Natural Convection In Porous Enclosure Research Articles

A fully interior penalty discontinuous Galerkin method for variable density groundwater flow problems

Discontinuous Galerkin (DG) methods due to their robustness properties, e.g. local conservation, low numerical dispersion, and well-capturing strong shocks and physical discontinuities, are well-suited for the simulation of Variable Density Flow (VDF) in porous media. This paper aims at introducing, in a unified format, the general class of Interior Penalty DG (IPDG) methods to solve the VDF equations. A combination of symmetric, non-symmetric and incomplete IPDG methods is used to discretize both head and concentration variables. Compatibility analysis is performed to prevent the loss of accuracy of the IPDG methods in simulations of coupled flow and transport equations. An accurate technique is used for time integration, based on a non-iterative procedure and adaptive time stepping with embedded error control. Several benchmarks are investigated to validate the proposed DG scheme and to examine its performance in simulating VDF problems. The new DG scheme reproduces better the experimental data than the conventional SEAWAT model. Its results are in excellent agreement with a recent semi-analytical solution of the Henry problem, dealing with seawater intrusion under convection-dominating conditions. The performance of the DG scheme is examined by simulating the challenging problem of natural convection in porous enclosure. The method is compared against a finite element solution obtained with COMSOL multi-physics. The numerical experiments indicate clearly that high-order DG method is much more appropriate than standard conforming Galerkin method in simulating VDF problems while at the same time, guaranteeing a better precision and high-fidelity solutions. The proposed numerical method can be extended to 3D problems.

Numerical Analysis on the Effect of Wavy Partitions on Natural Convection in Porous Enclosure

Abstract The influence of partitions on natural convection in a differentially heated porous enclosure has been investigated for three different partition shapes, namely, sine-wave, corrugated and square-wave shape. The objective is to identify the best partition shape with regard to achieve maximum reduction in the rate of convection heat transfer. Darcy flow model has been used to describe flow in porous media. Coordinate transformation has been used to formulate the governing equations for sine-wave partition owing to its wavy nature. To assess the effectiveness of various partition shapes, the results are compared with porous enclosure without partition and with straight partition. The governing equations are solved using the successive accelerated replacement scheme for a wide range of parameters like partition amplitude, position, Rayleigh number, enclosure aspect ratio (AR), and inclination angle. One of the findings reveals that for the same amplitude and position, the square-wave partition yields the maximum suppression in the value of Nusselt number.

Effect of partially thermally active wall on natural convection in porous enclosure

Effect of partially thermally active wall on natural convection in porous enclosure

Analyzing natural convection in porous enclosure with polynomial chaos expansions: Effect of thermal dispersion, anisotropic permeability and heterogeneity

In this paper, global sensitivity analysis (GSA) and uncertainty quantification (UQ) have been applied to the problem of natural convection (NC) in a porous square cavity. This problem is widely used to provide physical insights into the processes of fluid flow and heat transfer in porous media. It introduces however several parameters whose values are usually uncertain. We herein explore the effect of the imperfect knowledge of the system parameters and their variability on the model quantities of interest (QoIs) characterizing the NC mechanisms. To this end, we use GSA in conjunction with the polynomial chaos expansion (PCE) methodology. In particular, GSA is performed using Sobol’ sensitivity indices. Moreover, the probability distributions of the QoIs assessing the flow and heat transfer are obtained by performing UQ using PCE as a surrogate of the original computational model. The results demonstrate that the temperature distribution is mainly controlled by the longitudinal thermal dispersion coefficient. The variability of the average Nusselt number is controlled by the Rayleigh number and transverse dispersion coefficient. The velocity field is mainly sensitive to the Rayleigh number and permeability anisotropy ratio. The heterogeneity slightly affects the heat transfer in the cavity and has a major effect on the flow patterns. The methodology presented in this work allows performing in-depth analyses in order to provide relevant information for the interpretation of a NC problem in porous media at low computational costs.

