The onset of longitudinal convective rolls in a porous medium saturated by a nanofluid with non-uniform internal heating and chemical reaction

Abstract

The aim of this article is to investigate the combined effect of chemical reaction and non-uniform internal heating on the onset of longitudinal convective rolls in a porous medium saturated by nanofluid. Non-uniform internal heating modifies the basic profiles for temperature and concentration of nanoparticle from linear to nonlinear with layer height, which in turn affects the stability extensively. To treat this problem, the Buongiorno’s two-phase mathematical model is used for nanofluid, while for porous medium Darcy model is utilized. Using the framework of linear stability theory, the stability equations are derived and solved analytically using the Galerkin weighted residuals method. Results show that the effect of increasing the Lewis number $$L_{\text{e}}$$ , internal heating parameter $$S$$ , modified diffusive ratio $$N_{\text{A}}$$ and the nanoparticle Rayleigh–Darcy number $$R_{\text{N}}$$ is to accelerate the onset of convection, while the chemical parameter $$K_{\text{r}}$$ and porosity parameter $$\varepsilon$$ is to delay the onset of convection. The size of convection cell increases with the increase in internal heating parameter $$S$$ and porosity parameter $$\varepsilon$$ , while it decreases with the chemical parameter $$K_{\text{r}}$$ , the Lewis number $$L_{\text{e}}$$ , modified diffusive ratio $$N_{\text{A}}$$ and the nanoparticle Rayleigh–Darcy number $$R_{\text{N}}$$ .