TY - JOUR

T1 - Similarity solutions for boundary layer flows with prescribed surface temperature

AU - Tsai, Je Chiang

N1 - Funding Information:
The author is very grateful to the anonymous referees for careful reading and helpful suggestions which improve our original manuscript significantly. This work was partially supported by the National Science Council of the Republic of China under the grant NSC 95-2115-M-194-015.

PY - 2008/1

Y1 - 2008/1

N2 - We are concerned with the third-order nonlinear equation f‴ + [(m + 1) / 2] f f″ - m f ′2 = 0 on (0, ∞), satisfying the boundary conditions f (0) = a ∈ R, f′ (0) = 1 and f′ (∞) = 0. The problem arises in the study of similarity solutions in two physically different contexts of fluid mechanics: free convection in a porous medium and flow adjacent to a stretching wall. We shall address two open questions: the first one is the uniqueness of bounded solutions for m ∈ (- 1 / 3, 0) and a < 0, and the second one is the structure of solutions for m ∈ (- 1 / 2, - 1 / 3) and a ≤ 0. Our results complement earlier results in the literature.

AB - We are concerned with the third-order nonlinear equation f‴ + [(m + 1) / 2] f f″ - m f ′2 = 0 on (0, ∞), satisfying the boundary conditions f (0) = a ∈ R, f′ (0) = 1 and f′ (∞) = 0. The problem arises in the study of similarity solutions in two physically different contexts of fluid mechanics: free convection in a porous medium and flow adjacent to a stretching wall. We shall address two open questions: the first one is the uniqueness of bounded solutions for m ∈ (- 1 / 3, 0) and a < 0, and the second one is the structure of solutions for m ∈ (- 1 / 2, - 1 / 3) and a ≤ 0. Our results complement earlier results in the literature.

KW - Boundary value problem

KW - Initial value problem

KW - Phase plane analysis

KW - Similarity solution

KW - Third-order differential equation

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U2 - 10.1016/j.aml.2007.03.005

DO - 10.1016/j.aml.2007.03.005

M3 - Article

AN - SCOPUS:36249026450

SN - 0893-9659

VL - 21

SP - 67

EP - 73

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 1

ER -