WALL HEAT CONDUCTION EFFECT ON NATURAL CONVECTION IN AN ENCLOSURE FILLED WITH A NON-DARCIAN POROUS MEDIUM

ABSTRACT

A numerical analysis has been made of the conjugate natural convection in a rectangular enclosure filled with a fluid-saturated porous medium and surrounded with four solid walls. The conductance of the walls is assumed to be much greater than that of the cavity filled with a porous medium. The main objective was to investigate the influences of the ratio of thermal conductivity of the wall to that of the fluid-porous matrix composite, the Darcy-modified Rayleigh number, the Prandtl number, and the aspect ratio. The streamlines and isotherms are presented; also, the local and average Nusselt numbers are presented along the interface between walls and cavity. A non-Darcian model was employed and the numerical method was SIMPLE-C. The numerical results indicate that the wall heat conduction effects decrease the heat transfer rate. When the wall heat conduction is considered, the greater the conductance of the solid walls surrounding the cavity, the greater is the rate of heat transfer.     

CONJUGATE FREE CONVECTION FROM VERTICAL FINS EMBEDDED IN A POROUS MEDIUM

The problem of conjugate free convection in a porous medium from a vertical plate and a vertical cylindrical fin is considered. The governing equations for the convective flow in the porous medium are coupled to the governing equation for the heat flow in the fin by the conditions of continuity of the temperature and the heat flux at the interface. The heat flow in the fin is taken to be either two-dimensional or one-dimensional, in order to compare the results provided by both approaches. The nondimensional parameters that appear are the convection-conduction parameter, N cc , and the aspect ratio of the fin, u p for the plate fin and u c for the cylindrical fin. The surface curvature parameter u C appears as a parameter which is directly dependent on u c in the case of the cylindrical fin. Considering two-dimensional conduction in the solid fin is a more realistic approach from a practical standpoint, but the shortcoming of specifying zero heat flux at the tip of the fin is discussed.     

MAGNETOHYDRODYNAMIC MIXED CONVECTION FROM A VERTICAL PLATE EMBEDDED IN A POROUS MEDIUM

Magnetohydrodynamic mixed convection flaw about a vertical flat plate embedded in a porous medium is considered. The effect of the magnetic field strength on the local Nusselt number and local wait shear stress is presented. The non-Darcian model including both the inertia and boundary effects is used. A particular transformation for the governing equations is adopted to cover the whole mixed convection regime within two finite limits. Appreciable effects of the magnetic field strength on the local Nusselt number as well as on the local wall shear stress in the mixed convection regime are found.     

EFFECTS OF HETEROGENEITY IN FORCED CONVECTION IN A POROUS MEDIUM: TRIPLE LAYER OR CONJUGATE PROBLEM

The effects of variation (in the transverse direction) of permeability and thermal conductivity, on fully developed forced convection in a parallel plate channel or circular duct filled with a saturated porous medium, is investigated analytically on the basis of a Darcy model, for the cases of isoflux and isothermal boundaries. Previous work is extended to the case of a medium composed of three layers, or two layers with an adjacent solid layer. For the parallel plate channel with isoflux boundaries, some general multilayer results are given.     

BUOYANT CONVECTION IN A SQUARE CAVITY PARTIALLY FILLED WITH A HEAT-GENERATING POROUS MEDIUM

Steady-state buoyant convection in a rectangular cavity, partially filled with a fluid-saturated porous medium with spatially uniform internal heat generation, is considered. The Brinkman-extended Darcy model in the porous region is adopted. The overall Rayleigh number is large to render a boundary-layer-type global flow pattern. Scale analysis is performed to obtain a rudimentary understanding of the flow characteristics. In parallel with the theoretical endeavors, numerical solutions are secured over broad ranges of nondimensional parameters. The results indicate that there exists an asymptotic convection regime where the flow is nearly independent of the permeability and conductivity of the porous medium. The effect of the thermal conductivity of porous material is appreciable in the intermediate regime. In the conduction-dominant regime, the porous region acts like a heat-generating solid block. The numerical study gives credence to the reliability of the theoretical arguments.     

INFLUENCE OF VIBRATION ON SORET-DRIVEN CONVECTION IN POROUS MEDIA

Two-dimensional thermosolutal natural convection with Soret effect under the simultaneous action of vibrational and gravitational accelerations is investigated. We consider a porous cavity saturated by a binary mixture and adopt the time-averaging formulation. For an infinite horizontal layer, a stability analysis is performed from which the threshold of stability is determined. Numerical simulations, using a pseudo-spectral Chebyshev collocation method, are performed to describe the convective motion. The problem is investigated for different aspect ratios with various directions of vibration. It is concluded that, for both the stationary and the Hopf bifurcation, the vertical vibration has a stabilizing effect while the horizontal vibration has a destabilizing effect on the onset of convection.     

