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Unsteady natural convection in a cubical cavity with a triangular heat source

Nikita Gibanov (Laboratory on Convective Heat and Mass Transfer, Tomskij Gosudarstvennyj Universitet, Tomsk, Russian Federation)
Mikhail Sheremet (Department of Theoretical Mechanics, Tomsk State University, Tomsk, Russian Federation and Institute of Power Engineering, Tomsk Polytechnic University, Tomsk, Russian Federation)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 7 August 2017



The purpose of this paper is to study natural convective fluid flow and heat transfer inside a cubical cavity having a local heat source of constant temperature.


The cubical cavity is cooled from two vertical opposite walls and heated from the local heater mounted on the bottom wall, while the rest walls are adiabatic. The governing equations formulated in dimensionless vector potential functions and vorticity vector have been solved using implicit finite difference method of the second-order accuracy. The effects of the Rayleigh number (Ra = 1e+04 – 1e+06), heat source position (l/L = 0.05 – 0.35) and dimensionless time (0 < tau < 100) on velocity and temperature fields, streamlines, isotherms and average Nusselt number at the heat source surface have been analyzed.


It is found that the extreme left position of the heater (l/L = 0.05) illustrates more essential cooling of the cavity where the thermal plume over the heat source is suppressed by low temperature waves from the cold vertical walls.


The originality of this work is to analyze transient 3D natural convection in a cubical cavity with a heater of triangular shape and compare obtained 3D data with 2D results. It should be noted that for numerical simulation, the authors used vector potential function and vorticity vector that for transient problems allows to reduce the computational time. The results would benefit scientists and engineers to become familiar with the analysis of transient convective heat and mass transfer in 3D domains with local heaters, and the way to predict the properties of convective flow in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors, ventilation, air-conditioning, etc.



This work was conducted as a government task of the Ministry of Education and Science of the Russian Federation (Project Number 13.9724.2017/8.9). The authors also wish to express their thanks to the very competent reviewers for their valuable comments and suggestions.


Gibanov, N. and Sheremet, M. (2017), "Unsteady natural convection in a cubical cavity with a triangular heat source", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 8, pp. 1795-1813.



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