Effective removal of heat from the heat-generating porous bed, particularly in a confined space, is essential due to its implications on thermal management and system safety. The safety aspect becomes particularly important during post-accident heat removal from decay heat-generating debris in nuclear reactors, as well as thermal management of self-igniting coal stockpiles. In spite of detailed research on thermal convection through porous media, only a handful of studies have considered mixed convective heat transport involving heat-generating porous bed along with external fluid injection. The situation, however, demands an in-depth analysis due to the associated practical implications. The present work addresses one cooling method providing side injection of cold fluid and assuming a typical conical heat-generating porous bed located centrally within a fluid-filled cylindrical enclosure. The study is carried out in a general way to suit other applications. The dimensionless governing equations, along with the boundary conditions in a two-dimensional coordinate system, are solved numerically assuming laminar and incompressible flow along with the Boussinesq approximation. The analysis is carried utilizing the local thermal non-equilibrium model within the porous bed. Injection of cold fluid can markedly affect the convective heat transport rate. Porous media permeability considerably influences the flow mechanism. The major findings of this study can be very useful in improving the management of thermal energy removal from self-igniting coal stockpiles, grain storages, porous debris, etc. Heat transport intensification from heat-generating porous bed is analyzed by injecting coolant through the sidewall and considering liquid water as the working medium. The impacts of pertinent parameters on the thermal convection characteristics are illustrated using the average Nusselt number and energy flux vectors.