This research inspects the liquid film flow of the nanofluid in a permeable medium with the consequence of thermal radiation over a stretching sheet. The viscidness and thermal conduction of the nanofluid varies with temperature in such a manner that the thermal conductivity considered in direct relation while the viscosity considered inversely proportional to the temperature field. The invariable magnetic field applies vertically to the flow field in the existence of entropy generation. For the above-mentioned nanofluid study, Buongiorno’s model is used. The leading equations are changed into a set of third- and second-order nonlinear coupled differential equations. These nonlinear ordinary differential equations are solved using the optimal approach of homotopy analysis method. The physical appearance of the modelled parameters based on the liquid film thickness is mainly focused. Furthermore, the influence of embedded parameters like variable viscosity parameter [Formula: see text] Prandtl number [Formula: see text] Schmidt number [Formula: see text] Brinkman number [Formula: see text] Brownian motion constraint [Formula: see text] thermophoresis constraint [Formula: see text] magnetic parameter [Formula: see text] thermal radiation parameter [Formula: see text] Reynolds number [Formula: see text] diffusion coefficient [Formula: see text] non-dimension temperature variation [Formula: see text] and non-dimension concentration variation [Formula: see text] is observed on the velocity pitch, temperature gradient and concentration sketch. The consequence of parameters due to entropy generation and Bejan number has also been observed in this work. The important physically quantities of skin friction coefficient, the local Nusselt number and Sherwood number have also been studied. Residual error and optimal values have been calculated for the range of each physical parameter. The present work is compared with the published work and the comparison has been shown physically and numerically.

The article explores the effect of Hall current, thermal radiation, and magnetic field on hybrid nanofluid flow over the surface of a spinning disk. The motive of the present effort is to upgrade the heat transmission rate for engineering and industrial purposes. The hybrid nanofluids as compared to the conventional fluids have higher thermal properties. Therefore, in the present article, a special class of nanoparticles known as carbon nanotubes (CNTs) and iron ferrite nanoparticles are used in the base fluid. The system of modeled equations is depleted into dimensionless differential equations through similarity transformation. The transform equations are further solved through the Parametric Continuation method (PCM). For the parametric study, the physical parameters impact on velocity, energy, mass transmission, and motile microorganism’s concentration profiles have been sketched. The obtained results are compared with the existing literature, which shows the best settlement. It concluded that the heat transmission rate reduces for Hall current and rises with radiative parameter. The results perceived that the addition of CNTs in carrier fluid is more efficacious than any other types of nanoparticles, due to its C–C bond. CNTs nanofluid can be more functionalized for the desired achievement, which can be utilized for a variety of applications by functionalization of non-covalent and covalent modification.

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In this article, the effects of magnetic field versus the thin liquid film water‐based ferrum oxide (Fe3O4) and carbon nanotubes (CNTs) nanofluids have been studied through stretching cylinder. The iron oxide and CNTs (single‐wall [SWCNTs] or multi‐wall [MWCNTs]) have been used as nanoparticles in carrier fluid water (H2O). To the flow field, magnetic effects are applied vertically. The modeled system of partial differential equations are transformed to nonlinear ordinary differential equations by selecting variables. The analytic solution has been obtained through homotopy analysis method. The obtained results are further compared with the numerical ND‐solve method. The embedded constraints impacts are focused on pressure distribution, velocity profile, heat transfer, Nusselt number, and Skin friction through graphical illustration and tables. The dispersion of Fe3O4 and CNTs in base fluid significantly enhanced the mechanism of heat transfer. Moreover, from the results, it has been observed that the MWCNTs have a greater impact on heat transfer, velocity, and pressure profile.

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