Heating and cooling are two important procedures in manufacturing as well as transportation industries. Rather than the conventional fluids, solutions of fluids with metal nanoparticles have higher thermal conductivity for effective cooling. Therefore, present paper is a comparative study of squeezing flow analysis of copper oxide–water and oil (kerosene)-based nanofluid between two parallel plates. Magnetohydrodynamic flow of kerosene-based nanofluid along with the dissipative heat energy may enhance the thermal properties of the fluid. Assuming self-similar variables, the governing equations get transformed into non-dimensional forms and approximate analytical techniques such as variation parameter method is employed for these transformed equations. With the well posed physical parameters, the computation is carried out using the mathematical package MATHEMATICA and displayed via graphs and numerical results are shown in tabular form. Favourable cases in comparison with earlier studies are also studied wherever possible. However, when the plates are away from each other, it is seen that the kerosene-based nanofluid velocity overrides the water-based nanofluid whereas the impact is reversed in the case of squeezing.