Investigation of Entropy in Two-Dimensional Peristaltic Flow with Temperature Dependent Viscosity, Thermal and Electrical Conductivity.

This study comprehensively explores the generalized form of two-dimensional peristaltic motions of incompressible fluid through temperature-dependent physical properties in a non-symmetric channel. Generation of entropy in the system, carrying Joule heat and Lorentz force is also examined. Viscous dissipation is not ignored, for viewing in-depth, effects of heat transmission and entropy production. The modeling of equations is tracked first in fixed and then in wave frame. The resultant set of coupled non-linear equations are solved numerically by utilizing NDSolve in Mathematica. Comparison between NDSolve and the numerical results obtained through bvp4c MATLAB is made for the validation of our numerical codes. The attained results are found to be in excellent agreement. The impact of control parameters on the velocity profiles, pressure gradient, heat transfer, streamlines and entropy production are studied and discussed graphically. It is witnessed that entropy production and heat transfer are increased significantly subject to the enhancement of Hartman number, Brinkman number and electrical conductivity parameter. Hence, choosing appropriate values of physical parameters, performance and efficiency of flow structure and system can be improved. The results reported provide a virtuous insight into bio energy systems providing a useful standard for experimental and extra progressive computational multiphysics simulations.

Bright-Dark and Multi Solitons Solutions of (3 + 1)-Dimensional Cubic-Quintic Complex Ginzburg-Landau Dynamical Equation with Applications and Stability.

In this paper, bright-dark, multi solitons, and other solutions of a (3 + 1)-dimensional cubic-quintic complex Ginzburg-Landau (CQCGL) dynamical equation are constructed via employing three proposed mathematical techniques. The propagation of ultrashort optical solitons in optical fiber is modeled by this equation. The complex Ginzburg-Landau equation with broken phase symmetry has strict positive space-time entropy for an open set of parameter values. The exact wave results in the forms of dark-bright solitons, breather-type solitons, multi solitons interaction, kink and anti-kink waves, solitary waves, periodic and trigonometric function solutions are achieved. These exact solutions have key applications in engineering and applied physics. The wave solutions that are constructed from existing techniques and novel structures of solitons can be obtained by giving the special values to parameters involved in these methods. The stability of this model is examined by employing the modulation instability analysis which confirms that the model is stable. The movements of some results are depicted graphically, which are constructive to researchers for understanding the complex phenomena of this model.

MHD flow of Maxwell fluid with nanomaterials due to an exponentially stretching surface.

In many industrial products stretching surfaces and magnetohydrodynamics are being used. The purpose of this article is to analyze magnetohydrodynamics (MHD) non-Newtonian Maxwell fluid with nanomaterials in a surface which is stretching exponentially. Thermophoretic and Brownian motion effects are incorporated using Buongiorno model. The given partial differential system is converted into nonlinear ordinary differential system by employing adequate self-similarity transformations. Locally series solutions are computed using BVPh 2.0 for wide range of governing parameters. It is observed that the flow is expedite for higher Deborah and Hartman numbers. The impact of thermophoresis parameter on the temperature profile is minimal. Mathematically, this study describes the reliability of BVPh 2.0 and physically we may conclude the study of stretching surfaces for non-Newtonian Maxwell fluid in the presence of nanoparticles can be used to obtain desired qualities.

Explicit Lump Solitary Wave of Certain Interesting (3+1)-Dimensional Waves in Physics via Some Recent Traveling Wave Methods.

This study investigates the solitary wave solutions of the nonlinear fractional Jimbo-Miwa (JM) equation by using the conformable fractional derivative and some other distinct analytical techniques. The JM equation describes the certain interesting (3+1)-dimensional waves in physics. Moreover, it is considered as a second equation of the famous Painlev'e hierarchy of integrable systems. The fractional conformable derivatives properties were employed to convert it into an ordinary differential equation with an integer order to obtain many novel exact solutions of this model. The conformable fractional derivative is equivalent to the ordinary derivative for the functions that has continuous derivatives up to some desired order over some domain (smooth functions). The obtained solutions for each technique were characterized and compared to illustrate the similarities and differences between them. Profound solutions were concluded to be powerful, easy and effective on the nonlinear partial differential equation.

