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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]

The influence of the Soret parameter, variable gravity field and viscous dissipation on the stability of convection with double-diffusion in a porous layer saturated by a viscous fluid is considered numerically. The impact of vertical throughflow on stability is also studied. Linear, quadratic, cubic and exponential functions are taken into consideration for gravity force variation. To solve the eigenvalue problem numerically, bvp4c method has been employed. The results show that Lewis number, gravity variation parameter, and Soret parameter are delaying the onset of convection, while solutal Rayleigh number and viscous dissipation parameter are enhancing the onset of convection in the flow field. It is distinguished that the system is becoming more stable for the exponential variation of the gravity field and more unstable for cubic variation of gravity variation. [ABSTRACT FROM AUTHOR]