The BEK family of flows have many important practical applications such as centrifugal pumps, steam turbines, turbo-machinery and rotor-stator devices. The Bödewadt, Ekman and von Kármán flows are particular cases within this family. The convective instability of the BEK family of rotating boundary-layer flows has been considered for generalised Newtonian fluids, power-law and Carreau fluids. A linear stability analysis is conducted using a Chebyshev collocation method in order to investigate the effect of shear-thinning and shear-thickening fluids for generalised Newtonian fluids on the convective Type I (inviscid crossflow) and Type II (viscous streamline curvature) modes of instability. The results reveal that shear-thinning power-law fluids have a universal stabilising effect across the entire BEK family of flows. However, the convective instability characteristics for the shear-thinning and shear-thickening Carreau fluids are affected by the value of the relaxation parameter k. The results reveal that Shear-thinning Carreau fluids have a small destabilising effect, while shear -thickening fluids have a slight stabilising effect on the Type I and Type II mode for the BEK family of flows when k =100. On the other hand, shear-thinning and shear-thickening Carreau fluids are found to have stabilising and destabilising effect, respectively for optimal relaxation value ko. The results are presented in terms of neutral curves and growth rates. Furthermore, an energy analysis is presented to gain insight into the underlying physical mechanisms behind the stabilising effects of generalized Newtonian fluids. In conclusion, the use of shear-thinning power-law and Carreau fluids with optimal value ko can be recommended to reduce skin-friction drag in enclosed rotor-stator devices for the entire BEK family of flows.
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... Show MoreIn this paper, we present new algorithm for the solution of the nonlinear high order multi-point boundary value problem with suitable multi boundary conditions. The algorithm is based on the semi-analytic technique and the solutions are calculated in the form of a rapid convergent series. It is observed that the method gives more realistic series solution that converges very rapidly in physical problems. Illustrative examples are provided to demonstrate the efficiency and simplicity of the proposed method in solving this type of multi- point boundary value problems.
Critical buckling and natural frequencies behavior of laminated composite thin plates subjected to in-plane uniform load is obtained using classical laminated plate theory (CLPT). Analytical investigation is presented using Ritz- method for eigenvalue problems of buckling load solutions for laminated symmetric and anti-symmetric, angle and cross ply composite plate with different elastic supports along its edges. Equation of motion of the plate was derived using principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. Various numerical investigation were studied to exhibit a convergence and accuracy of the present solution for considering some design parameters such as edge
... Show MoreBuckling analysis of a laminated composite thin plate with different boundary conditions subjected to in-plane uniform load are studied depending on classical laminated plate theory; analytically using (Rayleigh-Ritz method). Equation of motion of the plates was derived using the principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. The eigenvalue problem generated by using Ritz method, the set of linear algebraic equations can be solved using MATLAB for symmetric and anti-symmetric, cross and angle-ply laminated plate considering some design parameters such as aspect ratios, number of layers, lamination type and orthotropic ratio. The results obtained g
... Show MoreThis work aims to find a solution to the problem under investigation and to study non-local boundary-value problems for rectangular domains and two-dimensional thirdorder partial differential equations (PDEs). A finite-difference method combined with the trapezoidal rule is used to solve problems. The numerical results were determined to be steady and accurate.
Numerical study of separation control on symmetrical airfoil, four digits (NACA
0012) by using rotating cylinder with double steps on its upper surface based on the computation of Reynolds-average Navier- Stokes equations was carried out to find the optimum configuration of unconventional airfoil for best aerodynamics performance. A model based on collocated Finite Volume Method was developed to solve the governing equations on a body-fitted coordinate system. A revised (k-w) model was proposed as a known turbulence model. This model was adapted to simulate the control effects of rotating cylinder. Numerical solutions were performed for flow around unconventional airfoil with cylinder to main stream velocities ratio in the range
... Show MoreCriticism is inherently impolite and a face-threatening act generally leading to conflicts among interlocutors. It is equally challenging for both native and non-native speakers, and needs pre-planning before performing it. The current research examines the production of non-institutional criticism by Iraqi EFL university learners and American native speakers. More specifically, it explores to what extent Iraqi EFL learners and American native speakers vary in (i) performing criticism, (ii) mitigating criticism, and (iii) their pragmatic choices according to the contextual variables of power and distance. To collect data, a discourse-completion task was used to elicit written data from 20 Iraqi EFL learners and 20 American native speaker
... Show MoreThe present study considers to confirming the applicability of flow with double-sided square lid driven cavity flow by using the lattice Boltzmann equation with moment-based boundary conditions for no slip boundaries. The boundary conditions are applied over the hydrodynamic moments of the lattice Boltzmann equations locally at each node. The investigation is carried out numerically for both single and multiple relaxation time models. To simulate two-sided lid driven-cavity flow, the top and bottom walls are moving with constant velocity while other walls are stationary. Various Reynolds numbers are used in a range of 100 and up to 5000. The present method shows the effect of the moving boundaries on the two symmetrical cavities t
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