On the Convex and Convex-Concave Solutions of Opposing Mixed Convection Boundary Layer Flow in a Porous Medium

Abstract EN

In this paper, we are concerned with the solution of the third-order nonlinear differential equation f ″ ′ + f f ″ + β f ′ ( f ′ - 1 ) = 0 , satisfying the boundary conditions f ( 0 ) = a ∈ R , f ′ ( 0 ) = b < 0 , and f ′ ( t ) → λ , as t → + ∞ , where λ ∈ { 0,1 } and 0 < β < 1 .

The problem arises in the study of the opposing mixed convection approximation in a porous medium.

We prove the existence, nonexistence, and the sign of convex and convex-concave solutions of the problem above according to the mixed convection parameter b < 0 and the temperature parameter 0 < β < 1 .