Non-isothermal Poiseuille flow and its stability in a vertical annulus filled with porous medium

• The non-isothermal Poiseuille flow in vertical annulus filled with porous medium is studied.
• The non-Darcy model is used.
• Effect of curvature on the flow, heat transfer rate and stability is emphasized.
• Effect form drag on the flow regime as well as instability mechanism is also checked.

In this article, the non-isothermal Poiseuille flow and its stability in a vertical annulus filled with porous medium are investigated. The flow is induced by external pressure gradient and buoyancy force due to linearly varying inner wall temperature. The non-Darcy model along with Boussinesq approximation has been used. The Chebyshev spectral-collocation method has been adopted to solve the governing equations related to basic flow as well as its stability. Special attention is given to understand the effect of curvature parameter of the annular geometry on the flow, heat transfer rate and stability of the stably stratified flow. A comprehensive numerical experiment indicates that reducing gap between two concentric cylinders decreases the heat transfer rate as well as the maximum magnitude of the flow velocity. It stabilizes the flow which has been shown through stability analysis. Furthermore, appropriateness of the Forchheimer term in the momentum equation has been examined by investigating the flow regime as well as its stability in the presence and absence of Forchheimer term. Finally, it has been found from the energy analysis at critical point that the thermal-buoyant instability is the only mode of instability for the considered range of different parameters.