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Researchers and scientists were inspired by the enormous reactions from industry about heat transformation enhancements due to the entropy generation. The entropy generation shows as a extremes for complex mechanisms like solid state physics, two-phase flows, electro-magnetic air conditioning, and economic evaluation of manufacturing processes, as well as biological technologies chemistry, including biochemistry. We note here that many thermal mechanisms are related to the irreversibility system. The current work focused on the entropy generation impacts in viscous magnetized mono-nanofluids flow between stretchable rotating disks. Ferro and copper are considered as nanoparticles and Blood as a base fluid. The Darcy-Forchheimer porous medium and joule heating effects are considered. For simplifying the current analysis, suitable transformation were introduced in the mathematical description to renovate the partial differential equations (PDE's) into coupled ordinary ones. To solve the resulting ODEs well-known numerical algorithm bvp4c is used in Matlab in the light of Lobatto-IIIA formula. The consequence of sundry parameters against velocity components, pressure field, temperature distribution and entropy generation are described graphically. [ABSTRACT FROM AUTHOR]

Nonlinear evolution equations are employed in the representation of diverse intricate physical events, and the identification of precise solutions for these equations holds significance about their practical implementations. One of the significant challenges is the identification of traveling wave solutions inside established nonlinear evolution systems in the field of mathematical physics. In the present research, we employ the modified sub-equation approach, a very effective and strong technique, to ensure the solutions for the Klein–Gordon featuring cubic nonlinearity and Zakharov Kuznetsov–Benjamin Bona Mahony equations. Several restriction requirements that ensure the existence of these solutions are emphasized. By employing a linearization technique, we ascertain the stability gain. This methodology acquires original precise solutions of soliton nature. Furthermore, the nonlinear wave structures of both equations are illustrated through the consideration of several three-dimensional and two-dimensional plots. These plots are generated by selecting appropriate values for the parameters. It is expected that these innovative solutions would facilitate an in-depth understanding of the evolution and fluidity of these models. The solutions obtained comprise periodic functions, mixed periodic functions, rational solutions, and exponential solutions. • Two nonlinear evolution equations. • Modified sub-equation method. • Exact solution. • Stability analysis. [ABSTRACT FROM AUTHOR]

The primary objective of this study aims to carry out a more thorough investigation into a fractional nonlinear double dispersive equation that is used to represent wave propagation in an elastic, inhomogeneous Murnaghan's rod. By Murnaghan's rod, we mean the materials, which include the constitutive constant, Poisson ratio, and Lame'́s coefficient, are considered to be compressible in nature forming up the elastic rod. To solve the fractional version of Murnaghan's rod problem, we employed β -fractional and M -Truncated fractional derivative. Regarding the extraction of polynomial and rational function solutions of the Murnaghan's rod problem, which degenerate into several wave solutions including solitary, soliton (dromions), as well as periodic wave solutions. We employ the well-known unified and new auxiliary equation methods of nonlinear sciences. A finite series of certain functions satisfying an ordinary differential equation of first order, second degree is used to represent the projected solution. Based on the given approach, numerous types of solutions for exponential, hyperbolic, and trigonometric functions are generated. In this research study, the behavior of a dynamical planer system has been examined by giving various values to parameters and by depicting every possible situation as a phase portrait. The sensitivity analysis, where the soliton wave velocity and wave number parameters influence the water wave singularity, is demonstrated using the wave profiles of the constructed dynamical structural system. With the use of graphs, we have simulated the solitons to determine their kinds. All of solutions found in this manuscript is been confirmed through back substituting them into the original model using computational software. • An investigation to the wave propagation in an elastic, inhomogeneous Murnaghan's rod is considered. • The solutions under Beta and M-Truncated fractional derivatives for this model were found by two different analytical techniques. • The behavior of the dynamical planer system has been examined by depicting every possible situation as a phase portrait. • The sensitivity analysis is demonstrated using the wave profiles of the constructed dynamical structural system. [ABSTRACT FROM AUTHOR]

The activation energy model is used in this work to examine how hybrid nanoparticles affect the flow across a rotating disk. Here, we considered nanoparticles of silver (Ag) and titanium dioxide (TiO 2) dissolved in water, a base liquid. These nanoparticles have real applications such as photography, photocatalysis, water purification, and solar energy conversion. The current study investigates the combined effects of a changing magnetic field, Darcy Forchheimer, porosity, thermal radiation, Brownian motion, and thermophoresis on hybrid nanofluid flow across a rotating disk. By applying similarity transformations, the partial differential equations system of the current scheme is converted into an ordinary differential equations system, after which it is calculated with MATLAB using the bvp4c scheme. Graphs are used to assess the investigation of mass and heat transport. Also, the change in concentration, temperature, and velocity profiles for various non-dimensional factors are discussed briefly using corresponding graphs. It has been noted that the velocity gradient of mono and hybrid nanofluids is reduced as the magnetic parameter inputs increase. The velocity profiles decline as the input of the Darcy-Forchheimer parameter increases. The outcome demonstrates that temperature and concentration increase as the thermophoresis parameter rises. The concentration profile is enhanced as an activation energy parameter increases. Moreover, the average Nusselt number is 37.73 % at M = 0. 8 , and when M = 2. 2 , the value of the average number decreased by 29.43 %. The concentration of silver (Ag) and titanium dioxide (TiO 2) is (0 − 6) %. • Modified Buongiorno model. • Comparison heat transfer in mono and hybrid nanofluid. • Effects of magnetic field, thermal radiation and activation energy. • Bvp4c scheme is used. [ABSTRACT FROM AUTHOR]

In this research, the new auxiliary equation method (NAEM) for higher order nonlinear fractional Huxley equation is being employed to extricate the novel soliton solutions using Beta and M -Truncated fractional derivatives. For waves of finite amplitude, the Huxley equation demonstrates a substantial transfer of spectrum energy. A comparison of the solutions of the model with both fractional derivatives is also included in this research. Various kinds of solitary traveling wave solutions, such as trigonometric, hyperbolic, exponential, rational functions, etc., are found. These types of solutions demonstrate the superiority of the novelty of the method. This method's key advantage over others is that it provides more broad solutions with certain flexible parameters. 3D and 2D graphs are used graphically to demonstrate the dynamical structures of the solutions. The results are presented in a way that demonstrate the usefulness and competence of the approach used to handle various nonlinear fractional partial differential equations. Lastly, we investigate the comparison of the gain spectra for modulation instability and the depiction of certain noteworthy outcomes by illustratively depicting the 2 D figures produced by carefully considering the parameters • The solitons solutions of fractional Huxley equation is find out using new auxiliary equation method. • The behavior of the solutions is analyzed using fractional derivatives. • A comparative analysis is done on the behalf of fractional derivatives. • Modulation instability analysis is done of the fractional model. [ABSTRACT FROM AUTHOR]