Onset of Darcy-Brinkman convection with a uniform internal heat source and vertical throughflow

The problem of thermal convection in a horizontal fluid-saturated porous layer is examined, where the flow is governed by the Brinkman extension of Darcy's law. A uniform internal heat source and vertical throughflow are also considered. The linear and nonlinear stability analyses are performed in order to determine the stability characteristics of the system. The linear and nonlinear thresholds give good agreement in the absence of vertical throughflow. However, it is shown that there are potential regions of sub-critical instabilities for increasing values of internal heat source parameter Q, Péclet number Pe and Darcy number Da.