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This study presented various types of soliton solutions for the nonlinear integrable Kairat-X equation by utilizing the improved F-expansion technique with symbolic computational software Mathematica. Explored results for the nonlinear integrable Kairat-X equation are interesting, novel, and more general with different physical structures of solitary waves and solitons, such as kink wave, mixed dark–bright, peakon, anti-kink wave, bright, anti-kink dark, periodic, and dark solitons. With numerical simulations, the secured soliton solutions visualized in two-dimensional, three-dimensional, and contour graphs represent the physical phenomena of the demonstrated results. The explored soliton solutions will be helpful to comprehend interesting physical structures in fiber optics, nonlinear optics, ferromagnetic dynamics, and many other scientific fields. The extracted soliton structure sheds light that the enhanced technique is effective, powerful, concise, and reliable. We can also investigate the soliton results of other nonlinear integrable partial and fractional equations. [ABSTRACT FROM AUTHOR]

In this paper a free convection unsteady Brinkmann hybrid nanofluids including two or more nanoadditives to the host liquid is investigated. The physical flow phenomena are illustrated using PDE and thermophysical nanoparticle properties, and this paper addresses the Brinkmann fractional fluid along with chemical reaction and heat generation with ramped conditions over an inclined vertical plate. The heat and molecular fluxes are generalized using the novel fractional derivative. The present flow model are solved semi-analytically using the Laplace transform. The effects of different parameters specially fractional parameter are deliberated and plotted graphically. The acquired results reveal that fractional parameters have dual behavior in velocity profiles and temperature profile. Velocity and temperature are also compared to previous studies. Compared to the other fractional derivatives results, field variables and proposed hybrid fractional derivatives showed a more decaying trend. [ABSTRACT FROM AUTHOR]

The lattice Boltzmann method has become a promising numerical technique and is now being considered as an alternative to the conventional CFD methods owing a possibility to simulate more complex geometries at relatively low computational costs. The simulations of complex and very fine resolution computational domains in CFD is challenging due to the lack of memory resources and long processing times, therefore parallel computing is being considered as a promising way to cope with this ever increasing mission of computational power. In this work parallelization of 2-D lattice Boltzmann model based CFD code using message passing interface was performed to increase speedup factor for parallel computing. Lattice Boltzmann approach based CFD code of a benchmark Lid driven cavity flow problem was parallelized using different message passing interface subroutines and made to run on a cluster system of processors. The time and speed up factor for execution of the benchmark problem was investigated. The results showed that these message passing communications have little influence on the performance of the parallel lattice Boltzmann method. [ABSTRACT FROM AUTHOR]