Small nield number convection in a porous layer heated from below via a constant heat flux and subject to lack of local thermal equilibrium

The lack of local thermal equilibrium leads to distinct basic temperature proflles for the fluid and solid phases when a constant heat flux instead of a constant temperature is imposed on the lower boundary. Despite these distinct basic temperature proflles, the equations governing their linear stability for small Nield numbers eventually degenerate to the same form as for the case of local thermal equilibrium subject to constant heat flux on the lower boundary. A complete linear stability analysis is performed presenting an accurate solution to the latter; the corresponding neutral curves; accurate eigenvalues; and, in particular, the distinct type of eigenfunctions producing the shape of the convection patterns.