The magnetohydrodynamic thin film nanofluid sprayed on a stretching cylinder with heat transfer is explored. The spray rate is a function of film size. Constant reference temperature is used for the motion past an expanding cylinder. The sundry behavior of the magnetic nano liquid thin film is carefully noticed which results in to bring changes in the flow pattern and heat transfer. Water-based nanofluids like Al ${}_2$ O ${}_3$ -H ${}_2$ O and CuO-H ${}_2$ O are investigated under the consideration of thin film. The basic constitutive equations for the motion and transfer of heat of the nanofluid with the boundary conditions have been converted to nonlinear coupled differential equations with physical conditions by employing appropriate similarity transformations. The modeled equations have been computed by using HAM (Homotopy Analysis Method) and lead to detailed expressions for the velocity profile and temperature distribution. The pressure distribution and spray rate are also calculated. The comparison of HAM solution predicts the close agreement with the numerical method solution. The residual errors show the authentication of the present work. The CuO-H ${}_2$ O nanofluid results from this study are compared with the experimental results reported in the literature showing high accuracy especially, in investigating skin friction coefficient and Nusselt number. The present work discusses the salient features of all the indispensable parameters of spray rate, velocity profile, temperature and pressure distributions which have been displayed graphically and illustrated.

In this mathematical model, the consequences of Soret and Dufour’s effects on energy and mass transport have been reported. The hybrid nanofluid (hnf) comprised of silver (Ag) and magnesium oxide (MgO) nps is studied over a stretching rotating sheet. The influence of thermal radiation, second-order chemical reaction, activation energy, and the magnetic field is also applied to the fluid flow. The phenomena are designed in form of nonlinear Partial differential equations (PDEs), which are reduced to dimensionless ordinary differential equations through similarity replacement. Furthermore, the parametric continuation method (PCM) has been employed to estimate the reduced form of differential equations. The graphical results are obtained for velocity, mass, and energy profiles vs different physical interest entities. It has been noted that the velocity curve drops vs the variation of stretching sheet rotation factor, Hartmann number, and the mounting number of MgO and Ag nano particulates. Furthermore, the hnf (MgO–Ag/water) has greater efficiency for momentum and energy dissemination rate as compared to nanofluid.

Contaminant removal from water is accomplished using a variety of technologies, with adsorption being the simplest, successful, cost-effective, and long-term solution. Nanocomposites made from clay minerals and polymers have developed as a new method for cleaning contaminated water in recent years. Therefore, in this paper, clay-based water nanoliquid has been analyzed across a vertical sheet. For flow analysis, Brinkman-type fluid model has been considered along with the consequences of first-order chemical reaction and heat generation/heat absorption. Conditions for Slippage velocity and Newtonian heating also have been taken into account. Using relative constitutive equations, a mathematical model for the flow analysis has been formulated in terms of coupled partial differential equations and then generalized by using constant proportional caputo fractional derivative. The fractional Laplace transform approach was used to solve the problem for exact analytical solutions. The physics of several essential flow constraints vs velocity, thermal energy, and concentration propagation have been addressed graphically using the exact solutions. To check the validity and correctness, the obtained solution is evaluated with the published work. It is worth mentioning that the heat transition rate in the fluid increases by 8.7671% by the accumulation of clay nanoparticulates, while the rate of mass transmission increases by 11.830%.

The present computational model is built to analyze the energy and mass transition rate through a copper and cobalt ferrite water-based hybrid nanofluid (hnf) flow caused by the fluctuating wavy spinning disk. Cobalt ferrite (CoFe₂O₄) and copper (Cu) nanoparticles (nps) are incredibly renowned in engineering and technological research due to their vast potential applications in nano/microscale structures, devices, materials, and systems related to micro- and nanotechnology. The flow mechanism has been formulated in the form of a nonlinear set of PDEs. That set of PDEs has been further reduced to the system of ODEs through resemblance replacements and computationally solved through the parametric continuation method. The outcomes are verified with the Matlab program bvp4c, for accuracy purposes. The statistical outputs and graphical evaluation of physical factors versus velocity, energy, and mass outlines are given through tables and figures. The configuration of a circulating disk affects the energy transformation and velocity distribution desirably. In comparison to a uniform interface, the uneven spinning surface augments energy communication by up to 15%. The addition of nanostructured materials (cobalt ferrite and copper) dramatically improves the solvent physiochemical characteristics. Furthermore, the upward and downward oscillation of the rotating disc also enhances the velocity and energy distribution.

The heat transmission properties along the non-magnetized geometries have been numerically obtainedby various researchers. These mechanisms are less interesting in engineering and industrial processes because of excessive heating. According to current studies, the surface is magnetized and the fluid is electrically conductive, which helps to lessen excessive surface heating. The main objective of the current analysis is to numerically compute the temperature-dependent density effect on magnetohydrodynamic convective heat-transfer phenomena of electrical-conductive fluid flow along the vertical magnetized and heated plate placed in a thermally stratified medium. For the purpose of numerical analysis, the theoretical process governing heat and magnetic intensity along a vertical magnetic plate is examined. By using suitable and well-known similarity transformations for integration, the non-linear coupled PDEs for the aforementioned electrical-conductive fluid flow mechanism are changed and subsequently converted into non-similar formulation. The Keller Box method is used to numerically integrate the final non-similar equations. The MATLAB software program plots the transformed algebraic equations graphically and quantitatively. The behavior of the physical quantities such asvelocity graph, magnetic field graph, and temperature plot along with their slopes that arerate of skin friction, the rate of heat transfer, and the rate of magnetic intensity for different parameters included in the flow model. The novelty of the current work is to compute the magneto-thermo analysis of electrically conducting flow along the vertical symmetric heated plate. First, we secure the numerical solution for steady part and then these results are used to find skin friction, heat transfer, and magnetic intensity. In the current work, the fluid becomes electrically conducing due to a magnetized surface which insulates heat during the mechanism and reduces the excessive heating. The results are excellent and accurate because they are satisfied by its given boundary conditions. Additionally, the current problems have a big impact on the production of polymer materials, glass fiber, petroleum, plastic films, polymer sheets, heat exchangers, catalytic reactors, and electronic devices.