Natural Convection in Porous Media Induced by the Centrifugal Body Force: The Solution for Small Aspect Ratio

1992 ◽  
Vol 114 (3) ◽  
pp. 250-254 ◽  
Author(s):  
P. Vadasz
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Body Force ◽  
Small Aspect Ratio ◽  
Dependent Variables ◽  
Porous Domain ◽  
Convection Problem ◽  
The Mean ◽  
Natural Convection Problem ◽  
Convection In Porous Media

The analytical solution to the natural convection problem in a rotating rectangular porous domain is presented for a small aspect ratio of the domain. The convection results from differential heating of the horizontal walls leading to temperature gradients orthogonal to the centrifugal body force. The solution to the nonlinear set of partial differential equations was obtained through an asymptotic expansion of the dependent variables in terms of a small parameter representing the aspect ratio of the domain. The convection regime is apparent in the results, although it has a weak effect on the mean heat flux.

Reduced Basis Methods and a Posteriori Error Estimators for Heat Transfer Problems

2009 ◽  
Author(s):  
G. Rozza ◽  
C. N. Nguyen ◽  
A. T. Patera ◽  
S. Deparis
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Reduced Basis Method ◽  
Reduced Basis ◽  
Element Discretization ◽  
Convection Problem ◽  
Prandtl Numbers ◽  
Basis Method ◽  
Two Parameters ◽  
Natural Convection Problem

This paper focuses on the parametric study of steady and unsteady forced and natural convection problems by the certified reduced basis method. These problems are characterized by an input-output relationship in which given an input parameter vector — material properties, boundary conditions and sources, and geometry — we would like to compute certain outputs of engineering interest — heat fluxes and average temperatures. The certified reduced basis method provides both (i) a very inexpensive yet accurate output prediction, and (ii) a rigorous bound for the error in the reduced basis prediction relative to an underlying expensive high-fidelity finite element discretization. The feasibility and efficiency of the method is demonstrated for three natural convection model problems: a scalar steady forced convection problem in a rectangular channel is characterized by two parameters — Pe´clet number and the aspect ratio of the channel — and an output — the average temperature over the domain; a steady natural convection problem in a laterally heated cavity is characterized by three parameters — Grashof and Prandtl numbers, and the aspect ratio of the cavity — and an output — the inverse of the Nusselt number; and an unsteady natural convection problem in a laterally heated cavity is characterized by two parameters — Grashof and Prandtl numbers — and a time-dependent output — the average of the horizontal velocity over a specified area of the cavity.

Study of Steady Natural Convection With Laminar Flow in the Enclosures of Different Shapes

2016 ◽  
Author(s):  
Anuj Gupta ◽  
H. C. Thakur ◽  
Bhavyanidhi Vats
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Laminar Flow ◽  
Aspect Ratio ◽  
Maximum Heat ◽  
Grashof Number ◽  
Maximum Heat Transfer ◽  
Convection Problem ◽  
Different Shapes ◽  
Natural Convection Problem

This paper deals with the results of a simulative study of free convective heat transfer in the enclosure having different shapes. Problem has been characterized with the constant temperature on lower and upper walls while side walls have been considered as adiabatic walls. This study has been conducted for finding the shape of enclosure having maximum heat transfer rate considering different values for the aspect ratio and the Grashof number. Steady state natural convection problem has been formulated for all enclosures having laminar flow of air (at Pr = 0.7). Values for the aspect ratio vary from 0.2 to 0.5 while for the Grashof number from 10e4 to 10e8. ANSYS 14.0 has been used for modelling and simulation and for concluding study in the terms of Nusselt Number.

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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