Mathematical Modeling of Hybrid Nanofluids and Applications for Energy Conservation

Hybrid nanofluids are engineered suspensions containing two or more types of nanoparticles dispersed in a base fluid have emerged as advanced heat transfer media with superior thermophysical properties compared to conventional fluids and single-component nanofluids. Their enhanced thermal conductivity, tunable viscosity, and improved convective heat transfer characteristics make them promising candidates for energy conservation and advanced thermal management in renewable and sustainable energy systems. However, the inherent complexity of hybrid nanofluid behavior arising from particle-particle and particle-fluid interactions, agglomeration, sedimentation, and non-Newtonian rheology poses significant challenges for design, optimization, and large-scale deployment. This chapter provides a comprehensive overview of the mathematical modeling approaches developed to understand, predict, and optimize hybrid nanofluid behavior in energy systems. Governing equations of mass, momentum, and energy conservation are presented with modifications to incorporate Brownian motion, thermophoresis, buoyancy, variable thermophysical properties, and nanoparticle interactions. Classical theoretical models (e.g., Maxwell, Hamilton-Crosser) are critically examined alongside empirical and semi-empirical correlations, nanolayer theories, and population balance models for agglomeration and sedimentation. The chapter also highlights advanced modeling techniques , including molecular dynamics (MD), computational fluid dynamics (CFD), multiscale frameworks, and machine learning (ML)-based predictive tools, which enable more accurate and adaptive descriptions of hybrid nanofluid systems. Limitations of existing models, challenges in experimental validation, and discrepancies between predictions and measurements are analyzed, emphasizing the need for hybrid-specific formulations. Finally, emerging directions such as turbulence modeling, integration of multiphase flow effects, and data-driven optimization strategies are discussed in the context of energy conservation applications.