In this paper, we have investigated the recirculation flow of a nanofluid in the developed flow zones of an infinite periodic nanotube with a hexagonal cross-section. A numerical analysis is commenced to identify the existence of single and double recirculation zones for various geometric
parameters. The boundary element method (BEM) has been formulated for an unbound interim nanotube for solving the governing equations. We have developed the codes for the BEM method in FORTRAN 90, and the graphs have been plotted in MATLAB 2016. We have various geometric parameters to inaugurate
circumstances for the onset of recirculation. We have found recirculation flow through this type of periodic tube for a set of geometric parameters such as amplitude, wavelength and throat radius etc. Firstly recirculation flow in the expansion region of the nanotube is prophesied to arrive
beyond a critical amplitude and second order recirculation zone is also predicted for still higher amplitudes. The recirculation flow has great importance in the application, for example, it can be used in the particle separation process.
Wavelet analysis uses as a new class of orthogonal expansion in with regularity-approximation properties. In this study, we approximate any general function in by Haar wavelet in different smoothness spaces such as Lebesgue space, Lipschitz continuous space, Sobolev and Besov spaces.
When an integral equation is solved by using the Fourier series then the solution represents a stationary signal. Usually, integral equation is solved by the successive approximation method and the resolvent kernel method in which the solution is not of Fourier series type and this solution does not represent a stationary signal. In this paper, our main goal is to determine the solution of a Fredholm integral equation of first kind by using the Fourier series.
Matrix factorization is the process that transforms a matrix into the product of some constituent matrices. This is comparable to factoring a number into the product of several numbers. Matrix splitting methods are similar to matrix factorization process which transforms a matrix into the sum of some basis matrices. In this short review article, we address the different types of matrix factorization and matrix splitting methods as well as their applications in the physical problems rather than exhibiting their computational procedure. Some matrix structural facts are shown to exhibit the fundamental pattern of different matrix decompositions.
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