<p>This article examines an ensemble of spherical particles that are densely packed between two vertical flat plates, each maintained at a different temperature. The flow is analyzed in the context of quadratic convection and the effects of nonlinear heat generation and absorption. The mathematical modeling of granular materials is formulated using a continuum model. The mathematical modeling of fully developed granular material flow is reduced to a set of nonlinear differential equations. The finite difference method is employed to obtain numerical solutions for these nonlinear differential equations. The results are presented in terms of volume fraction, velocity distribution, and thermal distribution. The results for all relevant parameters are analyzed using graphical representations. The graphical results indicate that quadratic convection significantly enhances the velocity distribution, while its effects on the thermal distribution are negligible. Additionally, the heat generation parameter enhances the velocity distribution, whereas heat absorption exhibits opposite effects. However, a complex behavior is observed in the thermal distribution when the heat generation/absorption parameter is present.</p>