Natural convection in a mushy layer

1991 ◽  
Vol 224 ◽  
pp. 335-359 ◽  
Author(s):  
M. Grae Worster
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Solid Fraction ◽  
Convective Flow ◽  
Mushy Layer ◽  
Governing Equations ◽  
Downward Flow ◽  
Asymptotic Regime

Governing equations for a mushy layer are analysed in the asymptotic regime Rm [Gt ] 1, where Rm is an appropriately defined Rayleigh number. A model is proposed in which there is downward flow everywhere in the mushy layer except in and near localized chimneys, which are characterized by having zero solid fraction. Upward, convective flow within the chimneys is driven by compositional buoyancy. The radius of each chimney is determined locally by thermal balances within a boundary layer that surrounds it. Simple solutions are derived to determine the structure of the mushy layer away from the immediate vicinity of chimneys in order to demonstrate the gross effects of convection upon the solidification within the layer.

scholarly journals Natural Convection over Two Superellipse Shapes with a Porous Cavity Populated by Nanofluid

Energies ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 6952
Author(s):  
Noura Alsedais
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Darcy Number ◽  
Governing Equations ◽  
Porous Layers ◽  
Porous Cavity ◽  
The Mean ◽  
Volume Method

The influences of superellipse shapes on natural convection in a horizontally subdivided non-Darcy porous cavity populated by Cu-water nanofluid are inspected in this paper. The impacts of the inner geometries (n = 0.5,1,1.5,4) Rayleigh number (103 ≤ Ra ≤ 106), Darcy number (10−5 ≤ Da ≤ 10−2), porosity (0.2 ≤ ϵ ≤ 0.8), and solid volume fraction (0.01 ≤ ∅ ≤ 0.05) on nanofluid heat transport and streamlines were examined. The hot superellipse shapes were placed in the cavity’s bottom and top, while the adiabatic boundaries on the flat walls of the cavity were considered. The governing equations were numerically solved using the finite volume method (FVM). It was found that the movement of the nanofluid upsurged as Ra boosted. The temperature distributions in the cavity’s core had an inverse relationship with increasing Rayleigh number. An extra porous resistance at lower Darcy numbers limited the nanofluid’s movement within the porous layers. The mean Nusselt number decreased as the porous resistance increased (Da ≤ 10−4). The flow and temperature were strongly affected as the shape of the inner superellipse grew larger.

scholarly journals Numerical simulation of coupeld heat transfer through a concrete hollow brick

2019 ◽  
Vol 286 ◽  
pp. 08004
Author(s):  
B. Jamal ◽  
M. Boukendil ◽  
A. Abdelbaki ◽  
Z. Zrikem
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Fluid Flow ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Simple Algorithm ◽  
Governing Equations ◽  
Coupled Heat Transfer ◽  
Hollow Brick ◽  
Finite Volume Approach

The present study aims to investigate coupled heat transfer by natural convection and conduction through a concrete hollow brick. The governing equations for conservation of mass, momentum and energy are discretized by the finite volume approach and solved by the SIMPLE algorithm. The numerical simulations were conducted to investigate the effect of Rayleigh number (103≤ Ra ≤ 107) on the heat transfer and fluid flow within the structure.

Natural Convection in a Cavity With a Wavy Wall Heated From Below and Uniformly Cooled From the Top and Both Sides

2006 ◽  
Vol 128 (7) ◽  
pp. 717-725 ◽  
Author(s):  
Amaresh Dalal ◽  
Manab Kumar Das
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Wall ◽  
Wavy Wall ◽  
Governing Equations ◽  
Integral Forms ◽  
Nusselt Number Distribution ◽  
Lower Temperature ◽  
Volume Method ◽  
Spatially Varying

In this paper, natural convection inside a two-dimensional cavity with a wavy right vertical wall has been carried out. The bottom wall is heated by a spatially varying temperature and other three walls are kept at constant lower temperature. The integral forms of the governing equations are solved numerically using finite-volume method in the non-orthogonal body-fitted coordinate system. The semi-implicit method for pressure linked equation algorithm with higher-order upwinding scheme are used. The streamlines and isothermal lines are presented for three different undulations (1, 2 and 3) with different Rayleigh number and a fluid having Prandtl number 0.71. Results are presented in the form of local and average Nusselt number distribution for a selected range of Rayleigh number (100-106).

