The current study investigates the MHD flow of nanofluid across an elongating surface while taking into account non-uniform heat flux. For this, we have considered the flow of a boundary layer over a stretched sheet containing (water-based) Al₂O₃ nanoparticles. The convective boundary conditions for temperature have been invoked. The flow created by a surface that is exponentially expanding in the presence of a magnetic field and a non-uniform heat flux has been mathematically formulated by using laws of conservation. Transformed non-dimensional systems of governing equations have been analyzed numerically by using Adam’s Bashforth predictor corrector approach. The effects of emerging parameters on the fluid velocity and temperature profiles have been further described by plotting graphs. An experimental design and a sensitivity analysis based on Response Surface Methodology (RSM) are used to examine the effects of various physical factors and the dependence of the response factors of interest on the change of the input parameter. To establish the model dependencies of the output response variables, which include the skin friction coefficient and the local Nusselt number, on the independent input parameters, which include the magnetic field parameter, the nanoparticle volume fraction, and the heat transfer Biot number, RSM is used. On the basis of statistical measures such as $$Q - Q$$Q - Q residual plots, adjusted and hypothesis testing using p values, it is observed that both of our models for Skin Friction Coefficient (SFC) and the Local Nusselt Number (LNN) are best fitted. Further, it is concluded that the sensitivity of the SFC, as well as the LNN through heat transfer Biot number, is greater than that of nanoparticle volume fraction and magnetic field parameter. The SFC is sensitive to all combinations of the input parameters. At high levels of heat transfer Biot number, the LNN displays negative sensitivity via magnetic field parameters.

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.