Search results for "BIOT NUMBER"
showing 9 items of 9 documents
A fractional order theory of poroelasticity
2019
Abstract We introduce a time memory formalism in the flux-pressure constitutive relation, ruling the fluid diffusion phenomenon occurring in several classes of porous media. The resulting flux-pressure law is adopted into the Biot’s formulation of the poroelasticity problem. The time memory formalism, useful to capture non-Darcy behavior, is modeled by the Caputo’s fractional derivative. We show that the time-evolution of both the degree of settlement and the pressure field is strongly influenced by the order of Caputo’s fractional derivative. Also a numerical experiment aiming at simulating the confined compression test poroelasticity problem of a sand sample is performed. In such a case, …
A three-dimensional study of the onset of convection in a horizontal, rectangular porous channel heated from below
2012
Author's version of an article published in the journal: International Journal of Thermal Sciences. Also available from the publisher at: http://dx.doi.org/10.1016/j.ijthermalsci.2011.12.012 The onset of convection is studied in a rectangular channel filled with a fluid saturated porous medium, bounded above and below by impermeable isothermal walls at unequal temperatures and laterally by partially conducting walls. A three-dimensional linear stability analysis is carried out under the assumption of an infinite longitudinal channel length. Then, this assumption is relaxed in order to determine the threshold length for the three-dimensional convection to be the preferred mode at onset. Sens…
Onset of convective rolls in a circular porous duct with external heat transfer to a thermally stratified environment
2011
A horizontal circular duct filled with a fluid saturated porous medium is studied. The external wall is assumed to exchange heat with an external environment thermally stratified in the vertical direction. The external heat transfer is modeled through a third kind boundary condition, and a Biot number associated with the external heat transfer coefficient is defined. The linear stability of the basic state where the velocity field is zero is studied numerically. The condition of neutral stability is determined, by solving the system of elliptic governing equations for the disturbances through a Galerkin finite-element method. The neutral stability curves, together with the critical values o…
Onset of convection in a porous rectangular channel with external heat transfer to upper and lower fluid environments
2012
Published version of an article in the journal: Transport in Porous Media. Also available from the publisher at: http://dx.doi.org/10.1007/s11242-012-0018-9 The conditions for the onset of convection in a horizontal rectangular channel filled with a fluid saturated porous medium are studied. The vertical sidewalls are assumed to be impermeable and adiabatic. The horizontal upper and lower boundary walls are considered as impermeable and subject to external heat transfer, modelled through a third-kind boundary condition on the temperature field. The external fluid environments above and below the channel, kept at different temperatures, provide the heating-from-below mechanism which may lead…
Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem
2021
The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled by employing the fixed-stress split scheme, which leads to an iteratively solved semi-discrete system. The error bounds are derived by combining a posteriori estimates for contractive mappings with functional type error control for elliptic partial differential equations. The estimates are applicable to any approximation in the admissible functional space and are independent of the discretization method. They are fully computable, do not contain mesh-dependent constants, and provide r…
Effect of a finite external heat transfer coefficient on the Darcy-Bénard instability in a vertical porous cylinder
2013
Publised version of an article from the journal: Physics of Fluids. Copyright (2013) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. Article appears in Volume 25 issue 4 of the journal: http://dx.doi.org/10.1063/1.4799253 The onset of thermal convection in a vertical porous cylinder is studied by considering the heating from below and the cooling from above as caused by external forced convection processes. These processes are parametrised through a finite Biot number, and hence through third-kind, or Robin, temperature conditions imposed on the lower and upper b…
Creation of Temperature Field in a Finite Cylinder by Alternated Electromagnetic Force
2004
One of the modern areas of applications developed during last years is effective use of electrical energy produced by alternating current in production of heat energy. This process is ecologically clean.The water is weakly electrically conducting medium (electrolyte). Devices based on this principle are developed during last ten years. Compared to classical devices with heating elements, new devices are more compact.
Acoustic methods for measuring the porosities of porous materials incorporating dead-end pores
2013
International audience; The acoustic properties of porous materials containing dead-end (DE) pores have been proposed by Dupont et al. [J. Appl. Phys. 110, 094903 (2011)]. In the theoretical description, two physical parameters were defined (the dead-end porosity and the average length of the dead-end pores). With the knowledge of the open porosity (measured with non-acoustic methods), and the measurement of kinematic porosity (also called the Biot porosity in this article), it is possible to deduce the dead-end porosity. Two acoustic methods for measuring the Biot porosity for a wide range of porosities are proposed. These methods are based on acoustic transmission and on the low and high …
Acoustic spectroscopy of aerogel precursors
2007
We investigate the acoustical properties of silica gels, which are precursors in the aerogel production process. These gels exhibit a strong “ringing gel” behavior, that is they emit a characteristic sound if one knocks against the container. We study this sound emission with a very simple spectroscopic technique and observe resonances which are characteristic for natural frequencies of a cylindrical body. From a fit of the experimental frequency positions to calculated values, we determine a sound velocity of c T = 4 m/s for a gel sample with porosity φ = 97.5%. This low sound velocity can only be interpreted as the transverse sound mode predicted by Biot’s theory for sound propagation in …