This study is dedicated to analyze the heat transfer and flow of ethylene glycol and water based copper (Cu) nanoparticles between two squeezed parallel disks with suction/injection effects. The lower disk is assumed to be permeable. Additionally, we have considered the influence of MHD to keep the metallic particles in charge. These particles are normal to the surface and strongly effected by magnetic field. Constructed mathematical model consist of system of partial differential equations in cylindrical coordinates, based upon momentum and energy equations. The governing equations reduced to a nonlinear set of ordinary differential equations. The said set of nonlinear equations consists of squeezing number S, Hartmann number (M), nanoparticle volume fraction phi and suction/injection parameter (A) tackled by least square Galerkin method (LSGM). The outcomes are analyzed by means of temperature and velocity profiles for every Cu-water and Cu-ethylene glycol nanofluids. The heat transfer and flow behavior at the surface are studied via graphical plots for local Nusselt number and skin friction. It is observed that local Nusselt number achieved from Cu-water remain lesser than Cu-ethylene glycol while the behavior for skin friction coefficient is totally opposite. We support our theoretical study via a detailed evaluation of outcomes. The obtained results via least square Galerkin method (LSGM) are compared with RK (order-4) and already existing results. Moreover, graphical representation, the error, convergence and comparison analysis of outcomes endorsing that the least square method is extremely effective. The suggested method could be extended to other nonlinear problems. (C) 2018 Elsevier Ltd. All rights reserved.