Nonlinear stability analysis of thin micropolar film flows travelling down a vertical moving plate

Abstract

This paper employs linear and nonlinear stability theories to conduct a numerical characterization of thin micropolar film flows travelling down a vertical moving plate. Having applied the long-wave perturbation method to derive the generalized kinematic equations for a free film surface condition, the multiple scales method is used to solve the micropolar film flow in the cases of a stationary vertical plate, a vertical plate moving in the downward direction and a vertical plate moving in the upward direction. The numerical results indicate that both subcritical instability and supercritical stability conditions may occur in the micropolar film flow system. No obvious change in the supercritical stability condition is observed when the plate moves vertically in the upward or downward direction. The numerical results indicate that a downward motion of the vertical plate tends to enhance the stability of the film flow.

Nonlinear hydromagnetic stability analysis of a pseudoplastic film flow

“…(25)-(30), the governing equations of the thin-film system can be collected and solved on an order-by-order basis. In practice, the non-dimensional surface tension, S n , has a large value, and thus the term α 2 S n can be treated as a zeroth-order quantity [3][4][5]. Furthermore, for y h, the film thickness h is very small, using the power series solution ϕ = ∞ n=0 k n y n about 0, and hence power series approximation solutions can be obtained up to the order of y 5 at the zeroth-and first-orders of the stream function (given in Appendix A).…”

“…Accordingly, analyzing the microstructure of fluid flows has emerged as a major research area in both industrial and academic circles in recent years. Chang [3] and Cheng et al [5] investigated the nonlinear stability of thin micropolar fluid films flowing down a vertical moving plate and a vertical cylinder, respectively. Their results indicated that the micropolar parameters of the fluid play an important role in stabilizing the film flow.…”

“…The current study applies both linear and nonlinear stability analysis theories to investigate the stability of a thin electrically-conductive pseudoplastic fluid film flowing down the surface of a vertical wall in an applied magnetic field. In contrast to previous related studies [3][4][5], the problem is addressed using a numerical approximation method rather than an analytical solution procedure. The analysis focuses particularly on the respective effects of the Hartmann number and the flow index on the stability of the film flow.…”

“…The parameter ranges of the parameters considered in the analysis are as follows: (1) Reynolds number Re 1 = 0-10, (2) dimensionless perturbation wave number α = 0-0.12, (3) Hartmann number m = 0, 0.1 and 0.2, and (4) flow index n = 0.95, 0.98 and 1.00. Note that in performing the various analyses, a constant dimensionless surfacetension of S 1 = 6173.5 is assumed[3][4][5].…”

Hydrodynamic stability of a layer of viscous gravity-driven power-law fluid flow under rotating centrifugal force

“…In recent years, the microstructure of fluid flows has emerged as a research subject of great interest to many researchers. Chang (2006) indicated that the micropolar parameters of the fluid play an important role in stabilizing the film flow. Cheng and Lai (2009) employed the method of non-linear analysis to study the non-linear stability of a thin Bingham liquid film flowing down on a vertical plate.…”