This article aims to present the flow and heat transfer characteristics of a nanofluid past an elastic sheet having variable thickness in the presence of a magnetic field. Vanishing nanoparticle flux at the boundary has been taken into account for the passive control of nanoparticles. Two-phase model for the nanofluid has been considered. With the help of similarity transformations, the governing nonlinear partial differential equations are converted into nonlinear ordinary differential equations along with the appropriate boundary conditions. The reduced equations are then solved numerically. The effects of buoyancy parameter,magnetic parameter, Brownian motion, thermophoresis parameter etc. on velocity, temperature and nanoparticle volume fraction are presented graphically and analysed in detail. Velocity, temperature and nanoparticle volume fraction are decreasing functions of wall thickness parameter for decelerated flow. Due to increasing values of thermophoresis parameter, the rate of heat transfer at the surface reduces while with the increase in the Brownian motion parameter the mass transfer rate at the surface increases.

The objective of the article is to analyse the forced convection nanofluid flow over a permeable plate in an absorbent medium using slip boundary conditions. A single-phase model for the nanofluid is used with variable shapes of nanoparticles. The partial differential equations (PDEs) of the model are altered into a set ofnon-linear ordinary differential equations (ODEs) by a suitable alteration. To obtain the solutions of the system of equations numerically, Runge–Kutta method is used with a shooting technique. The effects of various parameters,like permeability, suction/injection, nanoparticle volume fraction, velocity slip, thermal slip and nanoparticle shape parameters on velocity and temperature profiles are presented graphically and analysed. In addition, fora clear understanding of the model, the flow and the heat transfer characteristics are presented through graphs and analysed. Fluid velocity is found to increase with the increasing values of permeability of the porous medium,whereas temperature is found to reduce in this case. Temperature is a rising function of the thermal slip parameter, whereas it is a decreasing function of the velocity slip parameter.