Global stability analysis of magneto convection in an inclined porous layer with the local thermal non-equilibrium model

The study investigates the onset of magneto convection in an inclined porous layer using the local thermal non-equilibrium (LTNE) model. To analyze the stability of flow, the linear and nonlinear theories are employed. The investigation of the basic flow through linear analysis is conducted by utilizing a decomposition of disturbances using normal modes. A detailed outcome on nonlinear stability is analyzed by defining an energy functional. The study examines the importance of non-dimensional parameters, namely the porosity-modified conductivity ratio ( τ ), the inter-phase heat transfer parameter ( H ), and the Hartmann number ( H a 2 ), on the onset of convection. The shooting method with sixth order Runge–Kutta method is used to solve the eigenvalue problem by using NDSolve and FindRoot commands in Mathematica. The investigation highlights that stationary transverse rolls in a non-traveling mode ( ω = 0 ) and oscillatory transverse rolls in a traveling mode ( ω ≠ 0 ) exhibit similar characteristics. As H a 2 increases, the inclination angle at which transverse rolls vanish also increases, contributing to system stabilization. The study emphasizes that the Hartmann number ( H a 2 ), the inter-phase heat transfer parameter ( H ), and the inclination angle ( γ ) all play significant roles in enhancing the system’s stability. • Onset of magnetoconvection analyzed using LTNE model in inclined porous medium. • Linear and nonlinear stability analyses performed using normal mode and energy methods. • Effects of τ , H , and H a 2 on the onset of convection are thoroughly examined. • Eigenvalue problem solved using shooting method with sixth-order Runge–Kutta scheme. • Increase in Ha 2 and γ stabilizes the system by suppressing transverse rolls.