The unsteady flow of nanoliquid film over a flexible surface has been inspected. Water and ethylene glycol are used as the base liquids for the graphene oxide platelets. The comparison of two sorts of nanoliquids has been used for heat transfer enhancement applications. The thickness of the nanoliquid film is kept as a variable. The governing equations for the flow problem have been altered into the set of nonlinear differential equations. The BVP 2.0 package has been used for the solution of the problem. The sum of the square residual error has been calculated up to the 10th order approximations. It has been observed that the graphene oxide ethylene glycol based nanofluid (GO-EG) is more efficient for heat transfer enhancement as compared to the graphene oxide water based nanofluid (GO-W). The impact of the physical parameters has been plotted and discussed.

This paper analyses the two-dimensional unsteady and incompressible flow of a non-Newtonian hybrid nanofluid over a stretching surface. The nanofluid formulated in the present study is${\mathrm{TiO}}_2+\mathrm{Ag}+\mathrm{blood}$, and ${\mathrm{TiO}}_2+\mathrm{blood}$, where in this combination ${\mathrm{TiO}}_2+\mathrm{blood}$ is the base fluid and ${\mathrm{TiO}}_2+\mathrm{Ag}+\mathrm{blood}$ represents the hybrid nanofluid. The aim of the present research work is to improve the heat transfer ratio because the heat transfer ratio of the hybrid nanofluid is higher than that of the base fluid. The novelty of the recent work is the approximate analytical analysis of the magnetohydrodynamics mixed non-Newtonian hybrid nanofluid over a stretching surface. This type of combination, where ${\mathrm{TiO}}_2+\mathrm{blood}$ is the base fluid and ${\mathrm{TiO}}_2+\mathrm{Ag}+\mathrm{blood}$is the hybrid nanofluid, is studied for the first time in the literature. The fundamental partial differential equations are transformed to a set of nonlinear ordinary differential equations with the guide of some appropriate similarity transformations. The analytical approximate method, namely the optimal homotopy analysis method (OHAM), is used for the approximate analytical solution. The convergence of the OHAM for particular problems is also discussed. The impact of the magnetic parameter, dynamic viscosity parameter, stretching surface parameter and Prandtl number is interpreted through graphs. The skin friction coefficient and Nusselt number are explained in table form. The present work is found to be in very good agreement with those published earlier.

The present research paper explains the influence of Marangoni convection on magnetohydrodynamic viscous dissipation and heat transfer on hybrid nanofluids in a rotating system among two surfaces. Then, the properties of heat and mass transfer are analysed. With the similarity transformation, the governing equations of the defined flow problem are converted into nonlinear ordinary differential equations. These compact equations are solved approximately and analytically using the optimal homotopy analysis method. The impact of different parameters is interpreted through graphs in the form of velocity and temperature profiles. The influence of the skin friction coefficient and Nusselt number are presented in the form of tables. The comparison of the present research paper and published works is also presented table.

The heat transfer ratio has an important role in industry and the engineering sector; the heat transfer ratios of CNT nanofluids are high compared to other nanofluids. This paper examines the analytical investigation of the time-dependent stagnation point flow of a CNT nanofluid over a stretching surface. For the investigation of the various physical restrictions, single and multi-walled carbon nanotubes (SWCNTs, MWCNTs) were used and compared. The defined similarity transformation was used, to reduce the given nonlinear partial differential equations (PDEs) to nonlinear ordinary differential equations (ODEs). The model nonlinear ordinary differential equations were solved, with an approximate analytical (OHAM) optimal homotopy asymptotic method being used for the model problem. The impact of different parameters such as magnetic field parameter, unsteady parameter, dimensionless nanoparticles volume friction, Prandtl number, and Eckert number are interpreted using graphs, in the form of the velocity and temperature profile.

The gradient of surface temperature is known as Marangoni convection and plays an important role in silicon melt, spray, atomic reactors, and thin fluid films. Marangoni convection has been considered in the liquid film spray of carbon nanotube (CNT) nanofluid over the unsteady extending surface of a cylinder. The two kinds of CNTs, single-wall carbon nanotubes (SWCNTs) and multiple-wall carbon nanotubes (MWCNTs), formulated as water-based nanofluids have been used for thermal spray analysis. The thickness of the nanofluid film was kept variable for a stable spray rate and pressure distribution. The transformed equations of the flow problem have been solved using the optimal homotopy analysis method (OHAM). The obtained results have been validated through the sum of the total residual errors numerically and graphically for both types of nanofluids. The impact of the physical parameters versus velocity, pressure, and temperature pitches under the influence of the Marangoni convection have been obtained and discussed. The obtained results are validated using the comparison of OHAM and the (ND-solve) method.

This research paper explains the effect of Marangoni convection on unsteady squeezing flow of water base CNTs for both MWCNT and SWCNT in the presence of magnetic field and variable thermal conductivity over a stretching surface. By using the similarity transformation, the partial differential equation is converted to nonlinear fourth order ordinary differential equations. The analytical method, namely Optimal Homotopic Analysis Method used to find the analytical solution of the nonlinear problem which analyze the problem. The result of important parameters for both velocity and temperature profiles are plotted and discussed. The BVPh 2.0 package is used to obtain the convergence of the problem up to 25 iteration. The skin friction coefficient and Nusselt number is explained in table form.