Normal solutions of a boundary-value problem arising in free convection boundary-layer flows in porous media

This paper is concerned with normal solutions of a two-point boundary-value problem of second order which arises in the steady free convection boundary-layer flow over a vertical permeable flat plate being embedded in a saturated porous medium with both prescribed heat flux and suction rate of the plate. We use a very simple argument to prove that there exists a λmin  ∈ (1.3782407, 1.4166499) such that this problem has no normal solution for all λ < λmin , a unique normal solution for λ=λmin, and exactly two normal solutions θ1(η) and θ2(η) with θ1(η) < θ2(η) on [0,+∞) for each fixed λ > λmin , which is applied to the reduced boundary-layer system.