Mathematical Modeling of Ionanofluids and Applications for Energy Conservation

Ionanofluids (IONFs), formed by dispersing nanoparticles in ionic liquid bases, represent a novel class of multifunctional heat transfer and energy storage fluids. By combining the exceptional thermal and electrochemical stability of ionic liquids with the tunable thermophysical properties of nanofluids, IONFs offer unique advantages for energy conservation, renewable integration, and advanced thermal management. Unlike conventional nanofluids, IONFs inherently possess ionic conductivity, wide electrochemical stability windows, and high chemical robustness, enabling their deployment in extreme operating environments such as batteries, supercapacitors, geothermal systems, and solar thermal technologies. This chapter provides a comprehensive overview of mathematical modeling approaches developed to predict and optimize IONF behavior. Governing transport phenomena, including mass, momentum, energy, and charge conservation, are revisited with additional terms accounting for electrokinetic effects, ionic layering, nanoparticle migration (thermophoresis, electrophoresis, diffusiophoresis), and temperature-dependent property variations. Classical models for thermal conductivity and viscosity are evaluated against the distinct electrostatic and interfacial interactions in IONFs, while new correlations are proposed to capture ionic contributions. Computational fluid dynamics (CFD), multiscale simulations, and molecular dynamics (MD) are highlighted as advanced tools for bridging nanoscale interactions with macroscale system performance, supported by emerging machine learning (ML) frameworks for predictive optimization. Applications in thermal management of electrochemical energy storage, waste heat recovery, geothermal extraction, and solar PV/T systems are critically reviewed. IONFs demonstrate enhanced convective and electroosmotic transport, reduced thermal hotspots, and significant efficiency improvements, while challenges persist in terms of long-term stability, recyclability, toxicity, and economic viability. The chapter also addresses model-experiment integration, sensitivity analysis, and uncertainty quantification as essential steps for reliable system-scale deployment. By uniting materials science, electrochemistry, and energy engineering, mathematical modeling of IONFs enables the design of next-generation working fluids that support sustainable energy conservation and decarbonization goals. Emerging opportunities, including hybrid multi-component IONFs, functionalized nanoparticles, and digital twin-assisted predictive control, are discussed as pathways toward pilot-scale demonstrations and industrial implementation.