Natural Convection Of Cold Water Research Articles

Numerical simulation of thermomagnetic convection of cold water near its density maximum in a square enclosure under a magnetic quadrupole field

Natural convection of cold water near its density maximum in a square enclosure is studied numerically under the influence of a magnetic quadrupole field without gravity. A generalized model which includes a non-Boussinesq parabolic density–temperature relationship is established. The governing equations in primitive variables are discretized using the finite-volume method and solved using the SIMPLE algorithm. The effects of magnetic force number, Rayleigh number and density inversion parameter on flow and heat transfer characteristics are analyzed. The results show that the primary flow pattern depends mainly on the density inversion parameter. Multi-cellular flow structures are observed for certain ranges of density inversion parameter independent of the value of Rayleigh number and magnetic force number. The heat transfer changes non-monotonically under combined actions of the quadrupole magnetic field and density inversion.

Transient natural convection of cold water in a vertical channel

The two-dimensional differential transform method (DTM) is applied to analyse the transient natural convection of cold water in a vertical channel. The cold water gives rise to a density variation with temperature that may not be linearized. The vertical channel is composed of doubly infinite parallel plates, one of which has a constant prescribed temperature and the other of which is insulated. Considering the temperature-dependent viscosity and thermal conductivity of the water, approximate analytical (series) solutions for the temperature and flow velocity are derived. The transformed functions included in the solutions are obtained through a simple recursive procedure. Numerical computation is performed for the entire range of water temperature conditions around the temperature at the density extremum point, i.e.\( 4 {}^{\circ} C\) . Numerical results illustrate the effects of the temperature-dependent properties on the transient temperature and flow velocity profiles, volumetric flow rate, and skin friction. The DTM is a powerful tool for solving nonlinear transient problems as well as steady problems.

Comparison investigation on natural convection of cold water near its density maximum in annular enclosures with complex configurations

In order to compare the characteristics of natural convection of cold water near its density maximum in annular enclosures with various complex configurations, a series of numerical simulations were carried out using the finite volume method. The effects of the Rayleigh number, the density inversion parameter and the aspect ratio on natural convective flow and heat transfer were analyzed, and the variations of local and average Nusselt numbers were discussed in these enclosures. The results show that the flow pattern depends mainly on geometrical configurations of the enclosures, the Rayleigh number and the density inversion parameter. The Rayleigh–Bénard convection cells appear in the top or bottom region for the R-C, T-C, E-S and E-T configurations at a large Rayleigh number. With the increase of the aspect ratio, the number of the vortex in the flow cell increases and the cell splitting phenomenon happens at a large aspect ratio in the R-C, D-C, T-C, E-S and E-T configurations. The heat transfer correlations for various configurations have been proposed, and the enclosure with the best heat transfer performance among various configurations is assured based on the simulation results.

Natural convection of cold water near its density maximum in an elliptical enclosure containing a coaxial cylinder

A numerical study of natural convection heat transfer of cold water near its density maximum from a heated cylinder to its cooled coaxial elliptical enclosure is performed using finite volume method. The analysis is done for different Rayleigh number ranged from 103 to 106, density inversion parameter from 0 to 1, aspect ratio from 0.1 to 0.7, and elliptical ratio from 0 to 0.9 to investigate the effects of these parameters on flow and heat transfer characteristics. In addition, the effect of inclination angle is examined as well by turning the enclosure in the clockwise direction. When the stable flow transits to the unstable flow, the mechanism of oscillations is also discussed. Detailed analysis results for the distribution of streamlines, isotherms and Nusselt number are presented and an empirical heat transfer correlation was deduced within an acceptable uncertainty in this paper.

Natural convection of water near its density maximum between horizontal cylinders

