Dual solutions of magnetized radiative flow of Casson Nanofluid over a stretching/shrinking cylinder: Stability analysis.

The enhanced thermal efficiency exhibited by Casson nanofluids offers significant practical applications across various industrial and engineering sectors. This study focuses on the mathematical investigation of the steady magnetohydrodynamic (MHD) boundary layer flow of Casson nanofluid through a stretched/shrinking cylinder, taking into account the effects of suction and thermal radiation. The governing partial differential equations (PDEs) have been subjected to a similarity transformation, resulting in a set of nonlinear ordinary differential equations (ODEs). These ODEs were solved numerically utilizing the code of bvp4c in the software of Matlab which offers high accuracy (4th order). The employed nanofluid model incorporates the effects of Brownian motion and thermophoresis. The present study illustrates the graphical depictions of the impacts of different governing parameters, namely Hartmann (M) number, curvature (γ) parameter, Brownian motion (Nb) parameter, mass suction (S) parameter, thermal radiation (Rd) parameter, and thermophoresis (Nt) parameter, on heat transfer, flow, and mass transfer characteristics. Comprehensive determination and visual presentation of the coefficient of skin friction, local Nusselt number, and local Sherwood number were conducted for a range of estimates of applied parameters. Based on our examination, it has been determined that dual similarity solutions are present within a specific range of mass suction parameters. The relationship between the Casson parameter and various fluid dynamic properties, such as skin friction coefficient, heat transfer rate, and mass transfer rates, has been found to exhibit a decreasing trend. Furthermore, the stability analysis discovered that the first solution exhibits linear stability, whereas the second solution displays linear instability. Additionally, the motivation behind this study is to enhance industrial performance through the optimization of thermal power generation systems, thereby increasing their overall efficiency.

Entropy generation in magneto couple stress bionanofluid flow containing gyrotactic microorganisms towards a stagnation point on a stretching/shrinking sheet.

The study focuses on the behavior of an electrically conducting non-Newtonian fluid with couple stress properties, using water-based bionanofluid. The fluid is analyzed as it flows across a porous stretching/shrinking sheet within its own plane. This Study also explores the Bejan Number and Entropy Generation. To facilitate this investigation, the governing nonlinear partial differential equations undergo a transformation, wherein they are converted into nonlinear ordinary differential equations through a suitable similarity transformation. An ideal strategy has been employed to achieve the desired results from the modeled challenge. The Homotopy Analysis Method is applied to determine the solution of the system of differential equations. The convergence of the applied method and their comparison with the numerical method are described through graphs and tables. The main features of the different profiles are briefly described. Graphs are used to analyze the impact of the Bejan number, concentration, temperature, velocity profile, and entropy production rate. Tables present the characteristics of skin friction, Nusselt, and Sherwood numbers for various limitations. The stretching and ambient fluid velocities should fluctuate linearly as the distance from the stagnation point increases. A rise in the magnetic and porosity parameters is accompanied by an increase in the velocity profile. While the velocity profile falls off as a Couple of fluid parameters are increased. The phenomenon of temperature boost is observed to be positively correlated with the increase in Brownian motion parameter while exhibiting no significant dependence on other parameters such as Brinkman number, Prandtl number Lewis number and Thermophoresis parameter. Entropy generation increases with the Brinkman number while decreasing with the radiation parameter and diffusion parameter as is plainly demonstrated.

A fractional modeling approach for the transmission dynamics of measles with double-dose vaccination.

Measles, a member of the Paramyxoviridae family and the Morbillivirus genus, is an infectious disease caused by the measles virus that is extremely contagious and can be prevented through vaccination. When a person with the measles coughs or sneezes, the virus is disseminated by respiratory droplets. Normally, the appearance of measles symptoms takes 10-14 d following viral exposure. Conjunctivitis, a high temperature, a cough, a runny nose, and a distinctive rash are some of the symptoms. Despite the measles vaccination being available, it is still widespread worldwide. To eradicate measles, the Reproduction Number (i.e. R0<1) must remain less than unity. This study examines a SEIVR compartmental model in the caputo sense using a double dose of vaccine to simulate the measles outbreak. The reproduction number R0 and model properties are both thoroughly examined. Both the local and global stabilities of the proposed model are determined for R0 less and greater than 1. To achieve the model's global stability, the Lyapunov function is used while the existence and uniqueness of the proposed model are demonstrated In addition to the calculated and fitted biological parameters, the forward sensitivity indices for R0 are also obtained. Simulations of the proposed fractional order (FO) caputo model are performed in order to analyse their graphical representations and the significance of FO derivatives to illustrate how our theoretical findings have an impact. The graphical results show that the measles outbreak is reduced by increasing vaccine dosage rates.