Analysis and Optimal Control of Fractional-Order Transmission of a Respiratory Epidemic Model.

The World Health Organization is yet to realise the global aim of achieving future-free and eliminating the transmission of respiratory diseases such as H1N1, SARS and Ebola since the recent reemergence of Ebola in the Democratic Republic of Congo. In this paper, a Caputo fractional-order derivative is applied to a system of non-integer order differential equation to model the transmission dynamics of respiratory diseases. The nonnegative solutions of the system are obtained by using the Generalized Mean Value Theorem. The next generation matrix approach is used to obtain the basic reproduction number R 0 . We discuss the stability of the disease-free equilibrium when R 0 < 1 , and the necessary conditions for the stability of the endemic equilibrium when R 0 > 1 . A sensitivity analysis shows that R 0 is most sensitive to the probability of the disease transmission rate. The results from the numerical simulations of optimal control strategies disclose that the utmost way of controlling or probably eradicating the transmission of respiratory diseases should be quarantining the exposed individuals, monitoring and treating infected people for a substantial period.

A numerical treatment of MHD radiative flow of Micropolar nanofluid with homogeneous-heterogeneous reactions past a nonlinear stretched surface.

The impact of nonlinear thermal radiation in the flow of micropolar nanofluid past a nonlinear vertically stretching surface is investigated. The electrically conducting fluid is under the influence of magnetohydrodynamics, heat generation/absorption and mixed convection in the presence of convective boundary condition. The system of differential equations is solved numerically using the bvp4c function of MATLAB. To authenticate our results, two comparisons with already studied problems are also conducted and an excellent concurrence is found; hence reliable results are being presented. Complete deliberation for magnetite nanofluid with Ferric Oxide (Fe3O4) nanoparticles in the water-based micropolar nanofluid is also given to depict some stimulating phenomena. The effect of assorted parameters on velocity, homogeneous-heterogeneous reactions, temperature and micropolar velocity profiles are discussed and examined graphically. Moreover, graphical illustrations for the Nusselt number and Skin friction are given for sundry flow parameters. It is examined that temperature distribution and its associated boundary layer thickness increase for mounting values of the magnetic parameter. Additionally, it is detected that the Nusselt number decays when we increase the values of the Biot number.

Nonlinear radiation effect on MHD Carreau nanofluid flow over a radially stretching surface with zero mass flux at the surface.

A mathematical model is envisaged to study the axisymmetric steady magnetohydrodynamic (MHD) Carreau nanofluid flow under the influence of nonlinear thermal radiation and chemical reaction past a radially stretched surface. Impact of heat generation/absorption with newly introduced zero mass flux condition of nanoparticles at the sheet is an added feature towards novelty of the problem. Further, for nanofluid the most recently organized model namely Buongiorno's model is assumed that comprises the effects thermophoresis and Brownian motion. Utilizing suitable self-similar transformations, the set of partial differential equations with high nonlinearity are converted into a dimensionless system of ordinary differential equations. Set of these transmuted equations are numerically solved by MATLAB built-in function bvp4c. Impact of germane parameters on all involved profiles are plotted to examine the heat and mass transfer characteristics. This study reveals that the temperature distribution is an escalating function of the heat generation and nonlinear radiation parameters. Also, it is noted that the incrementing values of chemical reaction parameter lowers the nanoparticles concentration profile. A comparison of the present investigation with already published explorations in limiting case is also added to authenticate the presented results; hence reliable results are being presented.

Entropy Analysis of 3D Non-Newtonian MHD Nanofluid Flow with Nonlinear Thermal Radiation Past over Exponential Stretched Surface.

