The effect of viscous dissipation on natural convection in a square cavity

About the authors:

Pavel T. Zubkov, Dr. Sci. (Phys.-Math.), Professor, Department of Fundamental Mathematics and Mechanics, University of Tyumen; eLibrary AuthorID, pzubkov@utmn.ru

Eduard I. Narygin, Postgraduate Student, Department of Fundamental Mathematics and Mechanics, University of Tyumen; e.i.narygin@yandex.ru

Abstract:

This article studies the natural convection of a viscous, incompressible fluid in a square cavity in a gravitational field. The temperature of vertical walls is constant. The temperature of the left wall is higher than temperature of the right wall; the horizontal walls are considered thermally insulated. The initial condition for the temperature of a fluid in a square caviry is the constant and equals the temperature of the right wall. The initial condition for the velocity is zero. We consider only those cases where the obtained flow in the cavity is laminar. All thermophysical characteristics are assumed constant, except for one when the motion equation accounts for the gravity. Mathematical model is the Boussinesq approximation but the equation of conservation of energy contains Rayleigh dissipation function.

In this article, the authors have researched the effect of viscous dissipation on natural convection heat transfer in square field. The results show that viscous dissipation significantly affects the heat transfer through the cavity. This problem was solved with the finite volume method by algorithm SIMPLER for Pr=1, Gr=10⁴, and 10⁻⁵≤Ec≤10⁻³.

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