The present investigation aims to study the combined effect of viscous dissipation, vertical throughflow, and variable gravity field on the onset convective instability in a horizontal porous layer of finite thickness restricted between two permeable boundaries. The Brinkman extended Darcy model is accounted into the momentum equation of the governing flow through the porous layer. Also, linear, quadratic, and exponential gravity variation has been considered to study the present problem. The linear stability of the basic state is studied for the normal mode perturbations, and the corresponding eigenvalue problem is solved numerically using the bvp4c routine in MATLAB. The influence of throughflow parameter (Q), viscous dissipation (Ge), Darcy number (Da), and gravity variation parameter (lambda) on the instability mechanism is discussed for the above three gravity field variations. The results indicate that the beginning of convection is postponed in the presence of Darcy number, throughflow, and gravity field parameter, while it is advanced in the presence of a significant viscous dissipation. Ra-c elevates to maximum at around 299% for linear variations of the gravity field, while it was 74% and 868% for quadratic and exponential varying gravity fields, respectively, when lambda increases from 0 to 1.5. The value of Ra-c increased 6.5%, 5.4%, and 10.6%, respectively, for the linear, quadratic, and exponential gravity field variables, respectively, on changing the values of throughflow parameter from 0 to 1 and the increase in Ra-c is more for enhancing the value of the throughflow parameter from 1 to 2. Further, the system becomes more stable in the presence of an exponential gravity field.
