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Publication date: 7 April 2015

Lahcen El Moutaouakil, Zaki Zrikem and Abdelhalim Abdelbaki

This work is devoted to the numerical analysis of laminar natural convection in two-dimensional vertical cavities, filled with air and of high aspect ratios. One of the sidewalls…

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Abstract

Purpose

This work is devoted to the numerical analysis of laminar natural convection in two-dimensional vertical cavities, filled with air and of high aspect ratios. One of the sidewalls is cooled isothermally while the other is heated by a uniform or linear heat flux whose average is located at mid-height of the wall. The paper aims to discuss these issues.

Design/methodology/approach

The governing equations are discretized by the finite volume method and solved, in transient regime, by using the SIMPLE algorithm.

Findings

The flow structure, air temperature field, local convective heat flux on the cold wall, variation of the temperature along the heated wall as well as its average and its maximum are analyzed for various combinations of the controlling parameters. These parameters are the linear heat flux slope γ (γ=0, 1 and −1, for a uniform, increasing and decreasing heat flux, respectively), the average Rayleigh number Ra m (103Ra m3×104) and the aspect ratio A (10A80). It was found that for a given A and Ra m, the highest (lowest) mean temperature of the hot wall is obtained when the linear heating is descending (ascending). While the maximum temperature increases with the three controlling parameters.

Practical implications

Accurate correlations which allow calculating the average and maximum temperatures of the heated wall are developed for each type of heating. Also, an empirical relationship for the position of the maximum temperature is provided for γ=−1.

Originality/value

Despite its fundamental and practical interest, natural convection in cavities with 10A80 and submitted to non-uniform heat flux was not examined before. Development of original correlations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 1 August 2016

Lahcen El Moutaouakil, Zaki Zrikem and Abdelhalim Abdelbaki

A detailed numerical study is conducted on the effect of surface radiation on laminar natural convection in a tall vertical cavity filled with air. The cavity is heated and…

145

Abstract

Purpose

A detailed numerical study is conducted on the effect of surface radiation on laminar natural convection in a tall vertical cavity filled with air. The cavity is heated and cooled, through its two vertical walls, by a linear or uniform heat flux q(y) and by a constant cold temperature, respectively. The horizontal walls are considered adiabatic. The paper aims to discuss these issues.

Design/methodology/approach

The radiosity method is employed to calculate the net radiative heat exchanges between elementary surfaces, while the finite volume method is implemented to resolve the governing equations of the fluid flow.

Findings

For each heat flux q(y) (ascending, descending or uniform), the effect of the emissivity ε (0ε1) on the local, average and maximum temperatures of the heated wall is determined as a function of the average Rayleigh number Ram (103Ram6×104) and the cavity aspect ratio A (10A80). The effect of the coupling on the flow structures, convective and radiative heat transfers is also presented and analyzed. Overall, it is shown that surface radiation significantly reduces the local and average temperatures of the heated wall and therefore reduces the convective heat transfer between the active walls.

Practical implications

The studied configuration is of practical interest in several areas where overheating must be avoided. For this purpose, a simple design tool is developed to estimate the mean and the maximum temperatures of the hot wall in different operating conditions (Ram, A et ε).

Originality/value

The originality lies in the study of the interaction between surface radiation and natural convection in tall cavities submitted to a non-uniform heat flux and a constant cold temperature on the active walls. Also, the development of an original simplified calculation procedure for the hot wall temperatures.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

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