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1 Journal of Applied Mathematics and Computational Mechanics

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Numerical solutions of steady free convective flow in a rectangular region with discrete wall heat and concentration sources

Ambethkar Vusala, Basumatary Lakshmi Rani

Journal of Applied Mathematics and Computational Mechanics

2019

Vol. 18, nr 4

5--18

In this paper, numerical solutions are obtained for steady free convective ﬂow in a rectangular region with discrete wall heat and concentration sources by using the ﬁnite volume method. The governing equations consist of the continuity, momentum, energy and mass transfer. These equations conjointly with suitable boundary conditions are solved numerically by using this method. The novel concept in this work is to generalize the SIMPLE algorithm suitably and thereby compute the numerical solutions of the ﬂow variables such as the temperature (θ) and the concentration (C) in addition to the components of velocity and the pressure. All non-dimensional parameters are chosen suitably in accordance with the physical signiﬁcance of the problem under investigation. With the help of these numerical solutions, we have depicted the proﬁles of the velocity, pressure, temperature and concentration along the horizontal and vertical directions of the geometric centre of the region. The validity of the numerical solutions are ensured by comparing the present solutions with the benchmark solutions. Code validation has been given for the present problem.