A two-dimensional numerical simulation is performed to investigate the drag reduction and vortex shedding suppression behind three square cylinders with attached splitter plates in the downstream region at a low Reynolds number (Re = 150). Numerical calculations are carried out using the lattice Boltzmann method. The study is carried out for various values of gap spacing between the cylinders and different splitter plate lengths. The vortices are completely chaotic at very small spacing, as observed. The splitter plates are critical in suppressing shedding and reducing drag on the objects. The splitter plates with lengths greater than two fully control the jet interaction at low spacing values. There is maximum percentage reduction in C_Dmean for small spacing and the selected largest splitter plate length. Furthermore, systematic investigation reveals that splitter plates significantly suppress the fluctuating lift in addition to drastically reducing the drag.

Numerical simulations are carried out to study the flow around two tandem square cylinders (SC) under the effect of spacing ratio(g/D) and splitter plate length (l/D) for a fixed Reynolds number (Re)=100. The g/D is varied from 0 to 10 and l/D is varied from 0.5 to 10. The splitter plate length is found to have strong effect on vortex shedding and fluid forces. The maximum reduction in mean drag coefficient is observed at l/D=8, that is 15 and 78 for upstream and downstream cylinders, respectively. The maximum reduction in root-mean-square value of lift coefficient is found at l/D=10, that is 99. The flow pattern at both of these points is steady flow. There is 100 vortex shedding suppression for l/D>5. The observed flow patterns for flow past tandem cylinders without splitter plate are; single bluff body (SBB), steady flow (SF), quasi-steady flow (QSF), fully developed flow (FDF) and fully developed two-row vortex street flow (FDTRVS) regimes. SBB, QSF and SF regimes were observed in presence of splitter plate.

The flow past three square cylinders of unequal size placed in an inline arrangement is studied using the lattice Boltzmann method at different Reynolds numbers [Re = (u∞ d)/ν] within the range of Re = 120, 150, 160, 175, and 200 for various gap spacings (g = s/d), ranging from 1 to 6. This study focused on the symmetric examination of flow behavior for various gap spacing within the three unequal-sized square cylinders. The main objective of this study was to investigate the effects of Reynolds numbers and gap spacing for flow structure mechanism and vortex shedding suppression in between the gap and down-stream position of all three cylinders. Results are obtained in terms of vorticity contours visualization, drag and lift coefficients, Strouhal number, and physical parameters. In vorticity contour visualization, different flow behaviors are observed, known as flow regimes, and are named according to their characteristics, and they are (i) steady flow regime, (ii) shear layer reattachment flow regime (SLR), (iii) fully developed vortex shedding flow regime, (iv) two-row fully developed vortex shedding flow regime, and (v) fully developed irregular vortex shedding flow regime. The present study also includes a discussion on aerodynamic forces, namely the mean drag coefficient (Cdmean), root mean square of the lift coefficient (Clrms), and Strouhal numbers (St) for three cylinders with sizes d = 20, d1 = 15, and d2 = 10, respectively. The maximum value of Cdmean for the first cylinder (C1) is obtained at (Re, g) = (200, 3) that is, 1.5156, where the existing flow regime is the SLR flow regime, while for C2 and C3, the maximum Cdmean values are examined at critical flow behaviors, where the existing flow regime is a fully developed irregular vortex shedding flow regime. Negative values of Cdmean are also examined for cylinders C2 and C3 at some combinations of (Re, g), attributed to the effect of thrust. Furthermore, it is noticed that the values of Strouhal number are increased with an increment in values of gap spacing. The highest value of the Strouhal number for all three cylinders is observed for C1 at (Re, g) = (120, 5), reaching 0.1556 along with a two-row fully developed flow regime. Furthermore, it is investigated from the present problem that the position of unequal sized square cylinders strongly influenced the flow structure mechanism. The information found and discussed in this study could be effective for structure designing arrangement in the case of three square cylinders of unequal size placed in a horizontal arrangement.

In this manuscript we recommend a new description of the modified Fourier transform for a function which is absolutely integrable, having finite number of maxima and minima and finite number of discontinuities which further takes the form of simple Fourier transform for substituting α = e where α > 0 and α ≠ 1. Moreover we prove various results of the modified Fourier transform and also we show that the set that consists of whole modified Fourier transformable functions under the convolution operation is a commutative semi group as well as form an abelian group under the operation of addition

In this article, we conducted a numerical study on the solution of the fractional diffusion equations combined with the temperature equation. These are one-dimensional coupled parabolic equations with a fractional derivative solved by the finite element method and the finite difference method. We applied the fractional Caputo operator to the Jeffrey fluid model equation and obtained the fractional diffusion equation as a result. Fractional differential terms are solved by the finite difference method, and non-fractional derivatives are solved by the finite element method. Numerical convergence of the scheme is applied through theoretical error estimation and the system is analyzed graphically. An algorithm simulated in MATLAB that graphs the results of various dimensionless physical and fractional parameters.