This paper investigates steady two dimensional flow of an incompressible magnetohydrodynamic (MHD) boundary layer flow and heat transfer of nanofluid over an impermeable surface in presence of thermal radiation and viscous dissipation. By using similarity transformation, the arising governing equations of momentum, energy and nanoparticle concentration are transformed into coupled nonlinear ordinary differential equations, which are than solved by homotopy analysis method (HAM). The effect of different physical parameters, namely, Prandtl number Pr, Eckert number Ec , Magnetic parameter M , Brownian motion parameter N _b , Thermophoresis parameter N _t , Lewis parameter Le and Radiation parameter R _d on the velocity, temperature and concentration profiles along with the Nusselt number and skin friction coefficient are discussed graphically and in tabular form in details. The present results are also compared with existing limiting solutions.

Purpose: The purpose of this study is to analyze magnetohydrodynamic three-dimensional flow of Casson nanofluid over a stretching sheet in presence of thermophoresis and Brownian motion effects. In contrast, the convective surface boundary conditions with the effects of radiation are applied. Design/methodology/approach: The governing partial differential equations are transformed into highly nonlinear coupled ordinary differential equations consisting of the momentum, energy and nanoparticle concentration via suitable similarity transformations, which are then solved the using optimal homotopy analysis method (OHAM) a Mathematica Package BVPh2.0. Findings: The influence of emerging physical flow parameters on fluid velocity component, temperature distribution and nanoparticle concentration are discussed in detail. Also, an OHAM solution demonstrates very good correlation with those obtained in the previously published results. It is noticed that OHAM can overcome the earlier restriction, assumptions and limitation of traditional perturbation method. The main advantage of this method is that OHAM can be applied directly to nonlinear differential equations without using linearization and round-off errors, and therefore, it cannot be affected by error associated to discretization. Originality/value: Here the approximate solutions are compared with the numerical results published in earlier work.

Current article is devoted with the study of MHD 3D flow of Oldroyd B type nanofluid induced by bi-directional stretching sheet. Expertise similarity transformation is confined to reduce the governing partial differential equations into ordinary nonlinear differential equations. These dimensionless equations are then solved by the Differential Transform Method combined with the Padé approximation (DTM-Padé). Dealings of the arising physical parameters namely the Deborah numbers β ₁ and β ₂ , Prandtl number Pr, Brownian motion parameter N _b and thermophoresis parameter N _t on the fluid velocity, temperature and concentration profile are depicted through graphs. Also a comparative study between DTM and numerical method are presented by graph and other semi-analytical techniques through tables. It is envisage that the velocity profile declines with rising magnetic factor, temperature profile increases with magnetic parameter, Deborah number of first kind and Brownian motion parameter while decreases with Deborah number of second kind and Prandtl number. A comparative study also visualizes comparative study in details.