转动惯量对水电机组动态性能的影响

研究ＧＤ＾２对水电机组动态性能的影响，结果表明：ＧＤ＾２的减小对并利运行的水轮发电机组的静态稳定是有利的，对孤立运行的水轮机调节系统的稳定是不利的，但可以通过改善调速器参数整定来弥补，随着ＧＤ＾２的减小，水轮机组动态品质的满足与否取决于转速最大偏差△ｘｍａｘ。     

FREE CONVECTION IN OPEN-TOP ENCLOSURES FILLED WITH A POROUS MEDIUM HEATED FROM BELOW

Free convection is studied for porous medium-filled enclosures that are open for fluid flow at the top. For such setups a mixed boundary condition for the transport variable at the top is examined, which is different from the classical approach (Lapwood problem) in systems where flow is governed by Darcy's law. While the latter led to open and to closed paths within each convection cell, the mixed boundary condition induces open convection cells only. By numerical means, the onset of convection, total heat and mass transfer, and the transition from the first to the second mode are examined. At 16.5, the critical Rayleigh number for the onset of convection in the system with mixed boundary condition is much lower than the classical value.     

TRANSIENT FREE CONVECTION ABOUT A VERTICAL FLAT PLATE EMBEDDED IN A SATURATED POROUS MEDIUM

An analysis is presented of the transient, buoyancy-induced flow and heat transfer in a Darcian fluid-saturated porous medium adjacent to a suddenly heated semi-infinite vertical wall. Transient profiles of the temperature field and the local Nusselt number are obtained by solving the unsteady boundary layer partial differential equations numerically. It is shown that the governing equations are of a singular parabolic type and can be solved accurately in a semi-similar, finite elliptic domain using a successive relaxation method. The solution thus obtained is compared with a solution obtained in the physical domain using an explicit upwind method. The results confirm that during the initial stage, before the effects of the leading edge are influential at a location, heat transfer and flow phenomena in porous media are governed by transient one-dimensional conduction. New data are presented for the transition from this initial conduction stage to a fully two-dimensional transient, which ultimately terminates in steady convection. It is also shown that in a Darcian medium the transient development of temperature field and local Nusselt number takes place monotonically, and unlike in homogeneous media, neither exhibits an overshoot.     

TRANSIENT NATURAL CONVECTION OF WATER NEAR ITS DENSITY EXTREMUM IN A RECTANGULAR CAVITY FILLED WITH POROUS MEDIUM

A numerical study is performed to analyze the transient flow field and heat transfer behavior of cold water in a rectangular enclosure filed with a porous medium. The numerical method was employed by the SIMPLE-C algorithm. The accurate nonlinear relation between density and temperature developed by Gebhart and Mollendorf was used. The numerical results show that, for R < 0 · 5, the size of the clockwise vortex beside the high-temperature surface increases as time increases. The clockwise vortex occupies almost the whole space when the steady state is reached. For R = 0 · 5, the size of the clockwise vortex adjacent to the high-temperature surface increases as time increases. However, two counterrotation vortices having the same strength and size exist in the space when steady state is reached. For R > l, only one counterclockwise vortex exists in the space the entire time. For τ > 10^?3, the heat transfer rate increases with increase in Darcy number for the entire time. However, as time increases, the heat transfer rate on the high-temperature surface decreases and that on the low-temperature surface increases.     

EFFECT OF BUOYANCY ON FORCED CONVECTION IN A CUSPED DUCT

ABSTRACT

In the event of a loss of coolant accident in a pressurized water reactor, swelling of the fuel rod cladding will lead to reduction of the subchannel flow area and worsening of the core heat transfer in the region of the blockage. The four-cusped duct is an ideal geometry for the simulation of such a channel blockage. Understanding the characteristics of flow and heat transfer in the cusped duct is essential for better design of the emergency core cooling system. Thus, in this paper, combined natural and forced convection in a vertical cusped duct has been investigated in the region of both hydrodynamically and thermally fully developed flow. The thermal boundary condition imposed on the cusped duct is the axial uniform heat flux with peripheral uniform temperature. The results indicate that the fluid flow and heal transfer in the comer region of the cusped duct are improved because of the influence of natural convection. As the Rayleigh number increases, the friction factor and Nusselt number increase accordingly. It was also found that the critical Rayleigh number is 1200, at which flow reversal occurs in the buoyancy-assisted flow ( heated upflow). The velocity, temperature, and local Nusselt number distribution are presented for a range of Rayleigh numbers.     

