In the present research analysis we have addressed comparative investigation of radiative electrically conducting Casson nanofluid. Nanofluid Flow is assumed over a nonlinearly stretching sheet. Heat transport analysis is carried via joule dissipation, thermal behavior and convective boundary condition. To employ the radiative effect radiation was involved to show the diverse states of nanoparticles. Furthermore entropy optimization with activation energy and chemical reaction are considered. Thermodynamics 2^nd law is applied to explore entropy generation rate. Nonlinear expression is simplified through similarity variables. The reduced ordinary system is tackled through optimal approach. Flow pattern was reported for wide range of scrutinized parameters. Computational consequences of velocity drag force, heat flux and concentration gradient are analyzed numerically in tables. Results verify that conduction mode augments with enhance of magnetic parameter.Increasing radiation boosts the temperature and entropy. Activation energy corresponds to augmented concentration. Heat transmission rate augments with the consideration of radiation source term.

A new condition on positive membership, neutral membership, and negative membership functions give us the successful extension of picture fuzzy set and Pythagorean fuzzy set and called spherical fuzzy sets $(\mathcal{SFS})$ . This extends the domain of positive membership, neutral membership, and negative membership functions. Keeping in mind the importance of similarity measure and application in data mining, medical diagnosis, decision making, and pattern recognition, several studies on similarity measures have been proposed in the literature. Some of those, however, cannot satisfy the axioms of similarity and provide counter-intuitive cases. In this paper, we proposed the set-theoretic similarity and distance measures. We provide some counterexamples for already proposed similarity measures in the literature and shows that how our proposed method is important and applicable to the pattern recognition problems. In the end, we provide an application of a proposed similarity measure for selecting mega projects in under developed countries.

In this article, the magnetohydrodynamic flow and heat transmission of a micropolar hybrid nanofluid between two surfaces inside a rotating system are examined. The Hall current and thermal radiations are also considered for the flow system. In this article, a base fluid is taken as water, while graphene oxide (GO) and copper (Cu) are applied as hybrid nanoparticles. The flow is assumed to be in a steady state. The governing partial differential equations along with boundary conditions for the modeled problem are transformed into a system of non-linear ordinary differential equations using similarity transformations. The set of resultant ordinary differential equations is solved by using an optimal approach. The main focus of this study is to examine the magnetohydrodynamic heat transmission and hybrid nanofluid flow in a rotating system between two parallel plates by taking into account the thermal radiations and Hall current impacts. Various physical parameters are discussed in detail graphically in this article. The main outcome of this study indicates that the augmented values of the magnetic parameter increase the velocity profile and decrease the rotational velocity profile.

This research work deals with investigation of the thermal characteristics of the Darcy–Forchheimer hydromagnetic hybrid nanofluid (Al₂O₃-Cu/H₂O) flow through a permeable stretching cylinder. The model equations, which consist of continuity, momentum, and energy equations, are converted to a set of coupled ordinary differential equations through similarity variables transformations and appropriate boundary conditions. Brownian motion and Thermophoresis effects are mainly focused in this work. The impacts of some interesting parameters over velocity, temperature, and concentrations profiles are graphically studied. The present study will be helpful in understanding the thermal characteristics of heat transfer liquids.

The effect of thermal radiation on the three-dimensional magnetized rotating flow of a hybrid nanofluid has been numerically investigated. Enhancing heat transmission is a contemporary engineering challenge in a range of sectors, including heat exchangers, electronics, chemical and biological reactors, and medical detectors. The main goal of the current study is to investigate the effect of magnetic parameter, solid volume fraction of copper, Eckert number, and radiation parameter on velocity and temperature distributions, and the consequence of solid volume fraction on declined skin friction and heat transfer against suction and a stretching/shrinking surface. A hybrid nanofluid is a contemporary type of nanofluid that is used to increase heat transfer performance. A linear similarity variable is–applied to convert the governing partial differential equations (PDEs) into corresponding ordinary differential equations (ODEs). Using the three-stage Labatto III-A method included in the MATLAB software’s bvp4c solver, the ODE system is solved numerically. In certain ranges of involved parameters, two solutions are received. The temperature profile $\theta \left(\eta \right)$ upsurges in both solutions with growing values of $EC$ and $Rd$. Moreover, the conclusion is that solution duality exists when the suction parameter $S\ge S_{ci}$, while no flow of fluid is possible when $S<S_{ci}$. Finally, stability analysis has been performed and it has been found that only the first solution is the stable one between both solutions.

Drinking or recreating water that has been polluted with disease-causing organisms or pathogens is what causes waterborne infections. It should be noted that many water-borne infections can also transmit from person to person, by contact with animals or their surroundings, or by ingesting tainted food or beverages. Schistosomiasis is a water-borne infection found in different areas of the globe. Mostly people with this viral infection live in Africa with limited resources and medications. Therefore, investigation of this infection is significant to reduce its economic burden on the society. We formulated a novel epidemic model for schistosomiasis water-borne infection with the help of the Atangana–Baleanu derivative. The rudimentary theory of fractional-calculus has been presented for the analysis of our system. We start by looking at the model solution’s non-negativity and uniqueness. The basic reproduction number and equilibria of the hypothesized water-borne infection model are next evaluated. Local stability of the infection-free steady-state has been established through Jacobian matrix method for $R_0<1.$ In addition, the suggested model’s solution is calculated using an iterative technique. Finally, we give numerical simulations for various input values to illustrate the impact of memory index and other input factors of the system. Our findings showed the influence of input parameters on the dynamical behaviour of the schistosomiasis infection. The results demonstrate the importance and persuasive behaviour of fractional order, and reveal that fractional memory effects in the model seem to be a good fit for this type of findings.