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1

Numerical predictions of laminar flow and free convection heat transfer from an isothermal vertical flat plate

Belhocine Ali, Stojanovic Nadica, Abdullah Oday Ibraheem

Archive of Mechanical Engineering

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2022

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LXIX, nr 4

749--773

EN

In this present work, the laminar free convection boundary layer flow of a two-dimensional fluid over the vertical flat plate with a uniform surface temperature has been numerically investigated in detail by the similarity solution method. The velocity and temperature profiles were considered similar to all values and their variations are as a function of distance from the leading edge measured along with the plate. By taking into account this thermal boundary condition, the system of governing partial differential equations is reduced to a system of non-linear ordinary differential equations. The latter was solved numerically using the Runge-Kutta method of the fourth-order, the solution of which was obtained by using the FORTRAN code on a computer. The numerical analysis resulting from this simulation allows us to derive some prescribed values of various material parameters involved in the problem to which several important results were discussed in depth such as velocity, temperature, and rate of heat transfer. The definitive comparison between the two numerical models showed us an excellent agreement concerning the order of precision of the simulation. Finally, we compared our numerical results with a certain model already treated, which is in the specialized literature.

2

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.

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.