Melting of a pure metal from an isothermal vertical wall in the presence of turbulent natural convection

2002 ◽  
Author(s):  
Luiz Joaquim Cardoso Rocha ◽  
Angela O. Nieckele
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Pure Metal ◽  
Turbulent Natural Convection

Numerical Calculation of Three-Dimensional Turbulent Natural Convection in a Cubical Enclosure Using a Two-Equation Model for Turbulence

1986 ◽  
Vol 108 (4) ◽  
pp. 806-813 ◽  
Author(s):  
H. Ozoe ◽  
A. Mouri ◽  
M. Hiramitsu ◽  
S. W. Churchill ◽  
N. Lior
Keyword(s):  
Natural Convection ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Spiral Flow ◽  
Vertical Side ◽  
Turbulent Natural Convection ◽  
Cubical Enclosure ◽  
Side Walls

This paper presents a model and numerical results for turbulent natural convection in a cubical enclosure heated from below, cooled on a portion of one vertical side wall and insulated on all other surfaces. Three-dimensional balances were derived for material, energy, and the three components of momentum, as well as for the turbulent kinetic energy k and the rate of dissipation of turbulent kinetic energy ε. The constants used in the model were the same as those used by Fraikin et al. for two-dimensional convection in a channel. Illustrative transient calculations were carried out for Ra = 106 and 107 and Pr = 0.7. Both the dominant component of the vector potential and the Nusselt number were found to converge to a steady state. Isothermal lines and velocity vectors for vertical cross sections normal to the cooled wall indicated three-dimensional effects near the side walls. A top view of the velocity vectors revealed a downward spiral flow near the side walls along the cooled vertical wall. A weak spiral flow was also found along the side walls near the wall opposing the partially cooled one. The highest values of the eddy diffusivity were 2.6 and 5.8 times the molecular kinematic viscosity for Ra = 106 and 107, respectively. A coaxial double spiral movement, similar to that previously reported for laminar natural convection, was found for the time-averaged flow field. This computing scheme is expected to be applicable to other thermal boundary conditions.

Turbulent Natural Convection Flow on a Heated Vertical Wall Immersed in a Stratified Atmosphere

1989 ◽  
Vol 111 (2) ◽  
pp. 378-384 ◽  
Author(s):  
A. K. Kulkarni ◽  
S. L. Chou
Keyword(s):  
Natural Convection ◽  
Numerical Solutions ◽  
Vertical Wall ◽  
Leading Edge ◽  
Transitional Flow ◽  
Convection Flow ◽  
Ambient Atmosphere ◽  
Ambient Conditions ◽  
Natural Convection Flow ◽  
Turbulent Natural Convection

This paper presents a comprehensive mathematical model and numerical solutions for a natural convection flow over an isothermal, heated, vertical wall immersed in an ambient atmosphere that is thermally stratified. The model assumes a laminar flow near the leading edge, which then becomes a transitional flow, and finally becomes fully turbulent away from the leading edge. Effects of several typical cases of ambient stratification on heat transfer to the wall, peak velocity, and temperature are examined. It is found that the velocity field is affected more significantly by the “memory” of upstream ambient conditions than the temperature field.

Lattice Boltzmann Modeling of Natural Convection in a Large-Scale Cavity Heated From Below by a Centered Source

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Noureddine Abouricha ◽  
Mustapha El Alami ◽  
Ayoub Gounni
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Heat Source ◽  
Flow Structure ◽  
Lattice Boltzmann ◽  
Large Scale ◽  
Vertical Wall ◽  
Convection Heat Transfer ◽  
Turbulent Natural Convection

Turbulent natural convection in a large-scale cavity has taken a great attention thanks to its importance in many engineering applications such as building. In this work, the lattice Boltzmann method (LBM) is used to simulate turbulent natural convection heat transfer in a small room of housing heated from below by means of a heated floor. The ceiling and the four vertical walls of the room are adiabatic except for a portion of one vertical wall. This portion simulates a glass door with a cold temperature θc = 0. The cavity is filled by air (Pr = 0.71) and heated from below with uniformly imposed temperature θh = 1. The effects of the heat source length (Lr) and Rayleigh number (Ra) on the flow structure and heat transfer are studied for ranges of 0.2 ≤ Lr ≤ 0.8 and 5 × 106 ≤Ra ≤ 108. The heat transfer is examined in terms of local and mean Nusselt numbers. The results show that an increase in Rayleigh number or in heat source length increases the temperature in the core of the cavity. The flow structure shows that turbulent natural convection regime is fully developed for Ra = 108. Correlations for mean Nusselt number as a function with Ra for different values of Lr are expressly derived.

