Abstract
The thin film flow of a power law fluid on a vertical cylinder for a lift and a drainage problem is studied. The goverming nonlinear differential equations have been derived from the continuity, momentum and constitutive equations. The resulting equations are then solved using binomial series method. Series solutions have been obtained for velocity, volume flow rate and average velocity in both cases. The graphical results for velocity profile is discussed and examined for different parameters of interest. Key words: Thin film flow, power law fluid, binomial series method.
Highlights
Over the years, non-Newtonian fluids have been considered due to their practical importance in industry, medicine and sciences
Non-linearity increases the mathematical complexity of the problems which reduces the chance of getting exact solutions. In view of such difficulties, in past three decades, researchers and scientists developed numerous analytic and numerical techniques to overcome non-linearity and get approximate solutions. Various analytical techniques such as binomial series method, perturbation method (PM), Adomian decomposition method (ADM), variational iteration method (VIM), homotopy analysis method (HAM), optimal homotopy analysis method (OHAM), homotopy perturbation method (HPM), optimal homotopy perturbation method (OHPM) and some others methods have proven to be valuable tools to understand the complexity of these type of problems (Siddiqui, 2006a, b; He, 2008, 2011, 2012; Siddiqui et al, 2007; Dita and Grama, 1997)
We investigate the thin film flow for lift and drainage on a vertical cylinder, two cases are discussed Newtonian and power law fluid, respectively
Summary
Non-Newtonian fluids have been considered due to their practical importance in industry, medicine and sciences. In view of such difficulties, in past three decades, researchers and scientists developed numerous analytic and numerical techniques to overcome non-linearity and get approximate solutions Various analytical techniques such as binomial series method, perturbation method (PM), Adomian decomposition method (ADM), variational iteration method (VIM), homotopy analysis method (HAM), optimal homotopy analysis method (OHAM), homotopy perturbation method (HPM), optimal homotopy perturbation method (OHPM) and some others methods have proven to be valuable tools to understand the complexity of these type of problems (Siddiqui, 2006a, b; He, 2008, 2011, 2012; Siddiqui et al, 2007; Dita and Grama, 1997). We investigate the thin film flow for lift and drainage on a vertical cylinder, two cases are discussed Newtonian and power law fluid, respectively. The average film velocity V for lift problem investigated comes out to be by using Equation (33) in (23), 2k 1 3
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