Analytical Study of Natural Convection in a Cavity With Volumetric Heat Generation

Volume 1 ◽  
2004 ◽  
Author(s):  
Mandar V. Joshi ◽  
U. N. Gaitonde ◽  
Sushanta K. Mitra
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Heat Generation ◽  
Central Region ◽  
Analytical Study ◽  
Vertical Direction ◽  
Maximum Temperature ◽  
Small Aspect Ratio ◽  
Governing Equations ◽  
Volumetric Heat Generation

A semi-analytical method for natural convection in a two dimensional rectangular enclosure, with uniform volumetric heat generation, having insulated horizontal boundaries, and isothermal vertical boundaries, has been studied here. In this method, the governing equations for natural convection, have been solved under the assumption that for a cavity with small aspect ratio, the flow in the central region of the cavity is only in the vertical direction. It is found that for the cavities with small aspect ratio, the temperature in central region of the cavity is nearly constant along the horizontal direction. However, there is a uniform temperature gradient in the vertical direction, which can be related to the maximum temperature in conduction. The velocity profiles and temperature profiles obtained in the present work, are compared with the numerical simulations by Fluent and a fair agreement is found between these results.

Analytical Study of Natural Convection in a Cavity With Volumetric Heat Generation

2005 ◽  
Vol 128 (2) ◽  
pp. 176-182 ◽  
Author(s):  
Mandar V. Joshi ◽  
U. N. Gaitonde ◽  
Sushanta K. Mitra
Keyword(s):  
Natural Convection ◽  
Heat Generation ◽  
Analytical Study ◽  
Vertical Component ◽  
Governing Equations ◽  
Biharmonic Equations ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
Volumetric Heat Generation ◽  
Good Agreement

An analytical study has been conducted for natural convection in a cavity of different aspect ratios with uniform volumetric heat generation. Two different boundary conditions are investigated for the cavity, viz., all walls are isothermal; two horizontal walls are adiabatic and two vertical walls are isothermal. A stream function vorticity formulation is used where the variables are expanded in terms of Rayleigh number, defined as Ra=gβh5q‴∕ανk. The governing equations are reduced, to biharmonic equations, and these biharmonic equations are solved using one of the methods, available in the literature. It is observed that the horizontal component of velocity is smaller than the vertical component near the center and the vertical walls of the cavity. The results for velocity profiles are compared with the simulations obtained from Fluent and they are found to be in good agreement.

Correlations for Natural Convection Between Heated Vertical Plates

1991 ◽  
Vol 113 (1) ◽  
pp. 97-107 ◽  
Author(s):  
S. Ramanathan ◽  
R. Kumar
Keyword(s):  
Rayleigh Number ◽  
Aspect Ratio ◽  
Prandtl Number ◽  
Vertical Direction ◽  
Numerical Results ◽  
Maximum Temperature ◽  
Parallel Plates ◽  
Plate Temperature ◽  
Aspect Ratios ◽  
Prandtl Numbers

This paper presents the numerical results of natural convective flows between two vertical, parallel plates within a large enclosure. A parametric study has been conducted for various Prandtl numbers and channel aspect ratios. The results are in good agreement with the reported results in the literature for air for large aspect ratios. However, for small aspect ratios, the present numerical results do not agree with the correlations given in the literature. The discrepancy is due to the fact that the published results were obtained for channels where the diffusion of thermal energy in the vertical direction is negligible. The results obtained in this paper indicate that vertical conduction should be considered for channel aspect ratios less than 10 for Pr = 0.7. Correlations are presented to predict the maximum temperature and the average Nusselt number on the plate as explicit functions of the channel Rayleigh number and the channel aspect ratio for air. The plate temperature is a weak function of Prandtl number for Prandtl numbers greater than 0.7, if the channel Rayleigh number is chosen as the correlating parameter. For Prandtl numbers less than 0.1, the plate temperature is a function of the channel Rayleigh number and the Prandtl number. A correlation for maximum temperature on the plate is presented to include the Prandtl number effect for large aspect ratio channels.

Natural Convection in a Cylindrical Porous Enclosure With Internal Heat Generation

1989 ◽  
Vol 111 (4) ◽  
pp. 916-925 ◽  
Author(s):  
V. Prasad ◽  
A. Chui
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Numerical Study ◽  
Vertical Wall ◽  
Internal Heat ◽  
Heat Removal ◽  
Maximum Temperature ◽  
Wall Boundary Conditions

A numerical study is performed on natural convection inside a cylindrical enclosure filled with a volumetrically heated, saturated porous medium for the case when the vertical wall is isothermal and the horizontal walls are either adiabatic or isothermally cooled. When the horizontal walls are insulated, the flow in the cavity is unicellular and the temperature field in upper layers is highly stratified. However, if the top wall is cooled, there may exist a multicellular flow and an unstable thermal stratification in the upper region of the cylinder. Under the influence of weak convection, the maximum temperature in the cavity can be considerably higher than that predicted for pure conduction. The local heat flux on the bounding walls is generally a strong function of the Rayleigh number, the aspect ratio, and the wall boundary conditions. The heat removal on the cold upper surface decreases with the aspect ratio, thereby increasing the Nusselt number on the vertical wall. The effect of Rayleigh number is, however, not straightforward. Several correlations are presented for the maximum cavity temperature and the overall Nusselt number.

scholarly journals Natural convection in a shallow cavity with differentially heated end walls. Part 1. Asymptotic theory

1974 ◽  
Vol 65 (2) ◽  
pp. 209-229 ◽  
Author(s):  
D. E. Cormack ◽  
L. G. Leal ◽  
J. Imberger
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Free Parameter ◽  
Asymptotic Theory ◽  
Core Region ◽  
Parallel Flow ◽  
Small Aspect Ratio ◽  
The Core ◽  
Asymptotic Expressions ◽  
Shallow Cavity

The problem of natural convection in a cavity of small aspect ratio with differentially heated end walls is considered. It is shown by use of matched asymptotic expansions that the flow consists of two distinct regimes: a parallel flow in the core region and a second, non-parallel flow near the ends of the cavity. A solution valid at all orders in the aspect ratio A is found for the core region, while the first several terms of the appropriate asymptotic expansion are obtained for the end regions. Parametric limits of validity for the parallel flow structure are discussed. Asymptotic expressions for the Nusselt number and the single free parameter of the parallel flow solution, valid in the limit as A → 0, are derived.

A Comparison of the Relative Effectiveness of Fin Aspect Ratio Under Natural Convective Heat Transfer With Top Mounted Fins

2009 ◽  
Author(s):  
Anthony S. Pruszenski
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Heat Load ◽  
Relative Effectiveness ◽  
Internal Heat ◽  
Maximum Temperature ◽  
Constant Heat ◽  
Aspect Ratios ◽  
Square Plate ◽  
Base Width

Mechanical engineers often design fins on metal enclosures to dissipate an internal heat load using natural convection. This paper gives the results of a series of CFD (Computational Fluid Dynamics) studies, and, supporting calculations for the maximum temperature rise on a plate with a constant heat load of 100 watts applied to the bottom of the plate. Vertical fins are formed on the top surface of the plate. In this study, the horizontal dimensions and thickness of a square plate are held constant, while, the aspect ratio of the top surface fins are varied between studies. The aspect ratio is defined as the ratio of the height of the fin to the width of the base of the fin. The study compares aspect ratios from 1:1 to 40:1 with a constant base width. In addition, comparisons between 20:1 aspect ratio fins with the same height but with different fin counts due to changes in fin separation distances are compared. Closely spaced fins are not always the best solution for natural convection.

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