Thermal systems of solar collectors, electronic cooling, nuclear reactors, and combustion operate at high thermal conditions, and in such circumstances, the density relation of the working fluids with the thermal field may not be linear. The working fluid features are significantly affected by nonlinear density temperature fluctuations. Therefore, a theoretical study of the quadratic Boussinesq approximation (with quadratic density temperature [QDT] variation) and quadratic Rosseland radiation on the three-dimensional boundary layer dynamics and heat transport of ethylene glycol-based titania nanomaterial is carried out. The phenomenon of the kinematics of nanoparticle aggregation is also analyzed by considering modified models proposed by Maxwell-Bruggeman and Krieger-Dougherty for thermal conductivity and dynamic viscosity. The flow is induced by the elongation of a flexible flat plate in two directions. A comparison of heat transfer features of linear elongation of the plate and nonlinear elongation of the plate is conducted. The Rosseland radiative heat flux is studied in three different forms. The governing nonlinear equations are treated using apt nondimensionalization,