Numerical and Experimental Study of Rayleigh–Bénard–Kelvin Convection

We performed experimental and numerical studies of combined effects of thermal buoyancy and magnetization force applied on a cubical enclosure of a paramagnetic fluid heated from below and cooled from top. The temperature difference between the hot and cold wall was kept constant. After considering neutral situation (i.e. a pure natural convection case), magnetic fields of different intensity were imposed. The magnetization force produced significant changes in flow (transition from laminar to turbulent regimes), wall-heat transfer (enhancement) and turbulence (turbulence structures reorganization). The strong magnetic field and its gradients were generated by a superconducting magnet which can generate magnetic field up to 10 T and where gradients of the magnetic induction can reach up to 900 T²/m. A good agreement between experiments and numerical simulations was obtained in predicting the integral wall heat transfer over entire range of considered working parameters. Numerical simulations provided a detailed insights into changes of the local wall-heat transfer and long-term time averaged first and second moments for different strengths of the imposed magnetic induction.     

Analysis of One-Dimensional Advection–Diffusion Model with Variable Coefficients Describing Solute Transport in a Porous medium

This work presents the analytical solution and temporal moments of one-dimensional advection–diffusion model with variable coefficients. Two case studies along with the two different sets of boundary conditions are considered at the inlet and outlet of the domain. In the first case, a time-dependent solute dispersion in the homogeneous domain along uniform flow is taken into account, whereas in the second case, due to inhomogeneity of domain, velocity is taken spatially dependent and the dispersion is assumed proportional to the square of the velocity. The Laplace transform is used to obtain the analytical solutions. The analytical temporal moments are derived from the Laplace domain solutions. To verify the correctness of the analytical solutions, a high-resolution second-order finite volume scheme is applied. Different case studies are considered and discussed. Both analytical and numerical results are in good agreement with each other.     

Effect of Conduction in Bottom Wall on Darcy–Bénard Convection in a Porous Enclosure

Conjugate natural convection-conduction heat transfer in a square porous enclosure with a finite-wall thickness is studied numerically in this article. The bottom wall is heated and the upper wall is cooled while the verticals walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and the COMSOL Multiphysics software is applied to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (100 ≤ Ra ≤ 1000), the wall to porous thermal conductivity ratio (0.44 ≤ K _r ≤ 9.90) and the ratio of wall thickness to its height (0.02 ≤ D ≤ 0.4). The results are presented to show the effect of these parameters on the heat transfer and fluid flow characteristics. It is found that the number of contrarotative cells and the strength circulation of each cell can be controlled by the thickness of the bottom wall, the thermal conductivity ratio and the Rayleigh number. It is also observed that increasing either the Rayleigh number or the thermal conductivity ratio or both, and decreasing the thickness of the bounded wall can increase the average Nusselt number for the porous enclosure.     

Mixed Convection of Water at 4°C Along a Wedge with Variable Surface Flux in a Porous Medium

In this study, the mixed convection of water at 4°C along a wedge in a porous medium is investigated numerically using finite difference method. In order to explore the effect of mixed convection, both forced and free convection-dominated regimes are considered. Non-similarity solutions are obtained for the variable wall flux boundary condition. Velocity and temperature profiles as well as local dimensionless skin friction and Nusselt number are obtained and compared with the available numerical results for various values of different parameters. The wedge angle geometry parameter m and mixed convection parameter ξ are ranged from 0 to 1 in both regimes whereas different values of λ are considered for the purpose of comparison of heat transfer results.     

Effect of Conduction in Bottom Wall on B��nard Convection in a Porous Enclosure with Localized Heating and Lateral Cooling

Darcy-Bénard convection in a square porous enclosure with a localized heating from below and lateral cooling is studied numerically in the present paper. A finite-thickness bottom wall is locally heated, the top wall is kept at a lower temperature than the bottom wall temperature, and the lateral walls are cooled. The finite difference method has been used to solve the dimensionless governing equations. The analysis in the undergoing numerical investigation is performed in the following ranges of the associated dimensionless groups: the heat source length?? ${0.2\leq H \leq 0.9}$ , the wall thickness?? ${0.05\leq D \leq 0.4}$ , the thermal conductivity ratio?? ${0.8\leq K_{\rm r} \leq 9.8}$ , and the Biot number?? ${0.1\leq Bi \leq 1.1}$ . It is observed that the heat transfer rate could increase with increasing heat source lengths, thermal conductivity ratio, and cooling intensity. There exists a critical wall thickness for a high wall conductivity below which the increasing wall thickness increases the heat transfer rate and above which the increasing wall thickness decreases the heat transfer rate.     

