Lattice Boltzmann Modeling of Heat Transfer in Porous Media

The Lattice Boltzmann Method has emerged as a versatile computational approach for simulating thermal transport in porous structures. By discretising fluid and thermal distribution functions on a mesoscopic lattice, the method captures complex interactions between fluid flow, conduction and convection within the pore space. In porous media, transport behaviour is governed by coupled momentum and energy equations incorporating Darcy drag, thermal dispersion and local thermal nonequilibrium. LBM allows for detailed pore-scale resolution, accommodating anisotropic permeability, variable porosity and multiphase effects. Recent advances include multi-relaxation time collision operators that enhance numerical stability and accuracy, and hybrid formulations integrating vorticity–velocity representations to reduce computational cost. Applications range from geothermal heat extraction and thermal energy storage to catalysis and advanced insulation. By resolving pore-scale phenomena and upscaling effective transport coefficients, LBM offers both fundamental insights and practical guidance for the design of porous thermal systems.

Research from Nature Portfolio

Recent studies have applied a multi-relaxation time LBM to optimise natural convection in a porous enclosure filled with copper–water nanofluid and fitted with horizontal fins. Sensitivity and optimisation analyses, including design-of-experiments, response surface methods and genetic algorithms, identified the most influential parameters for maximising the average Nusselt number. The interplay of fin geometry, porosity, Darcy number and nanoparticle concentration was quantified, yielding an optimal configuration that raises heat transfer efficiency. This work illustrates the power of LBM-based design tools for enhancing thermal performance in porous-nanofluid systems.

Lattice Boltzmann Modeling of Heat Transfer in Porous Media publication trend

The graph below shows the total number of articles in lattice boltzmann modeling of heat transfer in porous media across all publications each year (not limited to Nature Index journals).

Technical terms

Lattice Boltzmann Method: A mesoscopic simulation technique that models fluid and thermal transport by tracking distribution functions on a discrete lattice.

Multi-Relaxation Time (MRT): A collision operator in LBM that permits independent relaxation of distribution moments, improving stability and accuracy.

Porous Media: Materials containing a network of interconnected voids through which fluid and heat can be transported.

Darcy Number: A dimensionless group representing the ratio of porous medium permeability to a characteristic length squared, indicating flow resistance.

Nusselt Number: A dimensionless measure of convective heat transfer relative to conductive transfer across a boundary or within a medium.

References

1. Experimental velocity and temperature measurements for natural convection in a highly porous medium. International Journal of Thermal Sciences (2024).
2. Sensitivity analysis of natural convection in a porous cavity filled with nanofluid and equipped with horizontal fins using various optimization methods and MRT-LB. Scientific Reports (2024).
3. Integration of vorticity–velocity formulation in a lattice Boltzmann method for porous media. Physics of Fluids (2024).