Numerical simulation of flow around a triangular cylinder placed both in left and right position at Reynolds number Re = 80–200 is presented in this study. The single relaxation time lattice Boltzmann method is used. The results are obtained in terms of vorticity contour visualization, drag and lift coefficients, and force statistics. Regular vortex shedding is observed for both cases, but the vortices generated for a triangular cylinder placed in the right position move toward the top downstream position as the range of Reynolds number increases due to effect of pressure (effect of thrust). The drag coefficient is constant, and lift coefficient is containing negative values from Re = 80–150 for that case, but negative Cdmean values are not observed for a triangular cylinder placed in the left position. In that case, it is due to the reason that the effect of thrust diminishes. The maximum value of Cdmean is obtained at Re = 200, that is, 1.5006 for the left triangular cylinder, but the value of the mean drag coefficient for the right triangular cylinder is zero throughout the cases for Re = 80–200. No fluid forces are produced for right triangular case. The Strouhal number (St) values increased by increasing the Reynolds number, i.e., Re = 80–200, for the right triangular cylinder, and it has a mixed trend for the left triangular cylinder. In literature, a lot of work has been found on rectangular and square cylinders, but triangular cylinder has not been studied much.

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.

A two-dimensional numerical study is conducted to investigate the effect of a control plate length on flow past over a triangular rod through a lattice Boltzmann method. The Reynolds number (Vmax d/ν) is taken within the range from Re = 50–200, and the length (L) of the control plate is varied from L = 1–5. First, we checked the adequacy of a grid point by selecting different values of grids and studied the effect of a computational domain at different values of upstream (Lu), downstream (Ld) distances and changing the height (H) of the channel. After that, we studied the effect of fluid forces on flow past a single triangular rod and then by attaching the control plate by varying its length. The results are obtained in terms of vorticity contour, drag (CD) and lift (CL) coefficients, and calculation of physical parameters (CDmean, CDrms, CLrms, and St). In terms of vorticity contour, we examined four various types of flow regimes. These are (i) steady flow regime (SFR), (ii) quasi-steady flow regime (QSFR), (iii) shear layer reattachment flow regime, and (iv) single bluff body flow regime based on the flow structure mechanism. In calculation of physical parameters, we observed that the mean drag coefficient contains a maximum value for the case of the single triangular rod as compared to presence of the attached control plate. Second, it is noticed that, as the Reynolds number increases, the values of CDmean gradually decreases, but at the highest range of Reynolds number and largest length of the control plate, the value of the mean drag coefficient increases and produces more fluid forces. CDrms also shows similar behavior like CDmean. The root mean square values of lift coefficients become zero at (L, Re) = (1, 50), (2, 50), (2, 80), (3, 50), (3, 80), (3, 100), (4, 50), (4, 80), (4, 100), (4, 120), (5, 50), (5, 80), (5, 100), (5, 120), and (5, 150), respectively. The St containing maximum value at (L, Re) = (2, 200) and minimum value at (L, Re) = (5, 200). Furthermore, at lengths L = 1–5, the value of St = 0 due to no lift forces at (L, Re) = (1, 50), (2, 50), (3, 50), and (4, 50) and (2, 80), (3, 80), (3, 100), (4, 120), and (5, 150), respectively. The maximum reduction in CDmean is found to be about 16.89%. Overall, the findings suggest complex interactions between Reynolds number, control plate length, and various coefficients, impacting the flow structure and shedding characteristics.

This Paper is included fuzzy concepts of Mellin transform along with its operational properties. Mellin transform method is applicable in fuzzy context. The study involved the proposed techniques for solving initial and boundary value fuzzy differential equations under strongly generalized differentiability concepts.

This chapter has included the application of fractional integral transform in the fuzzy field by presenting the solution of fuzzy fractional differential equations with the help of different integral transforms Laplace, Mellin, and Sumudu fuzzy transforms. These integral transforms are properly defined with their operational properties and are particularly described in differential and integral fractional calculus. The main results and discussion of the present research study about the applications of fractional integral transform are analyzed in this chapter with analytical solutions. The key features of this work are to discuss different integral transforms in a fuzzy theory and name it fuzzy integral transform with all its basic concepts. A procedure is established to solve fuzzy initial value problems (FIVP) by the fractional Mellin transforms and fractional Laplace and fractional Sumudu integral transform techniques, by applying the differential properties of fractional integral transforms, under a mathematical framework to solve the several types of differential equations.