This thesis investigates the use of the Stagnation-Point Reverse-Flow (SPRF) combustor geometry for burning low-grade solid fuels that are attractive for specific industrial applications because of their low cost and on-site availability. These fuels are in general, hard to burn, either because of high moisture and impurity-content, e.g. biomass, or their low-volatiles content, e.g., petroleum-coke. This results in various challenges to the combustor designer, for example reduced flame stability and poor combustion efficiency. Conventional solutions include preheating the incoming flow as well as co-firing with high-grade fuels. The SPRF combustor geometry has been chosen because it was demonstrated to operate stably on standard gaseous and liquid-fuels corresponding to ultra fuel-lean conditions and power densities at atmospheric-pressure around 20-25 MW/m3. Previous studies on the SPRF combustor have proven that the unique, reverse flow-geometry allows entrainment of near-adiabatic products into the incoming reactants, thereby enhancing the reactivity of the mixture. Further, the presence of the stagnation-end created a region of low mean velocities and high levels of unsteadiness and mixing-rates that supported the reaction-zones. In this study, we examine the performance of the SPRF geometry on a specific low grade solid fuel, petroleum coke. There are three main goals of this thesis. The first goal is the design of a SPRF combustor to operate on solid-fuels based on a design-scaling methodology, as well as demonstration of successful operation corresponding to a baseline condition. The second goal involves understanding the mode of operation of the SPRF combustor on solid-fuels based on visualization studies. The third goal of this thesis is developing and using reduced-order models to better understand and predict the ignition and quasi-steady burning behavior of dispersed-phase particles in the SPRF combustor. The SPRF combustor has been demonstrated to operate stably on pure-oxygen and a slurry made from water and petroleum-coke, both at the baseline conditions (125 kW, 18 g/s, ~25 µm particles) and higher power-densities and powder sizes. For an overall combustor length less than a meter, combustion is not complete (global combustion efficiency less than 70%). Luminance imaging results indicate the incoming reactant jet ignites and exhibits intense burning at the mid-combustor region, around 15 jet diameters downstream of the inlet, most likely due to enhanced mixing as a result of the highly unsteady velocity field. This roughly corresponds to the location of the reaction zones in the previous SPRF combustors operating on gas and liquid fuels. Planar laser visualization of the reacting flow-field using particle-scattering reveals that ignition of a significant amount of the reactants occurs only after the incoming jet has broken into reactant packets. Post-ignition, these burning packets burn out slowly as they reverse direction and exit the combustor on either side of the central injector. This is unlike the behavior in liquid and gas-fueled operation where the incoming reactants burned across a highly corrugated, thin-flame front. Based on these findings, as well as the results of previous SPRF studies, an idealized model of combustor operation based on a plug flow reactor has been developed. The predictions suggest that fuel-conversion efficiency is enhanced by the combustor operating pressure and lowered by the heat-losses. Overall, this effort has shown the SPRF geometry is a promising compact-combustor concept for self-sustained operation on low-grade solid-fuels for typical high-pressure applications such as direct steam-generation. Based on these findings, it is recommended that future designs for the specific application previously mentioned have a shorter base-combustor with lower heat-losses and a longer steam-generation section for injection of water.