Existence, Uniqueness and Solution Properties of Transient Mixed Convection Flow in A Vertical Concentric – Annulus Filled with Porous Materials Having Constant Porosity
Mkpedem K. A. *
Sheffield Hallam University, Shefffield, United Kingdom.
Olayiwola R. O. *
Federal University of Technology Minna, Niger State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The existence, uniqueness, and solution characteristics of transient mixed convection flow of an incompressible viscous fluid in a vertical concentric annulus filled with a porous medium of constant porosity are investigated. Under the Boussinesq approximation, the governing momentum and energy equations incorporating buoyancy, pressure gradient, and magnetic field effects are formulated. The equations are non-dimensionalized using appropriate scaling to obtain key parameters such as Reynolds number (Re), Grashof number (Gr), Peclet number (Pe), and magnetic parameter (M). The reduced system is analyzed using similarity transformations. The existence and uniqueness of solutions are established using the Picard–Lindelöf theorem. The results confirm that the system admits a unique bounded solution, ensuring well-posedness of the model. The research shows how essential dimensionless characteristics such as Reynolds, Grashof, Peclet, and magnetic parameters affect flow and thermal behaviour. Overall, this study establishes a solid theoretical foundation for future analytical and numerical research of convection flows in porous annular geometries.
Keywords: Convection, annulus, porous medium, flow, existence and uniqueness