Numerical solution of the onset of Buoyancy‐driven nanofluid convective motion in an anisotropic porous medium layer with variable gravity and internal heating

Abstract

AbstractThe onset of buoyancy‐driven convective motion in a nanofluid saturated anisotropic porous medium layer is examined numerically in the occurrence of uniform internal heat source under the variable gravity field. Three kinds of gravity force variation functions: (a) G(z) = −z (linear), (b) G(z) = −z2 (parabolic), and (c) G(z) = −z3 (cubic) are considered. Wide‐range governing parameters impacts are inspected on the beginning of convective motion under the zero nanoparticle flux situation at the boundaries using the higher term Galerkin technique. It is established that the thermal anisotropy parameter η and the gravity variation parameter λ delay the arrival of convective motion, while the mechanical anisotropy parameter ξ, the internal heating parameter Hs, the nanoparticle Rayleigh‐Darcy number Rnp, the modified diffusivity ratio NAnf, and the modified nanofluid Lewis number Lenf rapid the start of convective motion. The size of the convective cells reduces on raising the internal heating parameter Hs, while the gravity variation parameter λ, the mechanical anisotropy parameter ξ, the thermal anisotropy parameter η, the nanoparticle Rayleigh‐Darcy number Rnp, the modified diffusivity ratio NAnf, and the modified nanofluid Lewis number Lenf amplify the dimension of the convective cells. It is also detected that the arrangement is more unstable for case (c), while it is more stable for case (a).