Numerical Study of Laminar Natural Convection in Porous Media: Darcy -Brinkman-Forcheimer Model

In this article, we present a two-dimensional study of laminar natural convection in porous enclosure. The horizontal walls of the enclosure are thermally insulated, where as the left and right vertical walls are maintained respectively at different temperatures TC (warm temperature) and Tf (cold temperature).we present the differential equations modeling the phenomenon studied according to Darcy- Brinkman – Forcheimer model. after the dimensionless form of the equation we have four dimensionless numbers: the Prandtl number Pr the thermal Grashof Gr, the aspect ratio A, the Darcy number Da. The results allowed us to conclude the following: Increasing of Grachof number with a constant Darcy number, so we areThe increase of convection and as a result the increase in flow velocity and heat transfer.at constant of Grachof number whith decreasing of the Darcy number, the medium is impermeable which slow motion of the convection phenomenon. so we are a degradation speed and heat transfer. Finaly We executed the program calculates with the real data of oil reservoir.

Conjugate Natural Convection in a Porous Enclosure Sandwiched by Finite Walls Under the Influence of Non-uniform Heat Generation and Radiation

Conjugate natural convection in a square porous enclosure sandwiched by finite walls under the influence of non-uniform heat generation and radiation is studied numerically in the present article. The horizontal heating is considered, where the vertical walls heated isothermally at different temperatures, while the horizontal walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and finite difference method is applied to solve the dimensionless governing equations. The governing parameters considered are the ratio of wall thickness to its width $$(0.02 \le D \le 0.3)$$ , the wall to porous thermal conductivity ratio $$(0.1 \le k_\mathrm{r} \le 10.0)$$ , the internal heating $$(0 \le \gamma \le 5)$$ , and the local heating exponent parameters $$(1 \le \lambda \le 20)$$ . It is found that the average Nusselt number on the hot and cold interfaces increases with increasing the radiation intensity. Very high non-uniformity heating does not affect the average Nusselt number at very thick walls.

Conjugate Natural Convection in a Porous Enclosure with Non-Uniform Heat Generation

Effects of a conductive wall on natural convection in a square porous enclosure having internal heating at a rate proportional to a power of temperature difference is studied numerically in this article. The horizontal heating is considered, where the vertical walls heated isothermally at different temperatures while the horizontal walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and finite difference method is applied to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (0 ≤ Ra ≤ 1000), the internal heating and the local exponent parameters (0 ≤ γ ≤ 5), (1 ≤ λ ≤ 3), the wall to porous thermal conductivity ratio (0.44 ≤ Kr ≤ 9.9) and the ratio of wall thickness to its width (0.02 ≤ D ≤ 0.5). The results are presented to show the effect of these parameters on the fluid flow and heat transfer characteristics. It is found a strong internal heating can generate significant maximum fluid temperature more than the conductive solid wall. Increasing value thermal conductivity ratio and/or decreasing the thickness of solid wall can increase the maximum fluid temperature. It is also found that at very low Rayleigh number, the heat transfer across the porous enclosure remain stable for any values of the thermal conductivity ratio.

Influence of periodicity of sinusoidal bottom boundary condition on natural convection in porous enclosure

In this paper, natural convective flow within a rectangular enclosure has been investigated numerically. All the walls of the enclosure are adiabatic except the bottom wall, which is partially heated and cooled by sinusoidal temperature profile. Both situations: medium is hydro-dynamically isotropic and anisotropic are considered. The governing equations are written under assumption of Brinkman-extended non-Darcy model, including material derivative, and then solved by numerically using spectral element method (SEM). Main emphasize is given on effect of periodicity parameter (N) on local heat transfer rate (Nux) as well as flow mechanism in the enclosure. The result shows that, as the periodicity is decreased on increasing N, the absolute value of Nux at the bottom left corner point increases in both situations. For odd values of N, the local heat transfer profile is symmetric about the line X=0.5. The entire flow is governed by two type convective cells: (i) rotating clockwise (ii) rotating anticlockwise. Furthermore, increasing of N increases the multiple cellular structures in the form of N+1. The relative impact of media permeability on Nux at (0,0) shows that enhancement of media permeability along Y-direction is much more effective than the same along X-direction. In contrast to isotropic porous media, the effect of the permeability and permeability orientation angle on the flow is complex and often non intuitive. In particular the present analysis shows that, different periodicity of temperature boundary condition has significant effect on the flow mechanism and consequently on the heat transfer rate for both situations.