Search results for "Rayleigh number"

Natural convection heat transfer in a partially—or completely—partitioned vertical rectangular enclosure

1991

Abstract The effect of symmetric partitions protruding centrally from the end walls of a rectangular vertical enclosure on heat transfer rates is investigated numerically. The enclosure has opposite isothermal walls at different temperatures. The Rayleigh number is varied from 10 4 to 10 7 and the aspect ratio from 0.5 to 10. The thickness of the partitions is fixed and equal to one tenth of the width of the enclosure. Their non-dimensional length ( L / H ) is varied from 0 (non-partitioned enclosure) to 0.5 (two separate enclosures). The effect of different thermal boundary conditions at the end walls and at the partitions is included in the investigation.

On natural convection in a single and two zone rectangular enclosure

1992

Abstract Convective heat transfer was investigated numerically for rectangular enclosures both undivided and divided in two zones by a vertical partition, and having opposite isothermal walls at different temperatures. The aspect ratio was varied from 0.1 to 16 and the Rayleigh number from 3.5 ∗ 10 3 to ∗ 10 7 (non-partitioned enclosures) and from 1.0 ∗ 10 5 to 1.6 ∗ 10 8 (partitioned enclosures). The thickness and conductivity of the partition were varied. The end wall thermal boundary conditions were adiabatic or LTP (Linear Temperature Profile). The continuity, momentum and energy equations for a 2-D laminar steady flow were solved under the Boussinesq approximation by using a finite-dif…

An experimental investigation on natural convection of air in a vertical channel

1993

Abstract The free convection of air in a vertical channel is studied experimentally in a laboratory model of height H = 2.6 m and rectangular cross-section b × s , with b = 1.2 m and the channel width s variable. One of the channel walls is heated with a uniform heat flux. Tests are made with different values of channel gap and heating power ( s = 7.5, 12.5, 17 cm; q c = 48–317 W m −2 ). On the basis of the results two empirical formulae are found, giving Nu and Re as functions of Ra and the geometrical parameter s/H ; Nu = 0.9282 Ra 0.2035 (s/H) 0.8972 ; Re = 0.5014 Ra 0.3148 (s/H) 0.418 . The mathematical form of these relationships reproduces other previously published formulae, valid fo…

Effects of Rayleigh number length thickness of continent on time of mantle flow reversal

1998

Abstract Numerical experiments are carried out to study the effects of continents on the structure of thermal convection in the mantle. The mantle is modelled by a viscous fluid occupying a horizontally extended rectangular 2-D region of aspect ratio 10:1. Continents are treated as thick rigid heat-conducting plates placed in the mantle, with free-slip and with no-slip conditions. Continents restrict the heat release from the underlying mantle; the mantle material heats up and becomes lighter; as a result, a hot upwelling flow replaces downwelling. We calculate the characteristic time τ of this restructuring for various values of model parameters and obtain analytical approximations for τ a…

Influence of Rayleigh Number and End Wall Boundary Conditions on Free Convection Heat Transfer in a Rectangular Enclosure

2000

Heat and mass transfer phenomena

2002

This section deals with main problems of the heat and mass transfer in magnetic colloids. The analysis is mainly based on the general model given in the Chapter written by R. E. Rosensweig. Hydrodynamic and thermal problems are simplified considering incompressible liquids and neglecting the effects of polarization and electric conductivity as well as ignoring some other secondary effects that usually can be neglected in ferrofluid experiments. Contrarily, the analysis of mass transfer accounts for new sedimentation phenomena and cross effects of interrelated heat and mass transfer. Since the description given by Rosensweig is of general theoretical nature, while the present work mainly foc…

Influence of a Magnetic Field on Liquid Metal Free Convection in an Internally Heated Cubic Enclosure

2002

The buoyancy‐driven magnetohydrodynamic flow in a cubic enclosure was investigated by three‐dimensional numerical simulation. The enclosure was volumetrically heated by a uniform power density and cooled along two opposite vertical walls, all remaining walls being adiabatic. A uniform magnetic field was applied orthogonally to the gravity vector and to the temperature gradient. The Prandtl number was 0.0321 (characteristic of Pb–17Li at 300°C), the Rayleigh number was 104, and the Hartmann number was made to vary between 0 and 2×103. The steady‐state Navier–Stokes equations, in conjunction with a scalar transport equation for the fluid's enthalpy and with the Poisson equation for the electr…

Convective Instability in a Horizontal Porous Channel with Permeable and Conducting Side Boundaries

2013

Published version of an article in the journal: Transport in Porous Media. Also available on Science Direct: http://dx.doi.org/10.1007/s11242-013-0198-y The stability analysis of the motionless state of a horizontal porous channel with rectangular cross-section and saturated by a fluid is developed. The heating from below is modelled by a uniform flux, while the top wall is assumed to be isothermal. The side boundaries are considered as permeable and perfectly conducting. The linear stability of the basic state is studied for the normal mode perturbations. The principle of exchange of stabilities is proved, so that only stationary normalmodes need to be considered in the stability analysis.…

Studies on Instabilities and Patterns in Evaporating Liquids at Reduced Pressure and/or Microwave Irradiation

1990

This paper summarizes our recent experimental and theoretical work on the instabilities in liquids and at interfaces which form during evaporation at reduced pressure and/or microwave irradiation. We have observed a variety of patterns (Benard rolls, Marangoni waves, Hickman interface deformations) which depend on the value of the reduced pressure and the power of the incident beam.

Thermally unstable throughflow of a power–law fluid in a vertical porous cylinder with arbitrary cross–section

2021

Abstract The present paper investigates how the cross–sectional shape of a vertical porous cylinder affects the onset of thermoconvective instability of the Rayleigh–Benard type. The fluid saturating the porous medium is assumed to be a non–Newtonian power–law fluid. A linear stability analysis of the vertical thorughflow is carried out. Three special shapes of the cylinder cross–section are analysed: square, circular and elliptical. The effect of changing the power–law index is investigated. The stability of a steady base state with vertical throughflow is analysed. The resulting stability problem is a differential eigenvalue problem that is solved numerically through the shooting method. …