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Unsteady natural convection in a partially porous cavity having a heat-generating source using local thermal non-equilibrium model

Marina S. Astanina (Laboratory on Convective Heat and Mass Transfer, Tomsk State University, 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)
C. Jawali Umavathi (Department of Mathematics, Gulbarga University, Gulbarga, India)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 6 December 2018

Issue publication date: 11 June 2019




The purpose of this study is a numerical analysis of transient natural convection in a square partially porous cavity with a heat-generating and heat-conducting element using the local thermal non-equilibrium model under the effect of cooling from the vertical walls. It should be noted that this research deals with a development of passive cooling system for the electronic devices.


The domain of interest is a square cavity with a porous layer and a heat-generating element. The vertical walls of the cavity are kept at constant cooling temperature, while the horizontal walls are adiabatic. The heat-generating solid element is located on the bottom wall. A porous layer is placed under the clear fluid layer. The governing equations, formulated in dimensionless stream function, vorticity and temperature variables with corresponding initial and boundary conditions, are solved using implicit finite difference schemes of the second order accuracy. The governing parameters are the Darcy number, viscosity variation parameter, porous layer height and dimensionless time. The effects of varying these parameters on the average total Nusselt number along the heat source surface, the average temperature of the heater, the fluid flow rate inside the cavity and on the streamlines and isotherms are analyzed.


The results show that in the case of local thermal non-equilibrium the total average Nusselt number is an increasing function of the interphase heat transfer coefficient and the porous layer thickness, while the average heat source temperature decreases with the Darcy number and viscosity variation parameter.


An efficient numerical technique has been developed to solve this problem. The originality of this work is to analyze unsteady natural convection within a partially porous cavity using the local thermal non-equilibrium model in the presence of a local heat-generating solid element. The results would benefit scientists and engineers to become familiar with the analysis of convective heat transfer in enclosures with local heat-generating heaters and porous layers, and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors and electronics.



This work of Marina S. Astanina and Mikhail A. Sheremet was supported by the Russian Science Foundation (Project No. 17-79-20141). The authors would also like to express their thank to the very competent reviewers for the valuable comments and suggestions.


Astanina, M.S., Sheremet, M. and Umavathi, C.J. (2019), "Unsteady natural convection in a partially porous cavity having a heat-generating source using local thermal non-equilibrium model", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 29 No. 6, pp. 1902-1919.



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