noted that the resulting heat transfer at the body surface is over 25% less than in the two-dimensional solution.
    Type of Medium: Electronic Resource
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