Integrated Flow-Cell Arrays (FCAs) represent a combination of integrated liquid cooling and on-chip power generation, converting chemical energy of the flowing electrolyte solutions to electrical energy. The FCA technology provides a promising way to address both heat removal and power delivery issues in 3D Multiprocessor Systems-on-Chips (MPSoCs). In this paper we motivate the benefits of FCA in 3D MPSoCs via a qualitative analysis and explore the capabilities of the proposed technology using our extended PowerCool simulator. PowerCool is a tool that performs combined compact thermal and electrochemical simulation of 3D MPSoCs with inter-tier FCA-based cooling and power generation. We validate our electrochemical model against experimental data obtained using a micro-scale FCA, and extend PowerCool with a compact thermal model (3D-ICE) and subthreshold leakage estimation. We show the sensitivity of the FCA cooling and power generation on the design-time (FCA geometry) and run-time (fluid inlet temperature, flow rate) parameters. Our results show that we can optimize the FCA to keep maximum chip temperature below 95 °C for an average chip power consumption of 50 W/cm2 while generating up to 3.6 W per cm2 of chip area.