The present study characterizes the flow of three-dimensional viscoelastic magnetohydrodynamic (MHD) nanofluids flow with entropy generation analysis past an exponentially permeable stretched surface with simultaneous impacts of chemical reaction and heat generation/absorption. The analysis was conducted with additional effects nonlinear thermal radiation and convective heat and mass boundary conditions. Apposite transformations were considered to transform the presented mathematical model to a system of differential equations. Analytical solutions of the proposed model were developed via a well-known homotopy analysis scheme. The numerically calculated values of the dimensionless drag coefficient, local Nusselt number, and mass transfer Nusselt number are presented, with physical insights. The graphs depicting the consequences of numerous parameters on involved distributions with requisite deliberations were also a part of this model. It is seen that the Bejan number is an increasing function of the thermal radiation parameter.

A numerical treatment of radiative nanofluid 3D flow containing gyrotactic microorganism with anisotropic slip, binary chemical reaction and activation energy.

A numerical investigation of steady three dimensional nanofluid flow carrying effects of gyrotactic microorganism with anisotropic slip condition along a moving plate near a stagnation point is conducted. Additionally, influences of Arrhenius activation energy, joule heating accompanying binary chemical reaction and viscous dissipation are also taken into account. A system of nonlinear differential equations obtained from boundary layer partial differential equations is found by utilization of apposite transformations. RK fourth and fifth order technique of Maple software is engaged to acquire the solution of the mathematical model governing the presented fluid flow. A Comparison with previously done study is also made and a good agreement is achieved with existing results; hence reliable results are being presented. Evaluations are carried out for involved parameters graphically against velocity, temperature, concentration fields, microorganism distribution, density number, local Nusselt and Sherwood numbers. It is detected that microorganism distribution exhibit diminishing behavior for rising values of bio-convection Lewis and Peclet numbers.

Buoyancy effects on the radiative magneto Micropolar nanofluid flow with double stratification, activation energy and binary chemical reaction.

A mathematical model has been developed to examine the magneto hydrodynamic micropolar nanofluid flow with buoyancy effects. Flow analysis is carried out in the presence of nonlinear thermal radiation and dual stratification. The impact of binary chemical reaction with Arrhenius activation energy is also considered. Apposite transformations are engaged to transform nonlinear partial differential equations to differential equations with high nonlinearity. Resulting nonlinear system of differential equations is solved by differential solver method in Maple software which uses Runge-Kutta fourth and fifth order technique (RK45). To authenticate the obtained results, a comparison with the preceding article is also made. The evaluations are executed graphically for numerous prominent parameters versus velocity, micro rotation component, temperature, and concentration distributions. Tabulated numerical calculations of Nusselt and Sherwood numbers with respective well-argued discussions are also presented. Our findings illustrate that the angular velocity component declines for opposing buoyancy forces and enhances for aiding buoyancy forces by changing the micropolar parameter. It is also found that concentration profile increases for higher values of chemical reaction parameter, whereas it diminishes for growing values of solutal stratification parameter.

Modified fractional variational iteration method for solving the generalized time-space fractional Schrödinger equation.

Based on He's variational iteration method idea, we modified the fractional variational iteration method and applied it to construct some approximate solutions of the generalized time-space fractional Schrödinger equation (GFNLS). The fractional derivatives are described in the sense of Caputo. With the help of symbolic computation, some approximate solutions and their iterative structure of the GFNLS are investigated. Furthermore, the approximate iterative series and numerical results show that the modified fractional variational iteration method is powerful, reliable, and effective when compared with some classic traditional methods such as homotopy analysis method, homotopy perturbation method, adomian decomposition method, and variational iteration method in searching for approximate solutions of the Schrödinger equations.

Homotopic approximate solutions for the perturbed CKdV equation with variable coefficients.

This work concerns how to find the double periodic form of approximate solutions of the perturbed combined KdV (CKdV) equation with variable coefficients by using the homotopic mapping method. The obtained solutions may degenerate into the approximate solutions of hyperbolic function form and the approximate solutions of trigonometric function form in the limit cases. Moreover, the first order approximate solutions and the second order approximate solutions of the variable coefficients CKdV equation in perturbation εu (n) are also induced.