Influence of Aperture Height and Width on Interzonal Natural Convection in a Full-Scale Air-Filled Enclosure

1989 ◽  
Vol 111 (4) ◽  
pp. 278-285 ◽  
Author(s):  
Charles R. Boardman ◽  
Allan Kirkpatrick ◽  
Ren Anderson
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Strong Dependence ◽  
Convection Heat Transfer ◽  
Test Cell ◽  
Cell Width ◽  
Height Range ◽  
Cell Height ◽  
Layer Flow

The topic of this paper is the influence of aperture height and width on interzonal high Rayleigh number, natural convection heat transfer. Experiments were conducted in an 8 ft. air-filled cube divided into two zones by a vertical partition which was centered between a constant flux hot wall and an isothermal cold wall. The partition was configured to form doorway-like apertures. The aperture height relative to test cell height range from 1/8 to 1 and the aperture width relative to test cell width ranged from 0.009 to 1. The zone-to-zone temperature difference and the overall Nusselt number were determined experimentally, and correlated with the overall Rayleigh number, aperture, and enclosure geometry, using a series resistance model for the enclosure. A turbulent boundary layer resistance was used to represent the hot and cold boundary layer flow, while an orifice resistance was used to represent the aperture flow. For flux Rayleigh numbers between 5*1011 and 5*1012, the enclosure Nusselt numbers ranged between 15 and 165, with a strong dependence on aperture height.

Scaling of Natural Convection of an Inclined Flat Plate: Sudden Cooling Condition

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Suvash C. Saha ◽  
John C. Patterson ◽  
Chengwang Lei
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Flow Regimes ◽  
Convection Boundary Layer ◽  
Numerical Verification ◽  
Inclined Plate ◽  
The Stability ◽  
Rayleigh Benard ◽  
Cold Boundary Layer

The natural convection boundary layer adjacent to an inclined plate subject to sudden cooling boundary condition has been studied. It is found that the cold boundary layer adjacent to the plate is potentially unstable to Rayleigh–Bénard instability if the Rayleigh number exceeds a certain critical value. A scaling relation for the onset of instability of the boundary layer is achieved. The scaling relations have been developed by equating important terms of the governing equations based on the development of the boundary layer with time. The flow adjacent to the plate can be classified broadly into a conductive, a stable convective, or an unstable convective regime determined by the Rayleigh number. Proper scales have been established to quantify the flow properties in each of these flow regimes. An appropriate identification of the time when the instability may set in is discussed. A numerical verification of the time for the onset of instability is also presented in this study. Different flow regimes based on the stability of the boundary layer have been discussed with numerical results.

Natural convection about a heated horizontal cylinder in a porous medium

1987 ◽  
Vol 184 ◽  
pp. 157-181 ◽  
Author(s):  
D. B. Ingham ◽  
I. Pop
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Finite Difference ◽  
Full Range ◽  
Second Order ◽  
Numerical Results ◽  
Experimental Results ◽  
Rayleigh Numbers

The natural convection from a heated circular cylinder in an unbounded region of porous medium is investigated for the full range of Rayleigh numbers. At small Rayleigh numbers a qualitative solution is obtained and at large Rayleigh numbers the second-order boundary-layer solution is found that takes into account the first-order plume solution. In order to find the solution at finite Rayleigh numbers the two governing coupled, nonlinear, elliptic partial differential equations are expressed in finite-difference form using a specialized technique which is second-order accurate everywhere. Further, methods are devised which deal with the plume and infinity boundary conditions. Although numerical results are presented for Rayleigh numbers up to 400 solutions of the finite-difference equations can be obtained for higher values of the Rayleigh numbers but in these cases the mesh size used is too large to adequately deal with the developing boundary-layer on the cylinder and the plume.The numerical results show how the theories at both low and high Rayleigh numbers are approached. The plume solution which develops with increasing Rayleigh number agrees with that predicted by the theory presented using the boundary-layer approximation. No separation of the flow at the top of the cylinder is found and there are no indications that it will appear at higher values of the Rayleigh number. The results presented here give reasonable agreement with the existing experimental results for Rayleigh numbers of order unity. However as the Rayleigh number increases to order 102 there is a large discrepancy between the theoretical and experimental results and this is because at these higher values of the Rayleigh number the Darcy approximation has been violated in the experimental results. This indicates the severe limitations of some of the existing theories which use boundary-layer analyses and the Darcy approximation for flows in a porous medium. The application of Darcy's law requires that the size of the pores be much smaller than the scale of the bulk flow and inertial and thermal lengthscales.