Melting and Solidification of a Pure Metal on a Vertical Wall

1986 ◽  
Vol 108 (1) ◽  
pp. 174-181 ◽  
Author(s):  
C. Gau ◽  
R. Viskanta
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Vertical Wall ◽  
Pure Metal ◽  
Convection Flow ◽  
Transfer Coefficients ◽  
Interface Motion ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Melting And Solidification

This paper reports on the role of natural convection on solid–liquid interface motion and heat transfer during melting and solidification of a pure metal (gallium) on a vertical wall. The measurements of the position of the phase-change boundary as well as of temperature distributions and temperature fluctuations were used as a qualitative indication of the natural convection flow regimes and structure in the melt during phase transformation taking place in a rectangular test cell heated or cooled from one of the vertical walls. For melting, the measured melt volume and heat transfer coefficients are correlated in terms of relevant dimensionless parameters. For solidification, the measured volume of metal solidified on the wall is compared with predictions based on a one-dimensional model.

High Grashof number turbulent natural convection on an infinite vertical wall

2021 ◽  
Vol 929 ◽  
Author(s):  
Junhao Ke ◽  
N. Williamson ◽  
S.W. Armfield ◽  
A. Komiya ◽  
S.E. Norris
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Natural Convection ◽  
Vertical Wall ◽  
Integral Model ◽  
Turbulent Regime ◽  
Grashof Number ◽  
Turbulent Natural Convection ◽  
Self Similar ◽  
Near Wall

The present study concerns a temporally evolving turbulent natural convection boundary layer (NCBL) adjacent to an isothermally heated vertical wall, with Prandtl number 0.71. Three-dimensional direct numerical simulations (DNS) are carried out to investigate the turbulent flow up to $\textit {Gr}_\delta =1.21\times 10^8$ , where $\textit {Gr}_\delta$ is the Grashof number based on the boundary layer thickness $\delta$ . In the near-wall region, there exists a constant heat flux layer, similar to previous studies for the spatially developing flows (e.g. George & Capp, Intl J. Heat Mass Transfer, vol. 22, 1979, pp. 813–826). Beyond a wall-normal distance $\delta _i$ , the NCBL can be characterised as a plume-like region. We find that this region is well described by a self-similar integral model with profile coefficients (cf. van Reeuwijk & Craske, J. Fluid Mech., vol. 782, 2015, pp. 333–355) which are $\textit {Gr}_\delta$ -independent after $\textit {Gr}_\delta =10^7$ . In this Grashof number range both the outer plume-like region and the near-wall boundary layer are turbulent, indicating the beginning of the so-called ultimate turbulent regime (Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56; Grossmann & Lohse, Phys. Fluids, vol. 23, 2011, 045108). Solutions to the self-similar integral model are analytically obtained by solving ordinary differential equations with profile coefficients empirically obtained from the DNS results. In the present study, we have found the wall heat transfer of the NCBL is directly related to the top-hat scales which characterise the plume-like region. The Nusselt number is found to follow $\textit {Nu}_\delta \propto \textit {Gr}_\delta ^{0.381}$ , slightly higher than the empirical $1/3$ -power-law correlation reported for spatially developing NCBLs at lower $\textit {Gr}_\delta$ , but is shown to be consistent with the ultimate heat transfer regime with a logarithmic correction suggested by Grossmann & Lohse (Phys. Fluids, vol. 23, 2011, 045108). By modelling the near-wall buoyancy force, we show that the wall shear stress would scale with the bulk velocity only at asymptotically large Grashof numbers.

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