POD-Galerkin Modeling and Sparse-Grid Collocation for a Natural Convection Problem with Stochastic Boundary Conditions

2014 ◽  
pp. 295-315
Author(s):  
Sebastian Ullmann ◽  
Jens Lang
Keyword(s):  
Natural Convection ◽  
Boundary Conditions ◽  
Sparse Grid ◽  
Convection Problem ◽  
Natural Convection Problem ◽  
Stochastic Boundary

A Natural Convection Problem Arising From the Study of Flame-Bubbles

1989 ◽  
Vol 42 (11S) ◽  
pp. S283-S288
Author(s):  
S. Weeratunga ◽  
J. Buckmaster ◽  
R. E. Johnson
Keyword(s):  
Natural Convection ◽  
Flow Field ◽  
Viscous Fluid ◽  
Boundary Conditions ◽  
Numerical Solutions ◽  
Spherical Surface ◽  
Heat Sources ◽  
Convection Problem ◽  
Natural Convection Problem

We describe numerical solutions of the flow-field generated by heat sources distributed continuously over a spherical surface that is rising at a fixed speed in a viscous fluid. This is a model for small, highly curved flames of the type that can be supported by very lean hydrogen/air mixtures (flame-bubbles). Heat swept into the wake behind the sphere generates finite disturbances at downstream infinity, and the boundary conditions there should be chosen accordingly. We compare results obtained in this way with results generated by imposing uniform conditions (Dirichlet or Neumann) at the downstream boundary.

The Effect of Thermal Wall Properties on Natural Convection in Inclined Rectangular Cells

1982 ◽  
Vol 104 (1) ◽  
pp. 111-117 ◽  
Author(s):  
B. A. Meyer ◽  
J. W. Mitchell ◽  
M. M. El-Wakil
Keyword(s):  
Heat Transfer ◽  
Cell Wall ◽  
Natural Convection ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Conductive Heat ◽  
Numerical Work ◽  
Aspect Ratios ◽  
Convection Problem ◽  
Natural Convection Problem

The effects of cell wall thickness and thermal conductivity on natural convective heat transfer within inclined rectangular cells was studied. The cell walls are thin, and the hot and cold surfaces are isothermal. The two-dimensional natural convection problem was solved using finite difference techniques. The parameters studied were cell aspect ratios (A) of 0.5 and 1, Rayleigh numbers (Ra) up to 105, a Prandtl number (Pr) of 0.72 and a tilt angle (φ) of 60 deg. These parameters are of interest in solar collectors. The numerical results are substantiated by experimental results. It was found that convection coefficients for cells with adiabatic walls are substantially higher than those for cells with conducting walls. Correlations are given for estimating the convective heat transfer across the cell and the conductive heat transfer across the cell wall. These correlations are compared with available experimental and numerical work of other authors.

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