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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.

2

Numerical solutions of a steady 2-D incompressible flow in a rectangular domain with wall slip boundary conditions using the finite volume method

Ambethkar V., Srivastava M. K.

Journal of Applied Mathematics and Computational Mechanics

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2017

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Vol. 16, nr 2

5--16

EN

In this study, a finite volume method (FVM) is suitably used for solving the problem of a fully coupled fluid flow in a rectangular domain with slip boundary conditions. Numerical solutions for the flow variables, viz. velocity, and pressure have been computed. The FVM, with an upwind scheme, has been implemented to discretize the governing equations of the present problem. The well known SIMPLE algorithm is employed for pressure-velocity coupling. This was executed with the aid of a computer program developed and run in a C-compiler. Computations have been performed for unknown variables with Reynolds numbers (Re) = 50, 100, 250, 500, 750 and 1000. The behavior of steady-state solutions of velocity and pressure of the fluid along horizontal and vertical through geometric center of the rectangular domain have been illustrated. We observed that, with the increase of the Reynolds number, the absolute value of velocity components decreases whereas the pressure value increases.

3

Numerical solutions for heat and mass transfer effects of an unsteady MHD free convective flow past an infinite vertical plate with constant suction (injection) and heat source

Ambethkar V.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 1

67-89

EN

The objective of this work is to study heat and mass transfer in an unsteady MHD free convective flow past an infinite vertical plate with constant suction (injection) and heat source numerically. Dimensionless governing equations of the problem have been solved by using the finite difference technique. Numerical solutions for temperature, velocity, concentration have been obtained for suitable parameters like the Grashof number, mass Grashof number, Prandtl number, Schmidt number and Eckert number. The rates of heat transfer and mass transfer are studied. The results obtained are discussed with the help of graphs and tables to observe the effect of various parameters concerned in the problem under investigation. Effects of suction, the Eckert number and heat source parameter on velocity and temperature distributions are discussed. Stability and convergence of the finite difference scheme is established.