Investigation of Interaction of Noble Metals (Cu, Ag, Au, Pt and Ir) with Nanosheets.

Two-dimensional nanomaterials, such as graphene and hexagonal boron nitride nanosheets, have attracted tremendous interest in the research community and as a starting point for the development of nanotechnology. Using classical applied mathematical modeling, we derive explicit analytical expressions to determine the binding energies of noble metals, including copper, silver, gold, platinum and iridium (Cu, Ag, Au, Pt and Ir) atoms, on graphene and hexagonal boron nitride nanosheets. We adopt the 6-12 Lennard-Jones potential function, together with the continuous approach, to determine the preferred minimum energy position of an offset metal atom above the surface of the graphene and hexagonal boron nitride nanosheets. The main results of this study are analytical expressions of the interaction energies, which we then utilize to report the mechanism of adsorption of the metal atoms on graphene and hexagonal boron nitride surfaces. The results show that the minimum binding energy occured when Cu, Ag, Au, Pt and Ir were set at perpendicular distances in the region from 3.302 Å to 3.683 Å above the nanosheet surface, which correspond to adsorption energies in the region ranging from 0.842 to 2.978 (kcal/mol). Our results might assist in providing information on the interaction energies between the metal atoms and the two-dimensional nanomaterials.

Instability and translocation through nanopores of DNA interacting with single-layer materials.

In this study, we use classical applied mathematical modelling to employ the 6-12 Lennard-Jones potential function along with the continuous approximation to investigate the interaction energies between a double-stranded deoxyribonucleic acid (dsDNA) molecule and two-dimensional nanomaterials, namely graphene (GRA), hexagonal boron nitride (h-BN), molybdenum disulphide (MoS2), and tungsten disulphide (WS2). Assuming that the dsDNA molecule has a perpendicular distance Δ above the nano-sheet surface, we calculated the molecular interaction energy and determined the relation between the location of the minimum energy and Δ. We also investigated the interaction of a dsDNA molecule with the surface of each nano-sheet in the presence of a circular hole simulating a nanopore. The radius of the nanopore that results in the minimum energy was determined. Our results show that the adsorption energies of the dsDNA molecule with GRA, h-BN, MoS2, and WS2 nano-sheets corresponding to the perpendicular distance Δ = 20 Å are approximately 70, 82, 28, and 26 (kcal mol-1), respectively, and we observed that the dsDNA molecule moves through nanopores of radii greater than 12.2 Å.

Energy behaviour for DNA translocation through graphene nanopores.

Nanoparticles have considerable promise for many applications in electronics, energy storage, bioscience and biotechnologies. Here we use applied mathematical modelling to exploit the basic principles of mechanics and the 6-12 Lennard-Jones potential function together with the continuum approach, which assumes that a discrete atomic structure can be replaced by an average constant atomic surface density of atoms that is assumed to be smeared over each molecule. We identify a circular hole in a graphene sheet as a nanopore and we consider the molecular interaction energy for both single-strand and double-strand DNA molecules assumed to move through the circular hole in a graphene sheet to determine the radius b of the hole that gives the minimum energy. By minimizing the interaction energy, we observe that the single-strand DNA and double-strand DNA molecules penetrate through a graphene nanopore when the pore radii b> 7.8Å and b> 12.7Å, respectively. Our results can be adopted to offer new applications in the atomic surface processes and electronic sensing.

Offset configurations for single- and double-strand DNA inside single-walled carbon nanotubes.

Nanotechnology is a rapidly expanding research area, and it is believed that the unique properties of molecules at the nano-scale will prove to be of substantial benefit to mankind, especially so in medicine and electronics. Here we use applied mathematical modelling exploiting the basic principles of mechanics and the 6-12 Lennard-Jones potential function together with the continuum approximation, which assumes that intermolecular interactions can be approximated by average atomic surface densities. We consider the equilibrium offset positions for both single-strand and double-strand DNA molecules inside a single-walled carbon nanotube, and we predict offset positions with reference to the cross-section of the carbon nanotube. For the double-strand DNA, the potential energy is determined for the general case for any helical phase angle ϕ, but we also consider a special case when ϕ = π, which leads to a substantial simplification in the analytical expression for the energy. As might be expected, our results confirm that the global minimum energy positions for a single-strand DNA molecule and a double-strand DNA molecule will lie off axis and they become closer to the tube wall as the radius of the tube increases.