Effects of a.c. Electric Field and Rotation on Bénard–Marangoni Convection

The coupled buoyancy and thermocapillary instability, the Bénard–Marangoniproblem, in an electrically conducting fluid layer whose upper surface is deformed and subject to a temperature gradient is studied. Both influences of an a.c. electric field and rotation are investigated. Special attention is directed at the occurrence of convection both in the form of stationary motion and oscillatory convection. The linear stability problem is solved for different values of the relevant dimensionless numbers, namely the a.c. electric Rayleigh number, the Taylor, Rayleigh, Biot, Crispation and Prandtl numbers. For steady convection, it is found that by increasing the angular velocity, one reinforces the stability of the fluid layer whatever the values of the surface deformation and the applied a.c. electric field. We have also determined the regions of oscillatory instability and discussed the competition between both stationary and oscillatory convections. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Effect of Conducting Boundaries on Weakly Nonlinear Darcy–Bénard Convection

We consider convection in a uniform fluid-saturated porous layer which is bounded by conducting plates and heated from below. The primary aim is to determine the identity of the postcritical convection planform as a function of the thicknesses and conductivities of the bounding plates relative to that of the porous layer. This work complements and extends an early paper by Riahi (J Fluid Mech 129:153–171, 1983) who considered a situation where the porous layer is bounded by infinitely thick conducting media. We present regions in parameter space wherein convection in the form of rolls is unstable and within which cells with square planform form the preferred pattern.     

Modeling of Heat and Mass Transfer in Absorption in Two–Phase Binary Systems used in Heat Pumps

Results of modeling of heat– and mass–transfer processes proceeding simultaneously in vapor absorption on tube banks are described. Theoretical models of film absorption are presented. The calculation results are compared with experimental data on steam absorption by the lithium bromide solution on a vertical tube. In calculation of transfer processes in absorption on horizontal tubes, the possibility of using solutions for the initial thermal length and for the section with a linear temperature profile is substantiated. The calculations are illustrated by the example of a multipass absorber.     

Weakly Nonlinear Stability Analysis of Temperature/Gravity-Modulated Stationary Rayleigh–Bénard Convection in a Rotating Porous Medium

The effect of time-periodic temperature/gravity modulation on thermal instability in a fluid-saturated rotating porous layer has been investigated by performing a weakly nonlinear stability analysis. The disturbances are expanded in terms of power series of amplitude of convection. The Ginzburg–Landau equation for the stationary mode of convection is obtained and consequently the individual effect of temperature/gravity modulation on heat transport has been investigated. Further, the effect of various parameters on heat transport has been analyzed and depicted graphically.     

Numerical Study of Hydrodynamics and Heat and Mass Transfer of a Ducted Gas–Vapor‐Droplet Flow

A computational model has been developed to predict heat and mass transfer and hydrodynamic characteristics of a turbulent gas–vapor–droplet flow. Turbulent characteristics of the gas phase are computed using the k– model of turbulence. It is shown that, with increasing inlet droplet diameter, the rate of heat transfer between the duct surface and the vapor–gas mixture decreases appreciably, whereas the wall friction increases only insignificantly. The predicted values agree fairly well with available experimental and numerical data     

Flow structures of turbulent Rayleigh–Bénard convection in annular cells with aspect ratio one and larger

Acta Mechanica Sinica - We present an experimental study of flow structures in turbulent Rayleigh–Bénard convection in annular cells of aspect ratios $$\varGamma =1$$ , 2 and 4, and...     

Modeling Variable Density Flow and Solute Transport in Porous Medium: 2. Re‐Evaluation of the Salt Dome Flow Problem

Case 5, Level 1 of the international HYDROCOIN groundwater flow modeling project is an example of idealized flow over a salt dome. The groundwater flow is strongly coupled to solute transport since density variations in this example are large (20%).Several independent teams simulated this problem using different models. Results obtained by different codes can be contradictory. We develop a new numerical model based on the mixed hybrid finite elements approximation for flow, which provides a good approximation of the velocity, and the discontinuous finite elements approximation to solve the advection equation, which gives a good approximation of concentration even when the dispersion tensor is very small. We use the new numerical model to simulate the salt dome flow problem.In this paper we study the effect of molecular diffusion and we compare linear and nonlinear dispersion equations. We show the importance of the discretization of the boundary condition on the extent of recirculation and the final salt distribution. We study also the salt dome flow problem with a more realistic dispersion (very small dispersion tensor). Our results are different to prior works with regard to the magnitude of recirculation and the final concentration distribution. In all cases, we obtain recirculation in the lower part of the domain, even for only dispersive fluxes at the boundary. When the dispersion tensor becomes very small, the magnitude of recirculation is small. Swept forward displacement could be reproduced by using finite difference method to compute the dispersive fluxes instead of mixed hybrid finite elements.     

