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Fractional analysis provides useful tools to describe natural phenomena, and therefore, it is more convenient to describe models of satellites. This work illustrates rich chaotic behaviors that exist in a fractional-order model for satellite with and without time-delay. The proof for existence and uniqueness of the satellite model’s solution with and without time-delay is shown. Chaos control is achieved in this system via a simple linear feedback control criterion. Chaotic attractors and chaos control are also found in a time-delay version of the proposed fractional-order satellite system. Various tools based on numerical simulations such as 2D and 3D attractors and bifurcation diagrams are used to illustrate the variety of rich chaotic dynamics in the satellite models.

There are many debates on the preparation methods and the role of ultrasonication on the stability, thermophysical properties, and heat transfer performance of nanofluids. The present study, which is the continuation of the authors previous study, the effects of ultrasonication on the thermal and fluid dynamic performance of MWCNT-water nanofluid, over a different range of temperatures and solid concentrations, based on the thermophysical properties of the nanofluid, has been investigated. The effects of ultrasonication time on the stability and thermophysical properties of the nanofluid were studied over 30 days of the samples preparation. The thermophysical properties of the nanofluid have been experimentally measured at the optimum ultrasonication time. Using the experimental data, and employing different figures-of-merit, the effects that the addition of MWCNTs had on the heat transfer effectiveness and pumping power have been studied. It was confirmed that the nanofluid is a good heat transfer fluid, with a negligible penalty in pumping power. The thermal and fluid dynamic performance of the nanofluid in a microchannel heat sink has also been studied, by comparing the enhancement ratio of the convective heat transfer coefficient and the increase in pumping power.

The thin film flow of micropolar fluid in a porous medium under the influence of thermophoresis with the heat effect past a stretching plate is analyzed. Micropolar fluid is assumed as a base fluid and the plate is considered to move with a linear velocity and subject to the variation of the reference temperature and concentration. The latitude of flow is limited to being two-dimensional and is steadily affected by sensitive fluid film size with the effect of thermal radiation. The basic equations of fluid flow are changed through the similarity variables into a set of nonlinear coupled differential equations with physical conditions. The suitable transformations for the energy equation is used and the non-dimensional form of the temperature field are different from the published work. The problem is solved by using Homotopy Analysis Method (HAM). The effects of radiation parameter R, vortex-viscosity parameter Δ, permeability parameter Mr, microrotation parameter Gr, Soret number Sr, thermophoretic parameter τ, inertia parameter Nr, Schmidt number Sc, and Prandtl number Pr are shown graphically and discussed.