Effect of a Porous Layer on the Flow Structure and Heat Transfer in a Square Cavity

Abstract: A two-dimensional rectangular enclosure containing a binary-fluid saturated porous layer of finite thickness placed in the centre of the cavity is considered. Phase change is neglected. Vertical and horizontal solid boundaries are assumed to be isothermal and adiabatic, respectively. A horizontal temperature gradient is imposed, driving convection of buoyancy nature. The Darcy equation, including Brinkman and Forchheimer terms is used to account for viscous and inertia effects in the momentum equation, respectively. The problem is then solved numerically in the framework of a Velocity-Pressure formulation resorting to a finite volume method based on the standard SIMPLER algorithm. The effects of the governing parameters (geometric, hydrodynamic and thermal) on fluid flow and heat transfer are investigated. Nomenclatur

Additional degrees of parallelism within the Adomian decomposition method

4th International Conference on Computational Engineering (ICCE 2017), 28-29 September 2017, DarmstadtThis is the author accepted manuscript. The final version is available from Springer via the DOI in this record.The trend of future massively parallel computer architectures challenges the exploration of additional degrees of parallelism also in the time dimension when solving continuum mechanical partial differential equations. The Adomian decomposition method (ADM) is investigated to this respects in the present work. This is accomplished by comparison with the Runge-Kutta (RK) time integration and put in the context of the viscous Burgers equation. Our studies show that both methods have similar restrictions regarding their maximal time step size. Increasing the order of the schemes leads to larger errors for the ADM compared to RK. However, we also discuss a parallelization within the ADM, reducing its runtime complexity from O(n^2) to O(n). This indicates the possibility to make it a viable competitor to RK, as fewer function evaluations have to be done in serial, if a high order method is desired. Additionally, creating ADM schemes of high-order is less complex as it is with RK.The work of Andreas Schmitt is supported by the ’Excellence Initiative’ of the German Federal and State Governments and the Graduate School of Computational Engineering at Technische Universit¨at Darmstadt

Modelisation mathematique de la degranulation des basophiles

SIGLECNRS T Bordereau / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Numerical analysis of combined natural convection-internal heat generation source-surface radiation

Numerical study of combined laminar natural convection and surface radiation with internal heat generation is presented in this paper and computations are performed for an air-filled square cavity whose four walls have the same emissivity. Finite volume method through the concepts of staggered grid and SIMPLER algorithm has been applied, and the view factors are determined by analytical formula. A power scheme is also used in approximating advection-diffusion terms. Representative results illustrating the effects of emissivity and the internal heat generation on the streamlines and temperature contours within the enclosure are reported. In addition, obtained results for local and average convective and radiative Nusselt, for various parametric conditions, show that internal heat generation modifies significantly the flow and temperature fields

Limit of the buoyancy ratio in Boussinesq approximation for double-diffusive convection in binary mixture

International audienceThis paper deals with a mathematical and numerical investigation of double-diffusive natural convective heat and mass transfer in a cavity filled with Newtonian fluid with significant density and mass diffusivity changes. In such a situation, the assumption of the Boussinesq approximation is not justified, and an appropriate model based on a set of Low Mach Number equations is used. The active parts of two vertical walls of the cavity are maintained at fixed but different temperatures and concentrations, while the other two walls, as well as inactive areas of the sidewalls, are considered to be adiabatic and impermeable to mass transfer. The coupled momentum, energy, and solute transfer equations in binary mixtures of ideal gases are solved through a global iterative procedure based on the finite volume methods in the context of the low Mach number approximation. The study includes the effect of the buoyancy ratio N with the aim to find its application limit in the Boussinesq conditions. The results show that if we use the Boussinesq approximation to study double-diffusive convection, the value of parameter N must be between -6 and 27

Numerical study of natural convection in a square cavity under non-boussinesq conditions

Natural convection in a differentially heated cavity has been carried out under large temperature gradient. The study has been performed by direct simulations using a two-dimensional finite volume numerical code solving the time-dependent Navier-Stokes equations under the Low Mach Number approximation. The LMN model constitutes an important numerical problem for low speed flows. It is based on the filtering of acoustic waves from the complete Navier-Stokes equations. Various simulations were conducted including constant or variable transport coefficients and both small and large temperature differences. A comparison between an incompressible code based on the Boussinesq approximation and the LMN compressible code shows that the incompressible model is not sufficient to simulate natural convective flow for large temperature differences

Sur la similarité entre la convection thermogravitaire et la convection thermomagnétique en zéro gravité dans une cavité rectangulaire différentiellement chauffée remplie d’un fluide paramagnétique

National audienc

Combined natural-convection and radiation in presence of internal heat generation source in absorbing-emitting-scattering medium

International audienceNumerical investigation of combined laminar natural convection and volumetric radiation with internal heat generation is presented in this paper and computations are performed for a grey gas-filled square cavity whose horizontal walls are adiabatic and vertical walls are differentially heated. The convection is treated under Boussinesq approximation by an approach based on finite-volumes and the volumetric radiation by the discrete ordinates method. Flow and heat transfer characteristics through isotherms, streamlines and average Nusselt numbers have been presented for an external Rayleigh number 106, internal Rayleigh number 0 to 4x1012, optical thickness 0 to 10 and Albedo 0 to 1. Representative results illustrating the effects of the optical thickness and the internal heat generation on the flow and the temperature distribution within the cavity are presented. The results reveal that the fluid flow and heat transfer are influenced significantly by the volumetric radiation and the internal heat generation. By comparing the solutions in pure convection, the results in combined convection-volumetric radiation show that when the medium is participating, the effect of internal source presence is very important