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1

Analogy between thermal and mass diffusion effects of a free convective flow in rectangular enclosure

Ambethkar Vusala

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 4

5--20

EN

In this investigation, the analogy between thermal and mass diffusive effects of a free convective flow in a rectangular enclosure is emphasized. The upwind finite volume method is used to discretize the governing equations of the continuity, momentum, energy and mass transfer. The novelty in this exploration is to appropriately modify the well-known Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm so that it suits to the present problem and thereby, the new flow variables such as the temperature and the concentration are computed. An empirical correlation for the average Sherwood number (Sh) that does not exist in literature is suggested in this work. The average Sherwood numbers for distinct fluids (gases and liquids) are calculated, and mass diffusion effects within the horizontal rectangle are analyzed. The average Nusselt numbers (Nu) are calculated for distinct fluids such as liquids (Pr ≫1), liquid metals (Pr≪1) and gases (Pr < 1) for different Rayleigh numbers in the range of 3x105 ≤ RaL ≤ 7x10 9 from relevant empirical correlations existing in the literature. Accordingly, the thermal diffusion effects within the horizontal rectangle are analyzed.

2

Solution of viscous flow in a rectangular region by using the hybrid finite volume scheme

Ambethkar Vusala, Basumatary Lakshmi Rani

Journal of Applied Mathematics and Computational Mechanics

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2019

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Vol. 18, nr 3

17--30

EN

In the present work, a solution to the problem of viscous flow in a rectangular region with two moving parallel walls is obtained by using a hybrid finite volume scheme. The discretized governing equations are solved iteratively, and thereby the flow variables are computed numerically. The results for velocity and pressure in horizontal and vertical directions through the centre of a rectangular region are elucidated. The nature of velocity profiles and pressure for different Reynolds numbers in the horizontal and vertical directions through the geometric centre was analyzed with the help of pictorial representations. The present results are compared with the available benchmark results and we have found that they are not in disagreement.

3

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

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2019

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Vol. 18, nr 4

5--18

EN

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.