Analyzing the topography of thermosolutal rotating convection of a Casson fluid in a sparsely packed porous channel

This paper discusses the thermosolutal rotating convection of a Casson fluid in a sparsely packed porous channel with variable boundaries. For linear analyses, the normal mode method is utilized to solve the governing equations. The system of equations are solved using a one-term Galerkin method for finding critical Rayleigh number. Meanwhile, the eigenvalue problem is numerically solved using the Chebyshev collocation method. Graphical representations are provided of the effects of the Casson fluid (beta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}) and separation parameters (chi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\chi $$\end{document}) on velocity, temperature, and solute concentration profiles for fixed parameter values of Rayleigh number (R), Darcy number (Da), and Taylor number (Ta). Influence of Casson fluid and separation parameters is demonstrated for the system growth rate, stability curves, and critical boundary conditions. However, it turns out that the Darcy number, Taylor number, Lewis number, and Prandtl number all stabilize the system in an unsteady flow. Multiple-scale analysis is used to develop the coupled Landau-Ginzburg equation in weakly nonlinear theory. Furthermore, the study develops amplitude cellular convections in a stability region.