The instability of the boundary layer over a disk rotating in an enforced axial flow

We consider the convective instability of stationary and traveling modes within the boundary layer over a disk rotating in a uniform axial flow. Complementary numerical and high Reynolds number asymptotic analyses are presented. Stationary and traveling modes of type I (crossflow) and type II (streamline curvature) are found to exist within the boundary layer at all axial flow rates considered. For low to moderate axial flows, slowly traveling type I modes are found to be the most amplified, and quickly traveling type II modes are found to have the lower critical Reynolds numbers. However, near-stationary type I modes are expected to be selected due to a balance being struck between onset and amplification. Axial flow is seen to stabilize the boundary layer by increasing the critical Reynolds numbers and reducing amplification rates of both modes. However, the relative importance of type II modes increases with axial flow and they are, therefore, expected to dominate for sufficiently high rates. The application to chemical vapour deposition(CVD) reactors is considered

Adomian decomposition method simulation of Von Kármán swirling bioconvection nanofluid flow

The study reveals analytically on the 3-dimensional viscous time-dependent gyrotactic bioconvection in swirling nanofluid flow past from a rotating disk. It is known that the deformation of the disk is along the radial direction. In addition to that Stefan blowing is considered. The Buongiorno nanofluid model is taken care of assuming the fluid to be dilute and we find Brownian motion and thermophoresis have dominant role on nanoscale unit. The primitive mass conservation equation, radial, tangential and axial momentum, heat, nano-particle concentration and micro-organism density function are developed in a cylindrical polar coordinate system with appropriate wall (disk surface) and free stream boundary conditions. This highly nonlinear, strongly coupled system of unsteady partial differential equations is normalized with the classical Von Kármán and other transformations to render the boundary value problem into an ordinary differential system. The emerging 11th order system features an extensive range of dimensionless flow parameters i.e. disk stretching rate, Brownian motion, thermophoresis, bioconvection Lewis number, unsteadiness parameter, ordinary Lewis number, Prandtl number, mass convective Biot number, Péclet number and Stefan blowing parameter. Solutions of the system are obtained with developed semi-analytical technique i.e. Adomian decomposition method. Validation of the said problem is also conducted with earlier literature computed by Runge-Kutta shooting technique

Non-Linear And Non-Stationary Modes Of The Lower Branch Of The Incompressible Boundary Layer Flow Due To A Rotating Disk

In this paper a theoretical study is undertaken to investigate the structure of the lower branch neutral stability modes of three-dimensional small disturbances imposed on the incompressible Von Karman's boundary layer flow due to a rotating disk. Particular attention is given to the short-wavelength non-linear non-stationary crossflow vortex modes at sufficiently high Reynolds numbers with reasonably small scaled frequencies. Following closely the asymptotic frameworks introduced in [Proc. Roy. Soc. London Ser. A 406 (1986), 93-106] and [Proc. Roy. Soc. London Ser. A 413 (1987), 497-513] for the stationary linear and non-linear modes, it is revealed here that the non-stationary modes with sufficiently long time scale can also be described by an asymptotic expansion procedure based on the triple-deck theory. Making use of this approach, which takes into account the non-linear and non-parallel effects, the asymptotic structure of the non-stationary modes is shown to be adjusted by a balance between viscous and Coriolis forces, and resulted from the fact of vanishing shear stress at the disk surface. As a consequence of the matching of the solutions in adjacent regions it is found that in the linear case the wavenumber and the orientation of the lower branch modes are governed by an eigenrelation, which is akin to the one obtained previously in [Proc. Roy. Soc. London Ser. A 406 (1986), 93-106] for the stationary modes. The asymptotic theory shows that the non-parallelism has a destabilizing effect. A Landau-type equation for the modulated vortex amplitude with coefficients that are often difficult to get from finite Reynolds number computations has also been obtained from a weakly non-linear analysis in the limit of infinitely large Reynolds numbers. The non-linearity has also been found to be destabilizing for both positive and negative frequency waves, though finite amplitude growth of a disturbance having positive frequency close to the neutral location is more effective.WoSScopu

Influence Of Suction/Blowing On The Finite Amplitude Disturbances Having Non-Stationary Modes Of A Compressible Boundary Layer Flow

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Is Homotopy Perturbation Method the Traditional Taylor Series Expansion

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