Unsteady nearshore natural convection induced by constant isothermal surface heating

2012 ◽  
Vol 707 ◽  
pp. 342-368 ◽  
Author(s):  
Yadan Mao ◽  
Chengwang Lei ◽  
John C. Patterson
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Flow Velocity ◽  
Thermal Boundary Layer ◽  
Scaling Analysis ◽  
Local Flow ◽  
Entire Flow ◽  
Flow Domain

AbstractThe present investigation is concerned with natural convection in a wedge-shaped domain induced by constant isothermal heating at the water surface. Complementary to the study of daytime heating by solar radiation relevant to nearshore regions of lakes and reservoirs previously reported by the same authors, this study focuses on sensible heating imposed by the atmosphere when it is warmer than the water body. A semi-analytical approach coupled with scaling analysis and numerical simulation is adopted to resolve the problem. Two flow regimes are identified depending on the comparison between the Rayleigh number and the inverse of the square of the bottom slope. For the lower Rayleigh number regime, the entire flow domain eventually becomes isothermal and stationary. For the higher Rayleigh number regime, the flow domain is composed of two distinct subregions, a conductive subregion near the shore and a convective subregion offshore. Within the conductive subregion, the maximum local flow velocity occurs when the thermal boundary layer reaches the local bottom, and the subregion eventually becomes isothermal and stationary. In the offshore convective subregion, a steady state is reached with a distinct thermal boundary layer below the surface and a steady flow velocity. The dividing position between the two subregions and the major time and velocity scales governing the flow development in both subregions are proposed by the scaling analysis and validated by corresponding numerical simulation.

Three-dimensional natural convection in a confined porous medium heated from below

1979 ◽  
Vol 92 (4) ◽  
pp. 751-766 ◽  
Author(s):  
Roland N. Horne
Keyword(s):  
Porous Medium ◽  
Energy Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Governing Equations ◽  
Flow Situation ◽  
Definition Of ◽  
The Relationship

Previous analyses of natural convection in a porous medium have drawn seemingly contradictory conclusions as to whether the motion is two- or three-dimensional. This investigation uses numerical results to show the relationship between previous contending observations, and demonstrates that there exists more than one mode of convection for any particular physical configuration and Rayleigh number. In some cases, a particular flow situation may be stable even though it does not maximize the energy transfer across the system.The methods used are based on the efficient numerical solution of the governing equations, formulated with the definition of a vector potential. This approach is shown to be superior to formulating the equations in terms of pressure.For a cubic region the flow pattern at a particular value of the Rayleigh number is not unique and is determined by the initial conditions. In some cases there exist four alternatives, two- and three-dimensional, steady and unsteady.

scholarly journals Natural convection in a porous trapezoidal enclosure with magneto-hydrodynamic effect

2010 ◽  
Vol 15 (2) ◽  
pp. 159-184 ◽  
Author(s):  
M. A. H. Mamun ◽  
Md. T. Islam ◽  
Md. M. Rahman
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Magnetic Force ◽  
Hydrodynamic Effect ◽  
Element Formulation ◽  
Governing Equations ◽  
Weighted Residual Method ◽  
Rotational Angle ◽  
Trapezoidal Enclosure

The effects of magnetic force, acting vertically downward on natural convection within a porous trapezoidal enclosure saturated with an electrically conducting fluid have been investigated numerically. The bottom wall of the enclosure is subjected to a constant hot temperature and the top wall experiences a constant cold temperature whereas the remaining sidewalls are kept adiabatic. The physical problems are represented mathematically by different sets of governing equations along with the corresponding boundary conditions. By using Galerkin weighted residual method of finite element formulation, the non-dimensional governing equations are discritized. For natural convection in a porous medium the influential parameters are the modified Rayleigh number Ram, the fluid Rayleigh number Raf , the inclination angle of the sidewalls of the cavity γ, the rotational angle of the enclosure Φ and the Hartmann number Ha, through which different thermo-fluid characteristics inside the enclosure are obtained. In the present study, the obtained results are presented in terms of streamlines, isotherms and average Nusselt number along the hot wall. The result shows that with increasing Ha, the diffusive heat transfer become prominent even though the modified Rayleigh number increases. Optimum heat transfer rate is obtained at higher values of Ram in the absence of magnetic force.

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