Effect of Variation of Heated Bottom Wall Area on Natural Convection in Square Enclosure with Inner Circular Cylinder

This paper performs a numerical analysis of the natural convection within two-dimensional enclosures (square enclosure and enclosures with curved walls) full of a H2O-Cu nanofluid. While their vertical walls are isothermal with a cold temperature [Formula: see text], the horizontal top wall is adiabatic and the bottom wall is kept at a sinusoidal hot temperature. The working fluid is assumed to be Newtonian and incompressible. Three values of the Rayleigh number were considered, viz., 103, 104, 105, the Prandtl number is fixed at 6.2, and the volume fraction [Formula: see text] is taken equal to 0% (pure water), 10% and 20%. The numerical simulation is achieved using a 2D-in-house CFD code based on the governing equations formulated in bipolar coordinates and translated algebraically via the finite volume method. Numerical results are presented in terms of streamlines, isotherms and local and average Nusselt numbers. These show that the heat transfer rate increases with both the volume fraction and the Rayleigh number, and that the average number of Nusselt characterizing the heat transfer raises with the nanoparticles volume fraction.

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Numerical Study of Natural Convection in a Square Enclosure with an Inner Circular Cylinder for Rayleigh Number of 107

Transactions of the Korean Society of Mechanical Engineers B ◽

10.3795/ksme-b.2010.34.8.739 ◽

2010 ◽

Vol 34 (8) ◽

pp. 739-747 ◽

Cited By ~ 3

Author(s):

Dong-Hun Yu ◽

Hyun-Sik Yoon ◽

Man-Yeong Ha

Keyword(s):

Natural Convection ◽

Rayleigh Number ◽

Circular Cylinder ◽

Numerical Study ◽

Square Enclosure

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Effect of Surface Radiation on Multiple Natural Convection Solutions in a Square Cavity Partially Heated from Below

Journal of Heat Transfer ◽

10.1115/1.2345429 ◽

2006 ◽

Vol 128 (10) ◽

pp. 1012-1021 ◽

Cited By ~ 5

Author(s):

El Hassan Ridouane ◽

Mohammed Hasnaoui

Keyword(s):

Steady State ◽

Natural Convection ◽

Numerical Study ◽

Heated Surface ◽

Steady State Solution ◽

Surface Radiation ◽

Bottom Wall ◽

Square Cavity ◽

Square Enclosure ◽

Surface Dimension

A numerical study of natural convection with surface radiation in an air filled square enclosure with a centrally heated bottom wall and cooled upper wall is presented. The vertical walls and the rest of the bottom wall are assumed to be insulated. The problem is studied for Rayleigh numbers Ra, ranging from 103 to 4×106 and surfaces emissivity ε, varying from 0 to 1. The governing equations, written in terms of stream function-vorticity formulation, are solved using a finite difference approach. It is found that, under these heating/cooling conditions, three different steady-state solutions are possible in the ranges of the parameters considered. Results are presented detailing the occurrence of each steady-state solution and the effect of Ra and ε on its range of existence. It is found that the surface radiation alters significantly the existence ranges of the solutions. For each solution, convective and radiative contributions to the global heat transfer are also quantified for various Ra and ε. The influence of the heated surface dimension on the fluid flow and thermal patterns is also presented by comparing the present results against those obtained by the authors in an earlier study within a square cavity totally heated from below.

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