This article explores an incompressible hybrid nanofluid flow over an infinite impermeable rotating disk. The influence of a magnetic field has been added to better examine the fine point of nanoliquid flow. The main purpose of this work is to enhance our understanding of the exhaustion of energy in industrial and engineering fields. This study is mainly concerned with the von Kármán traditional flow of a rotating disk, involving carbon nanotubes (CNTs) and magnetic ferrite nanoparticles together with a carrier fluid such as water. The nonlinear system of differential equations is transformed to the dimensionless ordinary differential equation by using an appropriate similarity framework, which is further treated with the “homotopy analysis method” for the analytic solution. A mathematical calculation is provided to prove and illustrate why the hybrid nanofluids are advantageous as far as the heat transfer enhancement is concerned. Although the physical features highly rely on CNTs and iron oxide nanoparticles, it is concluded that the heat and mass transfer rate is greatly enhanced by the addition of CNTs and Fe₃O₄ nanofluids. By increasing the velocity of disk rotation, fluid temperature and velocity are significantly increased. The use of CNT + Fe₃O₄/H₂O influences the performance of thermophysical characteristics of carrier fluids more compared to magnetic ferrite nanomaterials.

The thermal management of the flow of the hybrid nanofluid within the conical gap between a cone and a disk is analyzed. Four different cases of flow are examined, including (1) stationary cone rotating disk (2) rotating cone stationary disk (3) rotating cone and disk in the same direction and (4) rotating cone and disk in the opposite directions. The magnetic field of strength $$B_{0}$$B 0 is added to the modeled problem that is applied along the z-direction. This work actually explores the role of the heat transfer, which performs in a plate-cone viscometer. A special type of hybrid nanoliquid containing copper Cu and magnetic ferrite Fe₃O₄ nanoparticles are considered. The similarity transformations have been used to alter the modeled from partial differential equations (PDEs) to the ordinary differential equations (ODEs). The modeled problem is analytically treated with the Homotopy analysis method HAM and the numerical ND-solve method has been used for the comparison. The numerical outputs for the temperature gradient are tabulated against physical pertinent variables. In particular, it is concluded that increment in volume fraction of both nanoparticles $$\left( {\phi_{{Fe_{3} O_{4} }} ,\phi_{Cu} } \right)$$ϕ F e 3 O 4 , ϕ Cu effectively enhanced the thermal transmission rate and velocity of base fluid. The desired cooling of disk-cone instruments can be gained for a rotating disk with a fixed cone, while the surface temperature remains constant.

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.

This article analyzes the Darcy Forchheimer 2D thin film fluid of nanoliquid. Flow of nanoliquid is made due to a flat unsteady stretchable sheet. In nanoliquids, nanomaterial is in form of CNTs (carbon nanotubes). Also, in present analysis, single walled carbon nanotubes (SWCNTs) are accounted as nanoparticles. The classical liquid ‘water’ is treated as based liquid. The flow in permeable region is characterized by Darcy–Forchheimer relation. Heat transport phenomena are studied from convective point of view. The transformation of partial differential set of equations into strong ordinary differential frame is formed through appropriate variables. Homotopy Analysis Method (HAM) scheme is executed for solving the simplified set of equations. In addition, a numerical analysis (ND-Solve) is utilized for the convergence of the applied technique. The influence of some flow model quantities like P_r (Prandtl number), λ (unsteadiness factor), k (porous medium factor), F (Darcy-porous medium factor) on liquid velocity and thermal field are scrutinized and studied through sketches. Certain physical factors like f″(0) (friction factor coefficient) and −θ′(0) (rate of heat transport) are first derived and then presented through tables.