Numerical study on natural convection in a square enclosure containing a rectangular heated cylinder

In this paper, the natural convection in a square enclosure with a rectangular heated cylinder is investigated via the lattice Boltzmann method. A detailed study is conducted on the effect of the cylinder width and the Rayleigh number on the fluid flow and heat transfer. The flow structures and heat transfer patterns are classified into eight buoyant regimes, i.e., four steady regimes, two periodic regimes, one multiple periodic regime, and one chaos regime, two of which are reported for the first time.     

Numerical study on natural convection in a square enclosure containing a rectangular heated cylinder

In this paper, the natural convection in a square enclosure with a rectangular heated cylinder is investigated via the lattice Boltzmann method. A detailed study is conducted on the effect of the cylinder width and the Rayleigh number on the fluid flow and heat transfer. The flow structures and heat transfer patterns are classified into eight buoyant regimes, i.e., four steady regimes, two periodic regimes, one multiple periodic regime, and one chaos regime, two of which are reported for the first time.     

Numerical simulation of turbulent natural convection in a rectangular enclosure having finite thickness walls

Turbulent natural convection in a rectangular enclosure having finite thickness heat-conducting walls at local heating at the bottom of the cavity provided that convective-radiative heat exchange with an environment on one of the external borders has been numerically studied. Mathematical simulation has been carried out in terms of the dimensionless Reynolds averaged Navier–Stokes (RANS) equations in stream function–vorticity formulations. The formulation comprises the standard two equation k–ε turbulence model with wall functions, along with the Boussinesq approximation, for the flow and heat transfer. The special attention was paid to the effects of the Grashof number 10⁸ ? Gr < 10¹⁰, the transient factor 0 < τ < 1000 and the thermal conductivity ratio k_2,1 = 5.7 × 10^?4, 6.8 × 10^?5 both on local and on integral problem parameters. Detailed results including stream lines, temperature profiles and correlation for the average Nusselt number in terms of Grashof number have been obtained.     

Numerical study of natural convection in a tilted rectangular porous material

Two-dimensional natural convective flow in a tilted rectangular porous material saturated with fluid is analyzed by solving numerically the mass, momentum and energy balance equations, using Darcy's law and the Boussinesq approximation. Isothermal boundary conditions are considered, where two opposite walls are kept at constant but different temperatures and the other two are thermally insulated. The external parameters considered are the tilt angle, the aspect ratio and the Darcy-Rayleigh number. Three main convective modes are found: conduction, single and multiple cell convection and their features described in detail. Local and global Nusselt numbers are presented as functions of the external parameters. Multiplicity of solutions is explored for aspect ratio unity. The existence of more than one solution is found when the bottom wall is at a higher temperature and in a horizontal or close to horizontal position.     

Numerical analysis of natural convection in a rectangular enclosure horizontally divided into fluid and porous regions

This paper describes an analytical study of laminar natural convection heat transfer in a rectangular enclosure horizontally divided into fluid and porous regions. The Navier-Stokes equation governs the fluid motion in the fluid region, while Brinkman's extension of Darcy's law is assumed to hold within the porous region. These equations are solved using a finite-element method in the range 10³ ⩽ Ra_f ⩽ 10⁵ and 10⁻³ ⩽ Da ⩽ 10⁵. The experiment is also performed using a rectangular enclosure filled with silicone oil and glass beads. It is shown that the flow pattern, temperature distribution and Nusselt number obtained from the numerical calculation satisfactorily predict the experimental data.     

