Abstract
A new class of explicit second-order schemes is proposed for solving time-dependent partial differential equations. This class of proposed schemes is constructed on three-time levels. Stability is found for the scalar two-dimensional heat equation and the system of time-dependent partial differential equations. This partial differential equations system comprises a non-dimensional set of equations obtained from the governing equations of natural convection chemically reactive fluid flow in a rectangular enclosure with thermal radiations. Flow is generated by applying the force of pressure. Graphs of streamlines, contours plots of velocity, temperature and concentration profiles, local Nusselt number, and local Sherwood number are displayed with the variation of time and parameters in the considered partial differential equations. Results are shown in the form of streamlines and contour plots. It is found that local Nusselt number has dual behavior by enhancing radiation parameter whereas local Sherwood number de-escalates by upraising the reaction rate parameter. It is hoped that the results in this pagination will serve as a valuable resource for future fluid-flow studies in an enclosed industrial environment.