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.

In this study, the heat and mass transfer of combined free and forced convection in the horizontal rectangle is explored. The governing equations together with the boundary conditions are solved numerically by using the finite volume method. The innovative idea in this study is to appropriately modify the Semi‐Implicit Method for Pressure‐Linked Equations algorithm and thereby, the numerical solutions of the flow variables such as the temperature and the concentration in addition to the components of velocity and the pressure are computed. The Richardson numbers (Ri) for distinct gases and liquids are calculated for different Rayleigh numbers at low (Re = 50) and high (Re = 5000) Reynolds numbers. The dimensionless parameters, such as the Reynolds number (Re), the Prandtl number (Pr), and the Schmidt number (Sc) are appropriately chosen to calculate the Richardson numbers. Consequently, combined free and forced convection effects are analyzed. Furthermore, the heat and mass transfer aspect for distinct gases and liquids is critically examined using empirical correlations. The accuracy and the validation of these results are ensured owing to the solutions obtained from correlations being advised in this study and those are existing in the literature.

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.

In this work, we have investigated the heat transfer of a mixed convective flow in horizontal rectangular enclosure having a wall heat source. For the purpose of computing stable and convergent numerical solutions of the flow variables, the governing equations along with the boundary conditions are solved by using the upwind finite volume scheme and a modified SIMPLE algorithm. For discussing the heat transfer from the bottom wall of the enclosure, the average Nusselt numbers are computed from relevant empirical correlations existing in the literature. These correlations are in the range of 1708 ≤ Ra ≤ 108 and 1708 ≤ Ra ≤ 3.5×109 in terms of different Rayleigh numbers for the Newtonian fluids such as air and water. Numerical solutions obtained from this study are compared with available benchmark solutions.

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.