No abstract

The goal of the current analysis is to scrutinize the magneto-mixed convective flow of aqueous-based hybrid-nanofluid comprising Alumina and Copper nanoparticles across a horizontal circular cylinder with convective boundary condition. The energy equation is modelled by interpolating the non-linear radiation phenomenon with the assisting and opposing flows. The original equations describing the magneto-hybrid nanofluid motion and energy are converted into non-dimensional equations and solved numerically using a new hybrid linearization-Chebyshev spectral method (HLCSM). HLCSM is a high order spectral semi-analytical numerical method that results in an analytical solution in η-direction and thereby the solution is valid in overall the η-domain, not only at the grid points. The impacts of diverse parameters on the allied apportionment are inspected, and the fallouts are described graphically in the investigation. The physical quantities of interest containing the drag coefficient and the heat transfer rate are predestined versus fundamental parameters, and their outcomes are elucidated. It is witnessed that both drag coefficient and Nusselt number have greater magnitude for Cu-water followed by hybrid nanofluid and Al2O3-water. Moreover, the value of the drag coefficient declines versus the enlarged solid volume fraction. To emphasize the originality of the current analysis, the outcomes are compared with quoted works, and excellent accord is achieved in this consideration.

Recently, a conformable fractional derivative has been proposed to calculate the derivative of non-integer order of time functions. It has been shown that this new fractional derivative definition obeys many advantages over the preceding definitions. For mathematical models in applied sciences and to preserve the dimensionality of the physical quantities, an auxiliary parameter (σ) which has the dimension of seconds should be implemented in the fractional derivative definition. We obtain analytic solutions for the resulting conformable fractional differential equations describing the vertical velocity and the height of the falling body. It is shown that the dimensions of velocity and height are always correct without any restrictions on the auxiliary parameter σ which contradicts with the results in the literature when applying the Caputo definition to the same problem. This may open the door for many future works either to describe the role of such an auxiliary parameter or to derive a more suitable definition for the fractional derivative.

No abstract

No abstract

No abstract

No abstract

This paper re-analyzes the falling body problem in three dimensions, taking into account the effect of the Earth’s rotation (ER). Accordingly, the analytic solution of the three-dimensional model is obtained. Since the ER is quite slow, the three coupled differential equations of motion are usually approximated by neglecting all high order terms. Furthermore, the theoretical aspects describing the nature of the falling point in the rotating frame and the original inertial frame are proved. The theoretical and numerical results are illustrated and discussed.