Similarity solutions for non-Newtonian power-law fluid flow

• Published in: Applied mathematics and mechanics Vol. 35; no. 9; pp. 1155 - 1166
• Main Authors: Wei, D. M., Al-Ashhab, S.
• Format: Journal Article
• Language: English
• Published: Heidelberg Shanghai University 01.09.2014; Department of Mathematics, University of New 0rleans, LA 70148,U.S.A.%Department of Mathematics, Al Imam Mohammad Ibn Saud Islamic University, Riyadh 11623, Saudi Arabia
• Subjects: Applications of Mathematics; Classical Mechanics; Fluid- and Aerodynamics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; non-linear boundary value problem; 34B16; uniqueness; 76A05; existence; boundary layer flow; power law fluid; O357.1
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-014-1854-6

The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindelof theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curva- ture of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 〈 n ≤ 1, the solution has a positive curvature, while for n 〉 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.