<p>The paper aims to study the flow and heat transfer characteristics of non-Newtonian Maxwell nanofluid passing through a squeezing channel in the presence of thermal radiation. The system of partial differential equations governing the flow problem are transformed into a set of dimensionless ordinary differential equations with the help of similarity variables. The approximate numerical solution is computed using shooting technique along with 4^th order Runge-Kutta method. The impact of several physical parameters on the nanofluid velocity, temperature, the coefficient of skin friction, and heat transfer rate are also explored. Further, a multivariate quadratic regression analysis for skin friction coefficient and Nusselt number against the key parameter is also performed and expressions for the same is presented. The findings reported from the study suggests that the temperature of non-Newtonian graphene based nanofluid enhances with increasing strengths of magnetic field, nanoparticle volume fraction and Joule dissipation on the other way opposite nature of nanofluid temperature is observed for thermal radiation and Deborah number. The findings of present research may have bearings in the fields of biomedical engineering, automobiles, powder technology and high-energy devices<b>.</b> The findings indicate that as the nanoparticle volume fraction increases, there is a corresponding increase in both skin friction and Nusselt number values.</p>