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Investigation on the Film Flow of a Third Grade Fluid on an Inclined Plane Using HPM

Azimi M., Azimi A.

Mechanics and Mechanical Engineering

2014

Vol. 18, nr 1

5--10

This work concerns the study of the thin film flow problem arising in non–Newtonian fluid mechanics using analytical approach. The governing equations are reduced to ordinary nonlinear boundary value problem by applying the transformation method. Homotopy Perturbation Method (HPM) has been applied to obtain solution of reduced nonlinear boundary value problem. The analytical solutions of the flow velocity distributions for different cases have been presented. The effect of material constant has also discussed. Finally, analytical results have been compared with numerical one obtained by forth order Runge Kutta method. High accuracy and validity are the advantages of present study.

A linear and semilinear abstract initial value problem with singularity

Obłoza W.

Demonstratio Mathematica

2004

Vol. 37, nr 1

71--90

An abstracts second order Cauchy problem with non-densely defined operator, II

Bochenek J.

Demonstratio Mathematica

2002

Vol. 35, nr 2

293-302

By using the theory of the extrapolation space X-1 associated with an operator A which is non-densely denned in a Banach space X, the existence and uniqueness of solutions of the semilinear second order differential initial value problem (1) is proved.

Linear boundary value problem of a degenerate elliptic system of partial differential equations

Mamourian A.

Demonstratio Mathematica

1999

Vol. 32, nr 4

745-748

By application of function theoretic methods in partial differential equations (PDE), a nonlinear system of equations, elliptic in the sense of Lavrentiev with a linear boundary condition is investigated. Existence, uniqueness and stability for the boundary value problem (BVP) with degeneration of ellipticity have been proved.