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The convection in a vertical channel filled with a porous medium saturated by a nanofluid is studied numerically. The effects of Brownian motion and thermophoresis are incorporated in the model used for nanofluid. Also, the flow within the porous region is governed by Brinkman's equation. The generalized eigenvalue problem for the perturbed state is obtained from a normal mode analysis and solved using the Chebyshev spectral collocation method. The Rayleigh number is expressed as an implicit function of the wavenumber with other parameters. The critical wavenumber and the critical Rayleigh number are calculated for different parameters. The preferred modes under critical conditions are detected. [ABSTRACT FROM AUTHOR]

The effect of variable gravity on the onset of convection in a horizontal porous layer has been analyzed due to external heating. The third kind of thermal boundary conditions is considered on both the boundaries which are connected by Biot numbers B 0 and B 1. Also, the Brinkman model has been employed in the momentum equation. Further, linear and quadratic varying downward gravity fields depending on height have been taken to investigate the above observation. The bvp4c scheme is used in MATLAB to solve the eigenvalue problem for neutral stability mode. It is observed that the system's stability increases monotonically due to the rising effect of gravity variation parameter, Darcy number, and Biot numbers. Further, the onset of convection has been discussed for the two limiting cases of external heating on the boundaries where one boundary is associated with constant heat flux while another one is associated with an isothermal state. Finally, it is observed that the convection comes earlier for quadratic varying gravity field compared to linear varying gravity field when the external heat supplies from one boundary or both boundaries. [ABSTRACT FROM AUTHOR]