# EXACT SOLUTION FOR STEADY PAINT FILM FLOW OF A PSEUDO PLASTIC FLUID DOWN A VERTICAL WALL BY GRAVITY

• Alam, M.K. (NATIONAL UNIVERSITY OF COMPUTER & EMERGING SCIENCES) ;
• Rahim, M.T. (NATIONAL UNIVERSITY OF COMPUTER & EMERGING SCIENCES) ;
• Islam, S. (DEPARTMENT OF MATHEMATICS, ABDUL WALI KHAN UNIVERSITY) ;
• Siddiqui, A.M. (PENNSYLVANIA STATE UNIVERSITY, YORK CAMPUS)
• Accepted : 2012.09.14
• Published : 2012.09.25

#### Abstract

Here in this paper, the steady paint film flow on a vertical wall of a non-Newtonian pseudo plastic fluid for drainage problem has been investigated. The exact solution of the nonlinear problem is obtained for the velocity profile. Also the average velocity, volume flux, shear stress on the wall, force to hold the wall in position and normal stress difference have been derived. We retrieve Newtonian case, when material constant ${\mu}_1$ and relaxation time ${\lambda}_1$ equal zero. The results for co-rotational Maxwell fluid is also obtained by taking material constant ${\mu}_1$ = 0. The effect of the zero shear viscosity ${\eta}_0$, the material constant ${\mu}_1$, the relaxation time ${\lambda}_1$ and gravitational force on the velocity profile for drainage problem are discussed and plotted.

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