‎The main goal of this research work is to provide a numerical technique based on choosing a set of basis functions for handling the third-order time-fractional Korteweg–De Vries Burgers' equation‎. ‎The trial functions are selected for the shifted second-kind Chebyshev polynomials (S2KCPs) compatible with the problem's governing initial and boundary conditions‎. ‎The spectral tau method transforms the equation and its underlying conditions into a nonlinear system of algebraic equations that can be efficiently numerically inverted with the standard Newton's iterative procedures after the approximate solutions have been expressed as a double expansion of the two chosen basis functions‎. ‎The truncation error is estimated‎. ‎Various numerical examples are displayed together with comparisons to other approaches in the literature to show the applicability and accuracy of the provided methodology‎. ‎Different numerical models are displayed and compared to other methods in the literature‎.

In this article, the ways where thermal radiation, besides other sources of heat, influence the magnetohydrodynamic stream of a Jeffery nanofluid across a widening sheet is investigated. To recover the accuracy of the nanofluid model, the effects of viscous indulgence, chemical response, Brownian motion, and thermophoresis have all been incorporated. The mathematical model of this system is first determined in PDEs format and then turned into ODEs format by similarity process. The numerical simulation of the ensuing nonlinear ODEs with subsequent periphery conditions is established by employing the Runge-Kutta fourth-order integration scheme with the Shooting technique. The role of various stream considerations on stream, temperature, nanoparticle concentration, skin friction coefficient, Nusselt and Sherwood quantities are conveyed and explored in graphs and tables. In a limiting sense, the legitimacy of computational outcomes is assessed by comparing them to previously published data. The stream distribution quickens as the Deborah quantity accumulates, whereas the temperature and concentration profiles reflect the downward pattern.

The purpose of the present communication is to investigate the flow of a radiative electromagnetic-Casson nanofluid past a stretching sheet under the impacts of a chemical reaction and nonlinear thermal radiation. To enrich the blood flow, a modulated viscosity/thermal conductivity dependent temperature/nanoparticles concentration parameter is included in the governing equations. The system of PDEs is transformed to ODEs by invoking similarity transformations and then solved numerically by the well- known fourth-order Runge-Kutta integration scheme based on Shooting approach. The main factors affecting the Casson fluid’s temperature profiles are revealed.

Natural vibration sources are multiple. Those due to the explosions of mine can be dangerous. During the fracture a considerable energy propagated in the form of seismic waves generating a series of vibratory movements on the ground surface witch are transmitted to the constructions trough the foundations. The aim of this paper is to study the effects of the vibrations due to the Shootings of mine of the quarriers Socar and Altro companies located at Mechta Bouzitoune on neighbouring constructions of the city Elwième, 50 residences at Héliopolis, in the east of Algeria, which are characterized by the appearance of the cracks in the masonry walls on all the height of the buildings. It resides in the determination of the acceptable explosive load, particulate speed threshold, the radius of safety and the level of the vibrations on the level of constructions for compared with the principal standards and international recommendations.