A time fractional model of a Maxwell nanofluid through a channel flow with applications in grease.

Several scientists are interested in recent developments in nanotechnology and nanoscience. Grease is an essential component of many machines and engines because it helps keep them cool by reducing friction between their various elements. In sealed life applications including centralized lubrication systems, electrical motors, bearings, logging and mining machinery, truck wheel hubs, construction, landscaping, and gearboxes, greases are also utilized. Nanoparticles are added to convectional grease to improve its cooling and lubricating properties. More specifically, the current study goal is to investigate open channel flow while taking grease into account as a Maxwell fluid with MoS2 nanoparticles suspended in it. The Caputo-Fabrizio time-fractional derivative is used to convert the issue from a linked classical order PDE to a local fractional model. To determine the precise solutions for the velocity, temperature, and concentration distributions, two integral transform techniques the finite Fourier sine and the Laplace transform technique are jointly utilized. The resultant answers are physically explored and displayed using various graphs. It is important to note that the fractional model, which offers a variety of integral curves, more accurately depicts the flow behavior than the classical model. Skin friction, the Nusselt number, and the Sherwood number are engineering-related numbers that are quantitatively determined and displayed in tabular form. It is determined that adding MoS2 nanoparticles to grease causes a 19.1146% increase in heat transmission and a 2.5122% decrease in mass transfer. The results obtained in this work are compared with published literature for the accuracy purpose.

Dynamics of chaotic system based on circuit design with Ulam stability through fractal-fractional derivative with power law kernel.

In this paper, the newly developed Fractal-Fractional derivative with power law kernel is used to analyse the dynamics of chaotic system based on a circuit design. The problem is modelled in terms of classical order nonlinear, coupled ordinary differential equations which is then generalized through Fractal-Fractional derivative with power law kernel. Furthermore, several theoretical analyses such as model equilibria, existence, uniqueness, and Ulam stability of the system have been calculated. The highly non-linear fractal-fractional order system is then analyzed through a numerical technique using the MATLAB software. The graphical solutions are portrayed in two dimensional graphs and three dimensional phase portraits and explained in detail in the discussion section while some concluding remarks have been drawn from the current study. It is worth noting that fractal-fractional differential operators can fastly converge the dynamics of chaotic system to its static equilibrium by adjusting the fractal and fractional parameters.

Fractal fractional analysis of non linear electro osmotic flow with cadmium telluride nanoparticles.

Numerical simulations of non-linear Casson nanofluid flow were carried out in a microchannel using the fractal-fractional flow model. The nano-liquid is prepared by dispersing Cadmium Telluride nanoparticles in common engine oil. Using relative constitutive equations, the system of mathematical governing equations has been formulated along with initial and boundary conditions. Dimensionless variables have been used to obtain the non-dimensional form of the governing equations. The fractal-fractional model has been obtained by employing the fractal-fractional operator of the exponential kernel. As the exact solution of the non-linear fractal-fractional model is very tough to find, therefore the formulated model has been solved numerically via the Crank-Nicolson scheme. Various plots are generated for the inserted parameters. From the analysis, it has been observed that a greater magnitude of the electro-kinetic parameter slows down the fluid's velocity. It is also worth noting that the fractional and classical models can also be derived from the fractal-fractional model by taking the parameters tend to zero. From the analysis, it is also observed that in response to 0.04 volume fraction of cadmium telluride nanoparticles, the rate of heat transfer (Nusselt number) and rate of mass transfer (Sherwood number) increased by 15.27% and 2.07% respectively.

MHD flow of time-fractional Casson nanofluid using generalized Fourier and Fick's laws over an inclined channel with applications of gold nanoparticles.

Gold nanoparticles are commonly used as a tracer in laboratories. They are biocompatible and can transport heat energy to tumor cells via a variety of clinical techniques. As cancer cells are tiny, properly sized nanoparticles were introduced into the circulation for invasion. As a result, gold nanoparticles are highly effective. Therefore, the current research investigates the magnetohydrodynamic free convection flow of Casson nanofluid in an inclined channel. The blood is considered as a base fluid, and gold nanoparticles are assumed to be uniformly dispersed in it. The above flow regime is formulated in terms of partial differential equations. The system of derived equations with imposed boundary conditions is non-dimensionalized using appropriate dimensionless variables. Fourier's and Fick's laws are used to fractionalize the classical dimensionless model. The Laplace and Fourier sine transformations with a new transformation are used for the closed-form solutions of the considered problem. Finally, the results are expressed in terms of a specific function known as the Mittag-Leffler function. Various figures and tables present the effect of various physical parameters on the achieved results. Graphical results conclude that the fractional Casson fluid model described a more realistic aspect of the fluid velocity profile, temperature, and concentration profile than the classical Casson fluid model. The heat transfer rate and Sherwood number are calculated and presented in tabular form. It is worth noting that increasing the volume percentage of gold nanoparticles from 0 to 0.04 percent resulted in an increase of up to 3.825% in the heat transfer rate.