Natural Convection and Heat Transfer in Porous Media

Natural convection in porous media arises when buoyancy forces drive fluid flow through a solid matrix permeated by pores. This phenomenon underpins heat transfer in geotechnical, energy and environmental systems, from geothermal reservoirs to thermal insulation and chemical reactors. Heat transport emerges from the interplay of conduction within the solid skeleton and convective transport through the pore fluid, governed by dimensionless parameters such as the Rayleigh number, which quantifies the ratio of buoyancy to viscous damping, and the Darcy number, which measures permeability relative to characteristic length scales. Mathematical descriptions often extend Darcy’s law to incorporate viscous dispersion and inertial effects via Brinkman or Forchheimer corrections, while the local thermal non-equilibrium model accounts for distinct temperature fields in solid and fluid phases. Recent advances have addressed the impact of non-linear buoyancy, variable fluid properties near density extrema, oscillatory boundary temperatures and nano-enhancement strategies. Such efforts have clarified the conditions under which multi-cellular flow patterns emerge, entropy generation is minimised and overall heat transfer is optimised. The global significance of this research spans sustainable energy extraction, passive cooling in buildings and process intensification in chemical engineering, highlighting the need for integrated experimental, numerical and theoretical investigations to guide material design and operational strategies across diverse applications.

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Natural Convection and Heat Transfer in Porous Media publication trend

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

Technical terms

Rayleigh number: A dimensionless quantity expressing the ratio of buoyant to viscous forces affecting convection flow.

Darcy number: The ratio of medium permeability to the square of a characteristic length, indicating ease of fluid passage.

Nusselt number: A dimensionless index of convective heat transfer relative to conduction across a boundary layer.

Local Thermal Non-Equilibrium (LTNE): A modelling approach accounting for independent temperature fields in the solid matrix and pore fluid.

References

1. Free convective heat transfer flow in a glass bead porous medium varying permeability and sinusoidal wall temperature. Journal of Thermal Analysis and Calorimetry (2024).
2. Effects of Variable Properties on the Convective Flow of Water near Its Density Extremum in an Inclined Enclosure with Entropy Generation. Mathematics (2022).
3. A Numerical Investigation of the Free Flow in a Square Porous Cavity with Non-Uniform Heating on the Lower Wall. Engineering Technology & Applied Science Research (2022).