The MHD flow of ethylene glycol with four different nanoparticles has been modeled with the help of upper convected Maxwell model. Throughout the channel, the viscosity and thermal conductivity of the base fluid are assumed to be dependent on the temperature of the fluid. The effect of addition of Cu, Ag, Al 2 O 3 and TiO 2 nanoparticles on the base fluid (ethylene glycol) is investigated for various volume fractions. The effect of variable properties, viscoelasticity, and wall motion on Ag–ethylene glycol nanofluid are studied through relevant non-dimensional parameters with shooting technique. The numerical results show that the variable viscosity and viscoelasticity have a considerable effect on the flow of the fluid, and viscous nanofluid case is in good agreement with earlier literature. It is observed that the temperatures and Nusselt numbers of metallic oxide nanofluids are greater than the metallic nanofluids in both expanding and squeezing regimes. © 2018, Akadémiai Kiadó, Budapest, Hungary.