# Similarity solutions for boundary layer flows with prescribed surface temperature

Research output: Contribution to journalArticle

8 Citations (Scopus)

### Abstract

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.

Original language English 67-73 7 Applied Mathematics Letters 21 1 https://doi.org/10.1016/j.aml.2007.03.005 Published - 2008 Jan 1

### Fingerprint

Similarity Solution
Boundary layer flow
Boundary Layer Flow
Free Convection
Fluid Mechanics
Fluid mechanics
Bounded Solutions
Natural convection
Nonlinear equations
Stretching
Porous Media
Porous materials
Nonlinear Equations
Uniqueness
Complement
Boundary conditions
Temperature
Context

### Keywords

• Boundary value problem
• Initial value problem
• Phase plane analysis
• Similarity solution
• Third-order differential equation

### ASJC Scopus subject areas

• Applied Mathematics

### Cite this

In: Applied Mathematics Letters, Vol. 21, No. 1, 01.01.2008, p. 67-73.

Research output: Contribution to journalArticle

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