Bivariate spectral computation of heat generation/absorption effects on quadratic mixed thermal-solutal convective nanofluid coating flow over a conical frustum

Abstract This study investigates nonlinear (quadratic) thermal and solutal buoyancy effects in nanofluid boundary-layer flow over the external surface of a truncated cone, motivated by applications in nanomaterial coating processes. The analysis incorporates Soret diffusion and internal heat generation or absorption, while accounting for both nanoparticle diffusion and solute mass transport. The Buongiorno two-component nanofluid model is employed to capture Brownian motion and thermophoretic effects. A non-similarity formulation yields a coupled system of nonlinear, dimensionless partial differential equations subject to appropriate boundary conditions. The governing equations are solved numerically using a bivariate pseudo-spectral local linearization method implemented in MATLAB, and the results are validated through comparison with asymptotic solutions. Parametric results demonstrate that enhanced nonlinear thermal and solutal buoyancy significantly increase surface shear stress and heat transfer rates. Increased Brownian motion and thermophoretic effects reduce heat transfer, whereas stronger Soret diffusion enhances it. Solutal mass transfer to the cone surface is promoted by nonlinear buoyancy and heat generation but is suppressed under heat absorption conditions.