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1

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.

2

A numerical method for viscous flow in a driven cavity with heat and concentration sources placed on its side wall

Ambethkar V., Basumatary L. R.

Journal of Applied Mathematics and Computational Mechanics

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2018

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Vol. 17, nr 3

17--30

EN

This paper proposes a method to numerically study viscous incompressible two-dimensional steady flow in a driven square cavity with heat and concentration sources placed on its side wall. The method proposed here is based on streamfunction-vorticity (Ψ-ξ) formulation. We have modified this formulation in such a way that it suits to solve the continuity, x and y-momentum, energy and mass transfer equations which are the governing equations of the problem under investigation in this study. No-slip and slip wall boundary conditions for velocity, temperature and concentration are defined on walls of a driven square cavity. In order to numerically compute the streamfunction Ψ, vorticityfunction ξ , temperature θ, concentration C and pressure P at different low, moderate and high Reynolds numbers, a general algorithm was proposed. The sequence of steps involved in this general algorithm are executed in a computer code, developed and run in a C compiler. We propose that, with the help of this code, one can easily compute the numerical solutions of the flow variables such as velocity, pressure, temperature, concentration, streamfunction, vorticityfunction and thereby depict and analyze streamlines, vortex lines, isotherms and isobars, in the driven square cavity for low, moderate and high Reynolds numbers. We have chosen suitable Prandtl and Schmidt numbers that enables us to define the average Nusselt and Sherwood numbers to study the heat ad mass transfer rates from the left wall of the cavity. The stability criterion of the numerical method used for solving the Poisson, vorticity transportation, energy and mass transfer has been given. Based on this criterion, we ought to choose appropriate time and space steps in numerical computations and thereby, we may obtain the desired accurate numerical solutions. The nature of the steady state solutions of the flow variables along the horizontal and vertical lines through the geometric center of the square cavity has been discussed and analyzed. To check the validity of the computer code used and corresponding numerical solutions of the flow variables obtained from this study, we have to compare these with established steady state solutions existing in the literature and they have to be found in good agreement.

3

Heat transfer due to permeable stretching. Wall in presence of transverse magnetic field

Dandapat B. S., Singh S. N., Singh R. P.

Archives of Mechanics

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2004

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Vol. 56, nr 1

87-101

EN

Exact similarity solution for the viscous flow due to stretching surface in the presence of magnetic field is derived. Further exact solutions for the temperature distributions in terms of Kummer's functions are obtained. Two cases of heat transfer are considered: the sheet (i) with prescribed surface temperature and (ii) - the prescribed wall heat flux. Both the cases are further extended to study the heat transfer due to suction and injection. A simple relation for the two cases of heat transfer is obtained.