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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Three scolopacids out of 150 are found infected with Haemoproteus scolopaci Galli-
Valerio 1929 and H. tringae n. sp. A detailed description of the new taxon is presented along
with a comparison of the diagnostic measurements between the two species.
A numerical investigation has been performed to study the effect of eccentricity on unsteady state, laminar aiding mixed convection in a horizontal concentric and eccentric cylindrical annulus. The outer cylinder was kept at a constant temperature
while the inner cylinder was heated with constant heat flux. The study involved numerical solution of transient momentum (Navier-Stokes) and energy equation using finite difference method (FDM), where the body fitted coordinate system (BFC) was
used to generate the grid mesh for computational plane. The governing equations were transformed to the vorticity-stream function formula as for momentum equations and to the temperature and stream function for energy equation.
A computer progra
This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-
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In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi
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In this paper, our purpose is to study the classical continuous optimal control (CCOC) for quaternary nonlinear parabolic boundary value problems (QNLPBVPs). The existence and uniqueness theorem (EUTh) for the quaternary state vector solution (QSVS) of the weak form (WF) for the QNLPBVPs with a given quaternary classical continuous control vector (QCCCV) is stated and proved via the Galerkin Method (GM) and the first compactness theorem under suitable assumptions(ASSUMS). Furthermore, the continuity operator for the existence theorem of a QCCCV dominated by the QNLPBVPs is stated and proved under suitable conditions.
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