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An exact solution for the thin film flow of a third-grade fluid on an inclined plane is presented. This is a corrected version of the solution obtained by Hayat et al. (Chaos Solitons Fractals 38:1336-1341). An alternative parametric form for the solution is also derived. The variation of the dimensionless velocity and average velocity is given for a wide range of parameter values. An asymptotic solution for large parameter values is obtained giving rise to a boundary-layer structure at the free surface.

The problem of steady viscous flow of an incompressible fluid over a flat deformable sheet in a porous medium, when the sheet is stretched in its own plane is revisited. An exact solution is recovered for the two-dimensional case and a totally analytic approximate solution is developed for the axisymmetric case. Stretching rate of two-dimensional case is assumed as double the stretching rate of axisymmetric case. The analytical expressions of residual errors, horizontal, vertical velocity distributions, stream lines, vorticity lines, pressure distributions have been obtained and plotted. The values of skin friction, entrainment velocity, boundary layer thickness, momentum thickness and energy thickness have been tabulated. For the first time, two-dimensional and axisymmetric cases are compared by means of a unified scale.

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