A mathematical model is created to analyze the impact of Thompson and Troian slip boundaries over a contracting/expanding surface sustaining nanofluid-containing carbon nanotubes along a stagnation point flow. Both multi-wall (MWCNTs) and single-wall (SWCNTs) carbon nanotubes are taken into consideration, with water serving as the base liquid. The flow is obtained due to the stretching or contracting of the surface. The thermal radiation, activation energy, buoyancy impacts, and chemical processes called quartic autocatalysis are additionally added to the original mathematical model. The MATLAB-constructed bvp4c function involving the three-stage Lobatto IIIa formula for the numerical results of dimensionless velocity, concentration, and temperature profiles are used. By contrasting it against a published paper in this limited instance, it is determined whether the suggested mathematical model is legitimate. In this sense, a remarkable consensus is achieved. Graphical representations are used to depict the behavior of many non-dimensional flow variables, such as the slip velocity parameter, the inertia coefficient, the porosity parameter, and the solid volume fraction. Surface drag force computations are reported to examine the effects at the permeable stretching surface. It has been shown that increasing the slip velocity factor increases the fluid streaming velocity while decreasing the surface drag force. If the endothermic/exothermic coefficient increases, the local thermal transfer efficiency falls. For nanofluids, the changing viscosity factor increases axial velocity while decreasing temperature distribution. Additionally, the solid volumetric fraction improves the temperature distributions by lowering the concentration profile and speed.

The main objective of the present study is to explore the effects of electromagnetohydrodynamics electroosmotic flow of hybrid nanofluid through circular cylindrical microchannels. An analysis of hybrid nanofluid consisting of four different nanomaterials i.e., single and multiwall carbon nanotubes, silver, and copper is carried out. Yamada–Ota model is employed for the single and multi wall carbon nanotubes, whereas, Xue model is used for the Silver and Copper hybrid nanofluid for specifying the thermal conductivity. The imposed pressure gradient, electromagnetic field and electroosmosis actuated the fluid flow. The flow of heat transfer and Nusselt number with the account of various effects of Joule heating and viscous dissipation under the circumstances of constant heat flux are discussed graphically. The governing system of equations is molded into a system of coupled, nonlinear ordinary differential equations. The shooting technique is used to extract the numerical solutions of the converted system of equations. Also, the outturn of different parameters like Hartman number, the strength of lateral direction electric field, EDL (electric double layer) electrokinetic width, Joule heating parameters on the temperature, and velocity are investigated. The conversion of simple fluid to hybrid nanofluid has greatly alteration in the present model. It has enhanced the thermal properties of fluid. It is also noted that $$SWCNT-MWCNT$$S W C N T - M W C N T based hybrid nanofluid has most influential impact on Nusselt number, temperature distribution and velocity of the fluid. This attempt is useful for the designing of effectual electromagnetic appliances and exquisite.

This article is concerned with the study of MHD non-Newtonian nanofluid flow over a stretching/shrinking cylinder along with thermal radiation effects. Two-component slip mechanism models, namely Brownian motion and thermophoresis of nanofluid for the mass and energy transportation, developed by Buongiorno, are used. Convective heat transfer and nonuniform magnetic field are retained for the expanding/contracting cylinder. Variable thermal conductivity and heat generation effects along with slip boundary conditions are utilized over the cylinder surface. By utilizing the similarity transformation, these governing partial differential equations are converted into nonlinear ordinary differential equations (ODEs). To obtain numerical results, these ODE’S are solved by the shooting method using MATLAB software. The impact of different parameters like variable thermal conductivity, radiation parameter, magnetic parameter, Prandtl number, Brownian motion parameter, the magnetic parameter, Weissenberg number, the viscosity ratio parameter and mass transfer parameter, on the velocity, temperature and concentration is discussed graphically. Further, the Sherwood number, Nusselt number, the skin friction coefficient are also discussed through figures. It is noted through analysis that the speed of the nanofluid reduces for the higher Weissenberg number and expanding cylinder. For the contracting cylinder, i.e., for the negative unsteadiness parameter, the velocity increases.

The assessment of the Darcy–Forchheimer flow of magnetohydrodynamic Williamson nanofluid with entropy optimization is the main purpose of this article. This study was carried out to analyze the impacts on fluid flow via a stratified plate. The impacts of viscous dissipation, chemical reaction, and Joule heating are examined in the existence of nonlinear thermal radiation. The framework of partial differential expressions is transformed into ordinary differential equations by utilizing a suitable set of similarity transformations. The obtained differential equations are analytically tackled by the homotopy analysis approach. [ ]-curves, table of convergence, and graphical outcomes are displayed and examined by using MATHEMATICA software. A distinctive parameter chart, against the profiles of temperature, velocity, and concentration with relevant discussion is portrayed for emphasizing their physical importance. Through graphical representations, the Sherwood number, the coefficient of skin friction, local Nussel1t number, and entropy generation impact are examined. This kind of study is useful in many industries like solar engineering, polymer extrusion, electronic supplies, biomedical, etc.