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

Abstract

In this paper, we are concerned with the solution of the third-order nonlinear differential equation f″′+ff″+βf′(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.