Integrated microfluidic power generation and power delivery promises to be a disruptive packaging technology with the potential to combat dark silicon. It essentially consists of integrated microchannel-based electrochemical 'flow cells' in a 2D/3D multiprocessor system-on-chip (MPSoC), that generate electricity to power up the entire or part of the chip, while also simultaneously acting as a high-efficiency microfluidic heat sink. Further development of this technology requires efficient modeling tools that would assess the efficacy of such solutions and help perform early-stage design space exploration. In this paper, we propose a compact mathematical model, called PowerCool, that performs electro-chemical modeling and simulation of integrated microfluidic power generation in MPSoCs. The accuracy of the model has been validated against fine-grained multiphysics simulations of flow cells in the COMSOL software that is unsuitable for EDA because of large simulation times. PowerCool model is demonstrated to be up to 425x times faster than COMSOL simulations while incurring a worst-case error of only 5%. Furthermore, the PowerCool model has been used to study and assess the efficacy of this technology for a test MPSoC.