ANALYSIS OF THE FLOW OF BRINKMAN-TYPE NANOFLUID USING GENERALIZED FOURIER’S AND FICK’S LAWS

The enhancement of the working ability of the industrial fluid is the need of the present era; nanofluid is an emerging field in science and technology. In this study, the Brinkman-type fluid model is used and is generalized using the Fourier’s and Fick’s laws. The graphene oxide nanoparticles are dispersed in the base fluid water. The fractional partial differential equations are then solved via the Laplace and Fourier transform method. The obtained solutions for velocity, heat transfer, and mass transfer are plotted in graphs. The results show that velocity profile decreases for Brinkman-type fluid parameter and volume fraction of the nanoparticles. The plot for the fractional parameter shows that different plots can be drawn for a fixed time and other physical parameters, which is the memory effect.

A mathematical model for the spread of oil spills in high seas

This study aims to model the distribution pattern of oil spills in high seas with the influence of wind movements. The mathematical model is derived from the random walk process of the oil spill particles by using a probability measure on a unit circle with the help of Laplace and Fourier transform . The solution to the model is also obtained by using Laplace and the Fourier transform. Based on the analysis of the solution of the model, the oil spill tends to spread in the direction of wind movement.. The speed and direction of the wind movement affect the speed and direction of the spread of the oil spill particles. The larger the speed of wind movement, the faster the oil particles movement.

A numerical method for the fractional Schrödinger type equation of spatial dimension two

This work focuses on an investigation of the (n+1)-dimensional time-dependent fractional Schrödinger type equation. In the early part of the paper, the wave function is obtained using Laplace and Fourier transform methods and a symbolic operational form of the solutions in terms of Mittag-Leffler functions is provided. We present an expression for the wave function and for the quantum mechanical probability density. We introduce a numerical method to solve the case where the space component has dimension two. Stability conditions for the numerical scheme are obtained.

Generalized GL Fractional Derivative and Its Laplace and Fourier Transform

It is well known the difficulties that the Riesz fractional derivative present, as the spatial fractional derivative involved in many models of the dynamics of anomalous processes. The generalized Gru¨nwal-Letnikov fractional derivative is analysed in this paper. Its Laplace and Fourier Transforms are computed and some current results criticized. It is shown that only the forward derivative of a sinusoid exists. This result is used to define the frequency response of a fractional linear system.

On Dynamics of Bar of Rectangular Cross Section

The propagation of nonstationary waves in semi-infinite elastic rectangular bars is studied. It is assumed that two opposite lateral surfaces of the body are free of forces, while the two others are subjects to cross conditions. By introducing three new potential functions, the author succeeded in getting closed-form solutions in Laplace and Fourier transform parameters. Inversion of the transform solutions, carried out by an original method of inversion, is suggested herein.

Response of Systems With Damping Materials Modeled Using Fractional Calculus

The mathematical modeling of damping materials based on fractional calculus has been shown to be very effective in representing the frequency dependence of the properties of these materials. In this model, the integer order derivatives in the constitutive equations of the Kelvin model are replaced by derivatives of fractional order. In this paper, we examine the response of a single degree-of-freedom system in which the damping force is proportional to a derivative of order α < 1 of the displacements. Three methods are proposed to obtain the response: the Laplace and Fourier transform methods, and an operator method that results in a series solution. Some interesting features exhibited by the oscillator’s response due to the fractional representation of the damping are unveiled.

Sudden Appearance of a Crack in a Stretched Finite Strip

The dynamic response of a central crack in a finite elastic strip was considered in this study. The crack was assumed to appear suddenly when the strip is being stretched at its two ends. Laplace and Fourier transform techniques were used to formulate the mathematical solution. Numerical results on the dynamic stress-intensity factor were obtained. The influence of inertia, finite boundaries and their interactions on the load transmission to the crack tip were discussed.