Numerical analysis of natural convection in an inclined trapezoidal enclosure filled with a porous medium

A theoretical study of buoyancy-driven flow and heat transfer in an inclined trapezoidal enclosure filled with a fluid-saturated porous medium heated and cooled from inclined walls has been performed in this paper. The governing non-dimensional equations were solved numerically using a finite-difference method. The effective governing parameters are: the orientation or inclination angle of the trapezoidal enclosure , which varies between 0° and 180°, the Rayleigh number Ra, which varies between 100 and 1000, the side wall inclination angle θ_s and the aspect ratio A. The side wall inclination parameter θ_s is chosen as 67°, 72° and 81° and the calculations are tested for two different values of A=0.5 and 1.0. Streamlines, isotherms, Nusselt number and flow strength are presented for these values of the governing parameters. The obtained results show that inclination angle is more influential on heat transfer and flow strength than that of the side wall inclination angle θ_s. It is also found that a Bénard regime occurs around =90°, which depends on the inclination of the side wall, Rayleigh number and aspect ratio.     

Conjugate natural convection with radiation in an enclosure

Convective-radiative heat transfer in an enclosure having finite thickness heat-conducting walls at local heating at the bottom of the cavity has been numerically studied. Heat exchange with an environment due to convection and radiation has been considered on one of external sides of the decision region. The effect of parameters such as the Grashof number, the transient factor, the optical thickness and the solid wall thermal conductivity both on the local thermo-hydrodynamic characteristics such as streamlines and temperature fields and on the integral parameter like the average Nusselt number on the heat source surface has been analysed.     

Numerical study on effect of vent locations on natural convection in an enclosure with an internal heat source

Natural convection is a widely studied phenomenon because of the extensive applications in cooling of large scale electrical and electronic equipments. The current study involves study of effect of vent locations on natural convection in enclosures with partial openings having an internal heat source. It involves the numerical simulation of 2D steady state natural convection in enclosure of different aspect ratios (H/W = 1, 2 and 3) for lower Rayleigh numbers (Ra_h = 10³, 10⁴ and 10⁵). Four different configurations have been considered based on the number and position of vents — same side (SS), diagonal side (DS), one inlet two outlets (1I2O) and two inlets one inlet (2I1O). The mass flow rate driven through the enclosure and the average Nusselt number over the heater surface for all the four configurations have been compared. It is found that the 2I1O configuration yielded better heat transfer rates of the four considered. It was found that the mass flow rates and Nu increased with increase in Ra_h and decrease in the aspect ratio.     

MHD natural convection in an enclosure from two semi-circular heaters on the bottom wall

A computational study of the thermal and dynamical behavior of fluid in an enclosure with two isothermal semi-circular heaters is presented. The top wall and the flat surfaces on bottom wall are adiabatic while the vertical walls are kept at lower temperature than the semi-circular heaters. The radius of curvature of the semi-circular surfaces is chosen as one tenth of the cavity wall length. The governing equations are solved by the Galerkin weighted residual finite element method. The effect of magnetic field on the flow is another important parameter in this study. Numerical simulations were performed for several values of Rayleigh number (10³ ? Ra ? 10⁶), Hartmann number (0 ? Ha ? 50) and the distance between two semi-circular heaters (0.2 ? D ? 0.8). In all cases the Prandtl number is taken as 7. It is found that the distance between the semi-circular heaters is the most important parameter affecting the heat and fluid flow fields. In addition, Hartmann number was found to have an adverse affect on heat transfer.     

Numerical simulation of double-diffusive mixed convective flow in rectangular enclosure with insulated moving lid

The present study is concerned with the mixed convection in a rectangular lid-driven cavity under the combined buoyancy effects of thermal and mass diffusion. Double-diffusive convective flow in a rectangular enclosure with moving upper surface is studied numerically. Both upper and lower surfaces are being insulated and impermeable. Constant different temperatures and concentration are imposed along the vertical walls of the enclosure, steady state laminar regime is considered. The transport equations for continuity, momentum, energy and spices transfer are solved. The numerical results are reported for the effect of Richardson number, Lewis number, and buoyancy ratio on the iso-contours of stream line, temperature, and concentration. In addition, the predicted results for both local and average Nusselt and Sherwood numbers are presented and discussed for various parametric conditions. This study was done for 0.1 ≤ Le ≤ 50 and Prandtl number Pr = 0.7. Through out the study the Grashof number and aspect ratio are kept constant at 10⁴ and 2 respectively and ?10 ≤ N ≤ 10, while Richardson number has been varied from 0.01 to 10 to simulate forced convection dominated flow, mixed convection and natural convection dominated flow.     

