On the concave and convex solutions of a mixed convection boundary layer approximation in a porous medium

Abstract

In this paper we investigate the similarity solutions of a plane mixed convection boundary layer flow near a semi-vertical plate, with a prescribed power law function of the distance from the leading edge for the temperature, that is embedded in a porous medium. We show the existence and uniqueness of convex and concave solutions for positive values of the power law exponent.

Mechanical and thermal characteristics of a mixed convection boundary-layer flow in a saturated porous medium

“…Excellent reviews of the further development in the mixed convection in special and of that of the flows in saturated porous media in general, have been published recently by Nield and Bejan [4], Vafai [5], Pop and Ingham [6], Bejan and Kraus [7], Ingham et al [8], Bejan et al [9] and Vafai [10]. Further results concerning the mixed convection boundary-layer flows over a vertical plate in a porous medium have been reported recently by Aly [11], Aly et al [12], Nazar et al [13], Guedda [14] and Brighi and Hoernel [15].…”

“…(23b) and (26) of F n (g) also show that the solutions exist only for e > À1, but for e 6 À1 the condition (3c) is violated. Moreover, in the special case of the forced convection, e = 0, one immediately recovers in (28) the exact elementary solution (15). Furthermore, Eq.…”

“…Brighi and Hoernel [15] have proved that the f-problem (50), (51) admits for k > 0 unique convex solutions for À1 < e < 0 and unique concave solutions for e > 0. Surprisingly, a part of these results hold also in the case k = À1/3.…”

Estimation of Turning Point Location of Convex Solutions for Nonlinear Second-Order Differential Equations

“…The problem of existence and uniqueness of concave and convex solutions for third-order autonomous differential equation arising in the study of the mixed convection boundary layer flow along a semi-infinite vertical plate embedded in a saturated porous medium was examined in [1].…”

Steady Free Convection in a Bounded and Saturated Porous Medium

“…with m ∈ R is interesting too and results about it can be found in [1], [13], [25] and [34]. The Falkner-Skan equation…”