Fully Developed Mixed Convection Flow Between Inclined Parallel Plates Filled with a Porous Medium

A fully developed mixed convection flow between inclined parallel flat plates filled with a porous medium is considered through which there is a constant flow rate and with heat being supplied to the fluid by the same uniform heat flux on each plate. The equations governing this flow are made non-dimensional and are seen to depend on two dimensionless parameters, a mixed convection parameter λ and the Péclet number Pe, as well as the inclination γ of the plates to the horizontal. The velocity and temperature profiles are obtained in terms of λ, Pe and γ when the channel is inclined in an upwards direction as well as for horizontal channels. The limiting cases of small and large λ and small Pe are considered with boundary-layer structures being seen to develop on the plates for large values of λ.     

Flow past a suddenly cooled horizontal plate

The problem of unsteady laminar, incompressible free convection above a horizontal semi-infinite flat plate is studied theoretically. It is assumed that for timet<0 the plate is hotter than its surroundings and at timet=0 the plate is suddenly cooled to the same temperature of its surroundings. Three solutions of the momentum and energy equations are obtained, namely

1. an analytical solution which is valid for small time,
2. an asymptotic analytical solution which is valid for large time, and
3. a numerical solution which matches these two limiting analytical solutions.

It is found that the numerical solution matches the small and large time solutions accurately. Finally, the variation of the velocity, temperature, skin friction and heat transfer on the plate with time are discussed.     

The HERO project for the study of high-energy primary cosmic radiation

Proposals for the High-Energy Ray Observatory (HERO) comprising scientific equipment with increased power availability are presented. Under the long exposure (>7 years), it is proposed to investigate the spectrum and charge composition of cosmic-ray nuclei up to E ₀ ～ 10¹⁶ eV and to determine the behavior of the energy spectrum in the energy regions >100 GeV for cosmic-ray electrons and >50 GeV for γ radiation. The geometrical factor of the apparatus is 6.0–9.0 m² sr depending on the type of particles.     

The effects of a complexing agent on travelling waves in autocatalytic systems with applied electric fields

The effects of electric fields on the reaction fronts that arisein a system governed by an autocatalytic reaction and a complexationreaction between the autocatalyst and a complexing agent areconsidered. The complexation reaction is assumed to be fastrelative to the autocatalytic reaction and the equations forthis limit are derived. The corresponding travelling waves arediscussed, the case of quadratic autocatalysis being treatedin detail. The existence of minimum speed waves is examined,being dependent on the ratio of diffusion coefficients D, theconcentration S₀ and equilibrium constant K of the complexationreaction as well as the electric field strength E. It is seenthat, for some parameter values, minimum speed waves have negativeautocatalayst concentrations, and waves which have the lowestspeed consistent with non-negative concentrations are also obtained.Numerical integrations of the initial-value problem are performedfor representative parameter values. These show the developmentof the appropriate travelling wave (when it exists) as the largetime behaviour of the system, and, in cases where no travellingwave exists, the numerical integrations show the electrophoreticseparation of substrate and autocatalyst.     

Measurement of the amplitude and phase structures of an optical field and the transfer function for describing the effect of a medium in the form of a modulating function

The phase problem in optics is solved as applied to the detection and analysis of the amplitude and phase structures of two-dimensional optical fields forming or transmitting an image and the amplitude and phase structures of the transfer or instrumental functions of either the media containing optical inhomogeneities or the systems forming fields and involving instrumental distortions. The effect of the medium is characterized by a modulating function and described by a multiplication operation. Two variants of the optical scheme are considered. In each variant, the spatial-frequency spectrum is formed by the first optical system and the first spatial modulation is introduced in the spatial-frequency plane. The second optical system is arranged in the same plane. This system images the field under investigation into the plane located at the exit of the transmitting medium. In the first variant of the optical scheme, the second spatial modulation is introduced in the same plane. The third optical system forms a spatial-frequency spectrum in the detection plane. In the second variant of the scheme, an image of the plane positioned at the exit of the probing medium is formed in the detection plane by the third optical system. The second spatial modulation is introduced in the spatial-frequency plane of the third optical system. In both variants, four independent two-dimensional intensity distributions that make it possible to solve the problem posed are detected at the exit.     