Effect of aspect ratio on natural convection in an inclined rectangular enclosure with sinusoidal boundary condition

The aim of the present numerical study is to understand the natural convection flow and heat transfer in an inclined rectangular enclosure with sinusoidal temperature profile on the left wall. The top and bottom walls of the enclosure are kept to be adiabatic. The finite difference method is used to solve the governing equations with a range of inclination angles, aspect ratios and Rayleigh numbers. The results are presented in the form of streamlines, isotherms and Nusselt numbers. The heat transfer increases first then decreases with increasing the inclination of the enclosure for all aspect ratio and Rayleigh number. Increasing the aspect ratio shows a decreasing trend of the heat transfer for all Rayleigh numbers considered. A correlation equation is also introduced for the heat transfer analysis in this study.     

An analytical and numerical study of coupled transient natural convection and solidification in a rectangular enclosure

The transient process of the solidification of a pure liquid phase-change material in the presence of natural convection in a rectangular enclosure is considered both analytically and numerically. One vertical boundary is held at a temperature below the melting-point of the material, the other above; the horizontal boundaries are both assumed adiabatic. A nondimensional analysis of the problem, principally in terms of the Rayleigh (Ra) and Stefan (St) numbers, indicates that some asymptotic simplification is possible for materials often considered in the literature (water, gallium, lauric acid). This observation suggests a way to simplify the full problem when Ra  1 and St  1, giving a conventional boundary value problem for the liquid phase and pointwise-in-space first-order ODEs for the evolution in time of the solidification front. The method is tested against full 2D finite-element-based transient numerical simulations of solidification. In addition, simpler approaches for determining the average thickness of the solid layer, based on boundary-layer and enclosure flow correlations, are also investigated.     

Numerical analysis of natural convection for a porous rectangular enclosure with sinusoidally varying temperature profile on the bottom wall

Numerical investigations of steady natural convection flow through a fluid-saturated porous medium in a rectangular enclosure with a sinusoidal varying temperature profile on the bottom wall were conducted. All the walls of the enclosure are insulated except the bottom wall which is partially heated and cooled. The governing equations were written under the assumption of Darcy-law and then solved numerically using finite difference method. The problem is analyzed for different values of the Rayleigh number Ra in the range 10 ≤ Ra ≤ 1000, aspect ratio parameter AR in the range 0.25 ≤ AR ≤1.0 and amplitude λ of the sinusoidal temperature function in the range 0.25 ≤ λ ≤ 1.0. It was found that heat transfer increases with increasing of amplitude λ and decreases with increasing aspect ratio AR. Multiple cells were observed in the cavity for all values of the parameters considered.     

Numerical predictions of natural convection with liquid fluids contained in an inclined arc-shaped enclosure

In the present paper a numerical study has been performed of the flow behavior and natural convection heat transfer characteristics of liquid fluids contained in an inclined arc-shaped enclosure. The governing equations are discretized using the finite-volume method and curvilinear coordinates. The Prandtl number (Pr) of the liquid fluids is assigned to be 4.0 and the Grashof number (Gr) is ranged within the regime 1 × 10⁵ ≦ ≦ 4 × 10⁶. On the other hand, the inclination angle (θ) of the enclosure is varied within 0° ≦ θ ≦ 360°. Of major concern are the effects of the inclination and the buoyancy force on the flow and the thermal fields, and based on the numerical data of the thermal field the local and overall Nusselt numbers are calculated. Results show that the arc-shaped enclosure for Pr = 4.0 at Gr = 4 × 10⁶ and θ = 90° exhibits the best heat transfer performance. The poor heat transfer performance for Pr = 4.0 fixed at Gr = 1 × 10⁵ and θ = 180° exhibits the arc-shaped enclosure, respectively. As the value of Grashof number is elevated from 10⁵ to 4 × 10⁶, at θ = 90°, the magnitude of Nu is elevated from 13.946 to 25.3 (81.4% increase); however, at θ = 180°, the magnitude is elevated from 11.655 to 13.475 (15.6% increase) only.     

