Resolution of a Paradox Involving Viscous Dissipation and Nonlinear Drag in a Porous Medium

The modelling of viscous dissipation in a porous medium saturated by an incompressible fluid is discussed, for the case of Darcy, Forchheimer and Brinkman models. An apparent paradox relating to the effect of inertial effects on viscous dissipation is resolved, and some wider aspects of resistance to flow (concerning quadratic drag and cubic drag) in a porous medium are discussed. Criteria are given for the importance or otherwise of viscous dissipation in various situations.     

NMR study of ester-interchange reactions during melt mixing of poly(ethylene terephthalate)/poly(butylene terephthalate) blends

The occurrence of ester-interchange reactions during PET/PBT blend processing has been confirmed by ¹³C-NMR measurements. The limitations of the method for precise quantification of the extent of reaction between high molecular weight polyester blends have also been pointed out. Titanium alkoxide has been confirmed as an efficient catalyst, and, within experimental precision, the stabilizing effect of triphenyl phosphite addition has been demonstrated. © 1996 John Wiley & Sons, Inc.     

Comments on 'Finite Element Analysis of Convection Flow Through a Porous Medium in a Horizontal Channel' by D. V. Krishna,D. R. V. Prasada Rao and V. Sugunamma

Transport in Porous Media -     

Impracticality of MHD Convection in a Porous Medium

The subject of the title is discussed.     

The Life and Work of Robin A. Wooding

Robin A. Wooding (1926–2007) made many outstanding and original contributions to the field of convection in porous media throughout his research career. He was an applied mathematician who also worked on a wide variety of other important hydrological, meteorological, earth science and physical science problems. Important contributions included (i) the discovery of the occurrence of fingers in the context of mono-diffusive convection in a porous medium and an early body of associated papers on convection in porous media, (ii) the development of a novel hydraulic model for the catchment-stream problem and (iii) the mathematical solution to the problem of steady infiltration from a shallow circular pond that formed the basis for the disc permeameter method. This note documents biographical matters and assesses the importance of his scientific work. Robin A. Wooding 6 March 1926–19 November 2007 (Photograph circa 1975)

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The effect of a transition layer between a fluid and a porous medium: shear flow in a channel

Flow in a three-layer channel is modeled analytically. The channel consists of a transition layer sandwiched between a porous medium and a fluid clear of solid material. Within the transition layer, the reciprocal of the permeability varies linearly across the channel. The Brinkman model is used for the momentum equations for the porous medium layer and the transition layer. The velocity profile is obtained in closed form in terms of Airy, exponential, and polynomial functions. The overall volume flux and boundary friction factors are calculated and compared with values obtained with a two-layer model employing the Beavers–Joseph condition at the interface between a Darcy porous medium and a clear fluid.     

The Beavers–Joseph Boundary Condition and Related Matters: A Historical and Critical Note

This note is concerned with the historical background to the Beavers–Joseph boundary condition at the interface of a porous medium and a clear fluid. Relevant papers published prior to 1975 are discussed. The merits of the alternative methodology utilizing the Brinkman equation are also discussed.     

The effects of combined horizontal and vertical heterogeneity on the onset of convection in a porous medium: double diffusive case

The effects of both horizontal and vertical hydrodynamic, thermal and solutal heterogeneity, on the onset of convection in a horizontal layer of a saturated porous medium uniformly heated from below, are studied analytically using linear stability theory for the case of weak heterogeneity. The Brinkman model is employed. It is found that the effect of such heterogeneity on the critical value of the Rayleigh number Ra based on mean properties is of second order if the properties vary in a piecewise constant or linear fashion. The effects of horizontal heterogeneity and vertical heterogeneity are then comparable once the aspect ratio is taken into account, and to a first approximation are independent.     

Surface tension and buoyancy effects in the cellular convection of an electrically conducting liquid in a magnetic field

Zusammenfassung Eine frühere Analyse des Konvektionsanfangs in einer horizontalen Flüssigkeitsschicht, ausgelöst durch die gleichzeitige Einwirkung der Auftriebs- und Oberflächenspannungseffekte, wird auf eine elektrisch leitfähige Flüssigkeit in einem magnetischen Feld ausgedehnt. Zahlenresultate werden für den Fall gewonnen, wo die untere Fläche ein starrer Leiter ist und die obere freie Fläche für Temperaturstörungen entweder «leitet» oder «isoliert». Für die Wirkungen eines vertikalen magnetischen Felds ergibt sich folgendes: (1) Konvektion wird unter allen betrachteten Umständen gehemmt, (2) die horizontalen Dimensionen einer Konvektionszelle werden vermindert, und (3) die Kopplung zwischen den Oberflächenspannungs- und Auftriebswirkungen wird abgeschwächt. Die Wirkung (3) ist erstaunlich plötzlich, wenn die obere Fläche ein guter Leiter für Temperaturstörungen ist.