In order to understand the characteristics of natural convection of cold water near its density maximum between horizontal cylinders, a series of unsteady two-dimensional numerical simulations were conducted by using finite volume method. The radius ratio of horizontal cylinders ranged from 1.2 to 2.0, density inversion parameter from 0 to 1, and the vertical eccentricity from 0 to 1.0 for eccentric annulus. The results show that the flow pattern mainly depends on the density inversion parameter and Rayleigh number. The formation of small cell at the top or bottom of annulus corresponds to the Rayleigh–Bénard instability within the converse density gradient layer. The width of annulus has slightly influence on the flow structure. However, the number of Bénard cells decreases with the increase of the radius ratio. For the oscillatory flow at a large Rayleigh number, the vertical converse density gradient in the top of annulus or the horizontal density gradient in the middle of annulus plays an important role for the formation of oscillatory flow when the density inversion parameter is in a small or moderate range. But the vertical density gradient in the bottom of annulus and the horizontal density gradient in the middle of annulus work together for oscillatory flow when the density inversion parameter is high. Average Nusselt number on the inner wall increases with the increase of Rayleigh number and radius ratio. However, there exists the minimum value of average Nusselt number at a moderate density inversion parameter. The flow pattern in eccentric annulus has the characteristics of coupling flows in the narrow-gap at the bottom with in the large-gap at the top of annulus. With the increase of the eccentricity, heat transfer is enhanced and the average Nusselt number increases slightly. Based on the simulation results, the new heat transfer correlation has been proposed according to the multiple linear regression technique.

Buoyancy-driven convection of water near its density maximum with partially active vertical walls

Transient natural convection of cold water around its density maximum in a square cavity is studied numerically. Nine different positions of the active zones are considered. The governing equations are solved using Control volume method with power low scheme. The results obtained for various values of parameters are presented graphically in the form of streamlines and isotherms. It is found that the average Nusselt number behaves non-linearly as a function of Grashof number. The heat transfer rate is decreased in the density maximum regions.

Transition to oscillatory natural convection of cold water in a vertical annulus

In the present study laminar transition to oscillatory convection of cold water in a vertical annulus of aspect ratio 8 and radius ratio 2 is investigated by direct numerical simulations for two values of density inversion parameter, θ m = 0.4 and 0.5. The vertical walls of the annulus are maintained at constant bat different temperatures, while the horizontal walls are assumed adiabatic. Numerical results manifest that the buoyancy-driven flow in the annulus experiences a Hopf bifurcation into a periodic oscillation regime at the critical Rayleigh numbers, which are dependent on the density inversion parameter. The critical Rayleigh number for θ m = 0.4 is found to be more than two times of that corresponding to θ m = 0.5. Nature of the transition has also been identified by examining the contributions made by the flow shear and/or the buoyancy force to the generation of fluctuating kinetic energy for the self-sustained oscillatory convection in the annulus.

Natural Convection of Cold Water in a Vertical Annulus With Constant Heat Flux on the Inner Wall

A numerical solution for steady laminar natural convection of cold water in a vertical annulus with a constant-heat-flux heated inner wall and an isothermally cooled outer wall is examined. Results are generated for flow in annuli with aspect ratio 0.5 ≤ A ≤8, the radius ratio varying between 1.2 and 10, and the density inversion parameter ranging from −2 and 1 for 103 ≤ Ra* ≤ 106. The heat and fluid flow structures of cold water are vividly visualized by means of contour maps of heatlines and streamlines. The results clearly indicate that the mixed boundary conditions considered can have a significant influence on the geometric dependence of heat transfer characteristics and fluid flow structures in comparison with those reported for isothermal boundary conditions. Multicellular flow behavior of cold water can arise in a tall annulus of A = 8.

Laminar natural convection of cold water enclosed in a horizontal annulus with mixed boundary conditions

A computational analysis of steady laminar natural convection of cold water within a horizontal annulus with constant heat flux on the inner wall and a fixed temperature on the outer surface has been undertaken to explore the occurrence of density inversion of water and its effects on the flow and temperature fields. Results are generated for three values of radius ratio over various ranges of the modified Rayleigh number and density inversion parameter. For the flow circumstances considered, the occurrence of density inversion is found to be mainly dependent on the density inversion parameter. With a negative inversion parameter, the increase of either the modified Rayleigh number or the radius ratio results in a more pronounced effect of density inversion on the flow and temperature fields in the annulus.

Natural convection between horizontal concentric cylinders with density inversion of water for low Rayleigh numbers

A study is made of the natural convection of cold water between two horizontal concentric cylinders with constant surface temperatures. The governing equations are solved by the perturbation method and the solutions are expressed as power series of the nonlinear Rayleigh number. The flow patterns and heat transfer rates are presented in terms of the radius ratio R, the nonlinear Rayleigh number Ra, and the inversion parameter γ which essentially determines the size and effects of the additional convection cells that arise from the inversion of density of water at 4°C within the cavity. Good agreement is obtained with the existing numerical and experimental results.