Efficient approaches of determining the motion of a spherical particle in a swirling fluid flow using weighted residual methods

The motion of a spherical particle released in a swirling fluid flow is studied employing the least-squares method and method of moments. The governing equations are obtained and solved employing the two methods. The accuracy of the results is examined against the results of a fourth-order Runge-Kutta numer- ical method. The effects of various parameters, namely the initial radius, initial radial velocity, initial angular velocity, and drag-to-inertia ratio, on the non-dimensional velocity profiles and particle position distribution are considered. The results show that the radial velocity increases over time while the angular velocity decreases, and that an increase in the initial radial velocity increases the particle radial distance and angular velocity but decreases the radial velocity profile.

Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes by Algebraic Method

In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebraic Method （AGM）. Comparisons have been made between AGM and Numerical Solution, and these results have been indicated that this approach is very efficient and easy so it can be applied for other nonlinear equations. It is citable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods, so far, they have not had acceptable solutions. The simplification of the solution procedure in Algebraic Method and its application for solving a wide variety of differential equations not only in Vibrations but also in different fields of study such as fluid mechanics, chemical engineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlinear differential equations.

Analysis of turbulent MHD Couette nanofluid flow and heat transfer using hybrid DTM-FDM

Unsteady turbulent magnetohydrodynamic nanofluid hydrothermal treatment is studied. The zero- equation turbulence model is used to simulate turbulent flow. The modeling results obtained by applying the hybrid differential transformation method-finite difference method to solve this problem confirm its viability. An analytical procedure is used for finding the effects of the problem parameters. Results indicate that the average Nusselt number over the lower plate depends linearly on volume fraction of nanofluid, Hall parameter, turbulent Eckert number, and Reynolds number whereas it is inversely proportional on the Hartmann number and the turbulent parameter.

Mixed convection of alumina-water nanofluid inside a concentric annulus considering nanoparticle migration

A theoretical investigation was conducted of laminar fully developed mixed convection of alumina-water nanofluid through a vertical annulus, to improve its heating/cooling performance. We focused on con- trolling the nanoparticle migration and studying how it affected the heat transfer rate and pressure drop. Because the nanoparticles have very small dimensions, we only considered Brownian motion and ther- mophoretic diffusivity as the main causes of nanoparticle migration. Because thermophoresis is very sensitive to temperature gradients, we imposed various temperature gradients using asymmetric heat- ing. Considering hydrodynamically and thermally fully developed flow, the governing equations were reduced to two-point ordinary boundary value differential equations and were solved numerically. The imposed thermal asymmetry changed the direction of nanoparticle migration and distorted the velocity, temperature, and nanoparticle concentration profiles. Moreover, we found optimum values for the radius ratio （ζ） and heat flux ratio （ε）; with these optimum values, the nanofluid enhanced the efficacy of the system.