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.

Purpose: The complex behavior of viscoelastic fluids and its flow analysis under the impact of transverse magnetic field are becoming increasingly important in numerous emerging applications including biomedical engineering, aerospace engineering, geophysics and industrial applications. Additionally, the thermal analysis and fluid flow driven by propagating membranes will aid significant applications for microscale transport in bio-thermal systems. This study aims to investigate the thermal effects of viscoelastic fluids driven by membrane-induced propagation and transverse magnetic field. Design/methodology/approach: The propagation of the membranes will work as pump which pushes the fluids from bottom to top against the gravitation force; however, there is backflow due to compression and expansion phases of membrane propagation. The Jeffrey fluid model is employed to analyze the viscoelastic fluid flow, with entropy generation examined and equations solved analytically under low Reynolds number and long-wavelength assumptions. Findings: The findings reveal that an increase in magnetic field strength impedes fluid flow, while higher values of the Grashof number, heat source parameter and Jeffrey fluid parameter enhance fluid motion. The study’s findings have significant implications for optimizing magnetohydrodynamic systems in various emerging applications, including biomedical engineering, aerospace, geophysics and industrial processes. Originality/value: This study aims to investigate the impact of a transverse magnetic field on the flow and heat transfer characteristics of viscoelastic fluids driven by membrane propagation.