Porous medium modelling of microencapsulated phase change material slurry flow for high-performance microchannel heat sinks

This study presents a predictive two-equation framework to analyze heat transfer in microencapsulated phase change material (MPCM) slurry flowing through microchannel heat sinks, modeled as porous structures. Unlike conventional one-equation models assuming local thermal equilibrium, the two-equation approach resolves energy equations separately for the solid matrix and the slurry, accurately capturing interfacial heat exchange and latent heat effects during phase change. The Brinkman-extended Darcy equation accounts for wall effects and flow resistance, while microstructural parameters—porosity, Darcy number, MPCM volume fraction, and thermal conductance ratio—govern coupled momentum and energy transport. Analytical solutions, validated against numerical simulations, show deviations below 7% for heat transfer coefficient and pumping power. Results reveal that increasing MPCM concentration enhances thermal performance via higher effective heat capacity, improved thermal conductivity, whereas excessive concentration raises viscosity and pumping power. Narrower channels (lower Darcy number) intensify wall confinement and steepen velocity gradients, while a higher thermal conductance ratio reduces the temperature difference between fluid and solid matrix, together enhancing interphase heat transfer and promoting stronger thermal coupling. The framework delivers a systematic design approach that balances thermal performance with flow resistance, offering practical guidelines for the optimized design of microchannel heat sinks using MPCM slurries.