Numerical calculation of turbulent natural convection in a cylindrical transformer enclosure

Numerical calculations of turbulent natural convection in the enclosure of the 20 kVA oil-immersed transformer model are presented. The transformer is modeled as two concentric cylinders with different heights and diameters. The correlating equation between the mean Nusselt number and the Rayleigh number can be obtained for Ra = 10⁸ to 10⁹. The thermal boundary layers are well represented in the temperature distributions along the wall of the transformer model. The flow stratification between the hot and cold walls cannot be seen in the transformer model. The turbulence eddy viscosity has its maximum at the center of the core and its maximum values at the top of the core are slightly larger than those at the bottom of the core. © 1999 Scripta Technica, Heat Transfer Asian Res, 28(6): 429–441, 1999     

Numerical simulation of natural convection in a horizontal enclosure with a heat-generating conducting body

The physical model considered here is a horizontal layer of fluid heated below and cold above with heat-generating conducting body placed at the center of the layer. The dimensionless thermal conductivities of body considered in the present study are 0.1, 1 and 50. The dimensionless temperature difference ratios considered are 0.0, 0.25, 2.5 and 25. Two-dimensional solution for unsteady natural convection is obtained using an accurate and efficient Chebyshev spectral methodology for variety of Rayleigh number from 10³ to 10⁶. Multi-domain technique is used to handle square-shaped heat-generating conducting body. The fluid flow, heat transfer and time- and surface-averaged Nusselt number are investigated for various ranges of Rayleigh number, thermal conductivity ratio and dimensionless temperature difference ratio. The results for the case of conducting body with heat generation are also compared to those without heat generation to see the effects of heat generation from the conducting body on the fluid flow and heat transfer in the enclosure.     

Numerical simulation of developing natural convection in an enclosure due to rapid heating

Effects of thermoacoustic wave motion on the developing natural convection process in a compressible gas-filled square enclosure were investigated numerically. In the cases considered, the left wall temperature is raised rapidly (impulsively or gradually) while the right wall is held at a specified temperature. The top and the bottom walls of the enclosure considered are thermally insulated. The numerical solutions of the full Navier-Stokes equations were obtained by employing a highly accurate flux-corrected transport algorithm for the convection terms and by a central differencing scheme for the viscous and diffusive terms. The strength of the pressure waves associated with the thermoacoustic effect and resulting flow patterns are found to be strongly correlated to the rapidity of the wall heating process. Fluid thermal diffusivity was found to affect the strength of the thermoacoustic waves and the resulting interaction with the buoyancy-induced flow.     

Transient natural convection in an enclosure with vertical solutal gradients

Transient natural convection in an enclosure with vertical solutal gradients has been studied in this paper. Transfers in a rectangular cavity configuration translating hydrodynamic and thermal phenomena are numerically predicted by means of computational fluid dynamics (CFD) in transient regime.The objective of this numerical study is to give a fine knowledge of the hydrodynamic and thermal characteristics during energy storage in an enclosure filled with water stratified by downward salinity gradient. The enclosure is divided into three zones with different salinity level such as salt gradient pond (SGP). Water is heated by a heating device at the bottom of the cavity.The Navier–Stokes, energy and mass equations are discretized using finite-volume method, and a two-dimensional analysis of the hydrodynamic and thermal behaviors generated in transient regime in the cavity are performed. The mathematical modelling has allowed the prediction of the storage performances by developing parametrical study in view to search the convective heat transfer coefficient at the bottom of the enclosure. Velocity vector fields show the presence of recirculation zones caused only in the lower region and permit to explain the increase of the temperature in the lower convective zone (LCZ).This study shows also the importance of the salinity in the preservation of the high temperature in the bottom of the cavity, and the important reduction of the phenomenon of thermal transfer across the non-convective zone (NCZ).