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We focused on the analytical analysis of steady flow of nanofluid, viscous dissipation with convective boundary condition in this work. The MWCNT and SWCNT are used to described the nanofluid. A similarity transformation is applied to convert nonlinear PDE from their dimensional form to dimensionless nonlinear ODE. The developed nonlinear ODE for velocity and temperature profiles are solved by using an approximate analytical technique called the homotopy asymptotic method. Graphs are used to discuss and illustrate the results. Graphs are used to interpret the effects of several factors. Finally, the skin friction and Nusselt number are illustrated in the form of table. [ABSTRACT FROM AUTHOR]

The impact of coupled stress casson nanofluid-flow over a stretching surface will be examined in this paper. The fundamental controlling PDE are transformed using the stated similarity transformation into a pair of coupled, non-linear ODE, one for velocity and the other for temperature distribution. The modeled flow problem's approximate analytical solution was discovered using the approximate analytical approach. Graphs are used to illustrate the effects of different factors. A table illustrating the relationship between the Nusselt number and skin friction is provided. [ABSTRACT FROM AUTHOR]

In this research work, we will carry out analytical investigation of MgO–CuO∖H2O, hybrid nanofluid magnetohydrodynamics (MHD) stagnation point flow with the influence of viscous dissipation for enhancement of heat transfer ratio. The flow system takes into account the impact viscous dissipation and transport dependence on the shape factor. Furthermore, velocity and temperature at the stretching surface are also considered in this study. To convert a collection of PDEs to nonlinear ODEs, we applied appropriate transformations. We utilize the Homotopy analysis method (HAM) to solve this set of equations. A physical description is used to simulate and evaluate the structures of flow features such as velocity, skin friction, Nusselt number and temperature profiles in response to changes in developing factors, the effects of different factors on temperature and velocities are shown in the form of graphs. It is hoped that this theoretical approach would contribute positively to improve the heat transformation ratio to satisfy the demands of the manufacturing and engineering sectors. [ABSTRACT FROM AUTHOR]

Theoretical influence of the buoyancy and thermal radiation effects on the MHD (magnetohydrodynamics) flow across a stretchable porous sheet were analyzed in the present study. The Darcy–Forchheimer model and laminar flow were considered for the flow problem that was investigated. The flow was taken to incorporate a temperature-dependent heat source or sink. The study also incorporated the influences of Brownian motion and thermophoresis. The general form of the buoyancy term in the momentum equation for a free convection boundary layer is derived in this study. A favorable comparison with earlier published studies was achieved. Graphs were used to investigate and explain how different physical parameters affect the velocity, the temperature, and the concentration field. Additionally, tables are included in order to discuss the outcomes of the Sherwood number, the Nusselt number, and skin friction. The fundamental governing partial differential equations (PDEs), which are used in the modeling and analysis of the MHD flow problem, were transformed into a collection of ordinary differential equations (ODEs) by utilizing the similarity transformation. A semi-analytical approach homotopy analysis method (HAM) was applied for approximating the solutions of the modeled equations. The model finds several important applications, such as steel rolling, nuclear explosions, cooling of transmission lines, heating of the room by the use of a radiator, cooling the reactor core in nuclear power plants, design of fins, solar power technology, combustion chambers, astrophysical flow, electric transformers, and rectifiers. Among the various outcomes of the study, it was discovered that skin friction surges for 0.3 ≤ F 1 ≤ 0.6, 0.1 ≤ k 1 ≤ 0.4 and 0.3 ≤ M ≤ 1.0, snf declines for 1.0 ≤ G r ≤ 4.0. Moreover, the Nusselt number augments for 0.5 ≤ R ≤ 1.5, 0.2 ≤ N t ≤ 0.8 and 0.3 ≤ N b ≤ 0.9, and declines for 2.5 ≤ P r ≤ 5.5. The Sherwood number increases for 0.2 ≤ N t ≤ 0.8 and 0.3 ≤ S c ≤ 0.9, and decreases for 0.1 ≤ N b ≤ 0.7. [ABSTRACT FROM AUTHOR]

The behavior of hybrid nanofluid and stagnation point flow toward a stretched surface along with melting heat transfer, second-order slip, electric field, and magnetic field effect is investigated in this study. Hybrid nanoparticles alumina A l 2 O 3 and copper (Cu) are considered with the base fluids water H 2 O . The PDEs with corresponding boundary constraints are transformed into a set of nonlinear ODEs using similarities transformation. The set of nonlinear ODEs are analyzed analytically using semianalytical method HAM in Mathematica software. Dual solution is determined which relaying on the emerging parameters included magnetic field, volume fractions, electric field, dimensionless surface velocity slip factors, Eckert number, and Prandtl number. The results are shown in the velocity and temperature curves as well as skin friction coefficient and local Nusselt number. The analysis shows that velocity profile is an increasing function of slip parameter, electric field, while reducing function of magnetic field. Temperature profile is an increasing function of magnetic field parameter, electric field parameter, volume fraction parameter, and Eckert number, while reducing function of Prandtl number. The main outcomes are as follows that hybrid nanofluids are higher thermal properties as compared to conventional fluids. As a result, hybrid nanofluid has numerous uses in engineering cosmetics, automotive industry, home industry, for cancer treatment, food packaging, pharmaceuticals, fabrics, paper plastics, paints, ceramics, food colorants, and soaps as well. [ABSTRACT FROM AUTHOR]

In this paper, the Darcy–Forchheimer laminar thin film flow with MHD and heat transfer on an unsteady horizontal stretched surface is investigated. The impact of thermal radiation and viscous dissipation is also considered for thin film flow. The analysis of heat source with thermal radiation in a boundary layer flow can play a great role in manufacturing engineering procedures such as the production of electric power, solar energy modernization, and astrophysical flow. By using similarity transformation, the system of PDEs is converted to ODEs. Then HAM is applied for the solution of the problem. Moreover, the velocity and temperature profile for various embedded variables are discussed through graphs while the numerical solution of concerned physical quantities such as skin friction and Nusselt number are discussed through tables. The analysis shows that velocity profile is reducing function of M , K 1 , S , and F 1 . The temperature profile is an increasing function S and E c while a reducing function of Pr and R. The overall behavior of the proposed system is highlighted analytically. [ABSTRACT FROM AUTHOR]