The boundary-layer flow past a suddenly heated vertical surface in a saturated porous medium

The boundary-layer flow generated on an impermeable vertical surface in a saturated porous medium is considered in the case when wall heating at a rate proportional tox is switched on at timet=0, (x measures distance along the wall and is a constant). The similarity equations which hold in the limit of larget are discussed and are shown to have a solution only for >–1. The behaviour of the solution as –1 and as is obtained. Numerical solutions of the initial value problem are then obtained for a range of values of . A direct numerical integration is possible for 1, while an iterative procedure is required for <1, with the numerical scheme becoming unstable for =–0.5.

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Grenzschichtströmung an einer plötzlich aufgeheizten vertikalen Fläche, in einem gesättigten porösen Medium

Zusammenfassung Es wird die an einer undurchlässigen, vertikalen Fläche hervorgerufene Grenzschichtströmung im Falle eines Einschalten der Heizung beit=0 betrachtet. Die Stärke der Wandheizung is proportional zux , wobeix die Koordinate längs der Wand ist und eine Konstante. Die Ähnlichkeitsgleichungen werden für den Bereich von großen Zeitent besprochen und es wird gezeigt, daß eine Lösung nur für >–1 vorliegt. Es wird das Verhalten der Lösungen für –1 und erhalten. Numerische Lösungen für die Anfangsbedingungen des Problems werden für eine Reihe von -Werten errechnet. Eine direkte numerische Integration ist für 1 möglich, während für <1 eine Iteration erforderlich ist, wobei das numerische Verhalten für =–0.5 instabil wird.

     

On the similarity solutions for free convection in a saturated porous medium adjacent to impermeable horizontal surfaces

The similarity solutions for free convection about a horizontal surface in a saturated porous medium when the wall temperature is prescribed as a power law of distance from the origin, i.e. proportional tox ^m, are considered. Solutions valid form1 are obtained. Numerical solutions are obtained which reveal that there is a valuem ₀ such that a solution of the similarity equations is possible only form>m ₀. It is shown thatm ₀=–2/5 and the nature of the singularity is discussed and an asymptotic expansion is obtained.

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Ähnlichkeitslösungen für eine freie Konvektion in einem gesättigten porösen Medium, das an eine undurchlässige, horizontale Oberfläche grenzt

Zusammenfassung Die Ähnlichkeitslösungen sind für eine freie Konvektion über eine horizontale Oberfläche in einem gesättigten porösen Medium in Betracht gezogen worden, wenn die Wandtemperatur beschrieben ist als eine Potenzfunktion des Abstandes vom Ursprung, z. B. proportional zux ^m.Gültige Lösungen sind fürm1 bestimmt. Numerische Lösungen sind bestimmt worden, die offenbaren, daß es einen Wertm ₀ geben muß, so daß eine Lösung von ähnlichen Lösungen nur fürm>m ₀ möglich ist. Es wird gezeigt, daßm ₀=–2/5 und daß die Beschaffenheit der Singularität besprochen und die asymptotische Ausdehnung bestimmt worden ist.

     

Steady mixed convection boundary-layer flow over a vertical flat surface in a porous medium filled with water at 4°C: variable surface heat flux

The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water at 4°C (maximum density) when the surface heat flux varies as x ^m and the velocity outside the boundary layer varies as x ^(1+2m)/2, where x measures the distance from the leading edge, is discussed. Assisting and opposing flows are considered with numerical solutions of the governing equations being obtained for general values of the flow parameters. For opposing flows, there are dual solutions when the mixed convection parameter λ is greater than some critical value λ _c (dependent on the power-law index m). For assisting flows, solutions are possible for all values of λ. A lower bound on m is found, m > −1 being required for solutions. The nature of the critical point λ _c is considered as well as various limiting forms; the forced convection limit (λ = 0), the free convection limit (λ → ∞) and the limits as m → ∞ and as m → −1.