Linear and Weakly Nonlinear Stability Analyses of Two-Dimensional,Steady Brinkman–Bénard Convection Using Local Thermal Non-equilibrium Model

Effect of local thermal non-equilibrium (LTNE) on onset of Brinkman–Bénard convection and on heat transport is investigated. Rigid–rigid and free–free, isothermal boundaries are considered for investigation. The assumption of LTNE leads to an ‘advanced onset’ situation compared to that predicted by the local thermal equilibrium (LTE) assumption. This results in the ‘enhanced heat transport’ situation in the problem. Asymptotic analysis for small and large values of inter-phase heat transfer coefficient is also carried out on critical Rayleigh number, critical wave number and Nusselt number. In respect of boundary influences on onset and heat transport, it is found that classical results hold even under the LTNE assumption. The other parameters’ influences on onset and heat transport are qualitatively similar in LTNE and LTE cases.     

Algebraic Modeling of the Turbulent Heat Fluxes Using the Elliptic Blending Approach—Application to Forced and Mixed Convection Regimes

The present paper focuses on the application of the elliptic blending approach to the modeling of turbulent heat fluxes, in order to account for the influence of solid boundaries. The analytical justification of the extension to the temperature–pressure gradient correlation term of this approach, originally applied to the velocity–pressure gradient, is given. The assumption of weak equilibrium enables the derivation of two new algebraic flux models valid down to the wall. It is shown, with both a priori tests and computations in forced and mixed convection regimes, that the predictions of the streamwise heat-flux and the temperature variance are significantly improved by the use of elliptic blending. A particular attention is devoted to the issue of the modeling of the correlation length scale involved in the elliptic blending for the heat fluxes, which is shown to have a significant influence on the predictions.     

Heat transfer and fluid dynamics of air–water two-phase flow in micro-channels

Heat transfer, pressure drop, and void fraction were simultaneously measured for upward heated air–water non-boiling two-phase flow in 0.51 mm ID tube to investigate thermo–hydro dynamic characteristics of two-phase flow in micro-channels. At low liquid superficial velocity j_l frictional pressure drop agreed with Mishima–Hibiki’s correlation, whereas agreed with Chisholm–Laird’s correlation at relatively high j_l. Void fraction was lower than the homogeneous model and conventional empirical correlations. To interpret the decrease of void fraction with decrease of tube diameter, a relation among the void fraction, pressure gradient and tube diameter was derived. Heat transfer coefficient fairly agreed with the data for 1.03 and 2.01 mm ID tubes when j_l was relatively high. But it became lower than that for larger diameter tubes when j_l was low. Analogy between heat transfer and frictional pressure drop was proved to hold roughly for the two-phase flow in micro-channel. But satisfactory relation was not obtained under the condition of low liquid superficial velocity.     

Bénard-Marangoni Instability of a Two-Layer System with Allowance for Variations in the Interfacial Internal Energy

The effect of variations of the internal surface energy due to local increments in the interfacial area on the conditions of onset of thermocapillary Marangoni instability in a two-layer system of reduced-viscosity fluids is studied. It is shown that in the linear approximation the effect considered leads to stabilization of the development of the monotonic instability mode.     

Bifurcations and chaos in large-Prandtl number Rayleigh–Bénard convection

Rayleigh–Bénard convection with large-Prandtl number (P) is studied using a low-dimensional model constructed with the energetic modes of pseudospectral direct numerical simulations. A detailed bifurcation analysis of the non-linear response has been carried out for water at room temperature (P=6.8) as the working fluid. This analysis reveals a rich instability and chaos picture: steady rolls, time-periodicity, quasiperiodicity, phase locking, chaos, and crisis. Our low-dimensional model captures the reappearance of ordered states after chaos, as previously observed in experiments and simulations. We also observe multiple coexisting attractors consistent with previous experimental observations for a range of parameter values. The route to chaos in the model occurs through quasiperiodicity and phase locking, and attractor-merging crisis. Flow patterns spatially moving along the periodic direction have also been observed in our model.