THE EFFECT OF HEAT FLUX DISTRIBUTION ON THERMOCAPILLARY CONVECTION IN A SIDE-HEATED LIQUID BRIDGE

A numerical analysis is performed on thermocapillary convection in a liquid bridge. The effect of various imposed heat flux distributions on the free surface for axisymmetric liquid bridge flows, in zero gravity, is presented. Constant, polynomial, and different Gaussian profiles are considered, and the resulting velocity and temperature fields are compared. It is shown that a more concentrated heat flux distribution has a significant effect on the hydrodynamics of the liquid bridge. The transition from steady to unsteady flows also depends on the distribution of applied heat flux. The frequency of the oscillation increases with Ma increase.     

NUMERICAL STUDY OF CONVECTION HEAT TRANSFER DURING THE MELTING OF ICE IN A POROUS LAYER

A numerical study is made of the melting of ice in a rectangular porous cavity heated from above. The Landau transformation is used to immobilize the ice-water interface, and the Darcy-Boussinesq equations are solved by a finite-difference technique. Results are analyzed in terms of the heating temperature and the aspect ratio of the cavity. A comparison is made with the case of melting from below. It was found that melting from above is more effective than melting from below when the heating temperature is between 0 and 8°C: convection arises earlier, the melting process is faster, and the total melt at steady state is thicker. The critical time for onset of convection is minimum when the upper boundary is heated at 6°C. At this heating temperature, one also obtains a maximum heat transfer rate (Nusselt number).     

NATURAL CONVECTION IN POROUS ENCLOSURES: THE APPLICATION OF THE TWO-ENERGY EQUATION MODEL

The present investigation is concerned with the numerical simulation of a fluid-saturated porous medium emplaced inside a square enclosure. The flow field is modeled using the generalized form of the momentum equation by accounting for the viscous effects and the inertial effects as well. In addition, the local fluid and solid temperatures were both accounted for separately by employing the two-energy equation model. The sensitivity of the Darcy number and Grashof number values on the momentum and energy transport processes are highlighted in the range of 10 -5 h Da h 10 -1 and 10 4 h Gr h 10 6 , respectively. Furthermore, Nusselt number formulation, based on the overall energy balance, was developed for the two-energy equation model. Finally, an assessment of the local thermal equilibrium condition was carried out to weigh its significance over the range of flow conditions and porous configurations considered in the analysis.     

EFFECTS OF TRANSVERSE MAGNETIC FIELD,PRANDTL NUMBER AND REYNOLDS NUMBER ON NON-DARCY MIXED CONVECTIVE FLOW OF AN INCOMPRESSIBLE VISCOUS FLUID PAST A POROUS VERTICAL FLAT PLATE IN A SATURATED POROUS MEDIUM

The effect of transverse magnetic field parameter (Hartmann number, Ha), Reynolds number (Re) and Prandtl number (Pr) on the mixed convection flow past a semi-infinite vertical porous plate in a non-Darcian porous medium with variable viscosity and porosity, viscous dissipation and fluid–solid thermal conductivity ratio in the presence of plate transpiration (lateral mass flux) is investigated theoretically and numerically using Keller's implicit finite difference scheme. It is shown that the Hartmann number acts as a retarding force and increases the momentum boundary layer thickness, analogous to the flow against a positive pressure gradient, simultaneously decreasing local skin friction (shear stress). The heat transfer rate is however enhanced by the magnetic field (for positive values of the Eckert number) since the fluid is heated and temperature gradients become reduced between the fluid and the plate, with important potential applications in MHD power generators, materials processing and geothermal systems containing electrically-conducting fluids. The effects of high velocity flow (larger Re) and different Prandtl numbers corresponding to different industrial and geophysical fluids on heat transfer are also discussed. © 1997 by John Wiley & Sons, Ltd.     

多孔床料对生物质产气特性影响实验研究

在小型常压流化床内采用多孔介质为床料,对生物质进行了空气、空气.水蒸汽气化实验并与普通工业用砂为床料的气化结果进行了对比,分析不同气化介质、温度及流量时多孔床料对生物质产气特性的影响.实验结果表明:产气中可燃气含量随气化温度升高而增大,流量对生物质气化影响存在最佳范围.与普通床料相比,多孔床料对H2和CO的生成以及对低碳氢化合物(CxHx)的催化裂解有较强的促进作用.