Natural convection within a greenhouse cavity with a porous layer mimicking algerian soil heated by embedded hot pipes: effects of soil porosity and permeability

This study numerically investigates geothermal performance in selecting optimal soil properties for greenhouse applications. The analysis considers steady free convection within a two-dimensional cavity partially filled with a porous layer and featuring three embedded hot pipes beneath a semi-elliptical upper boundary, representing a greenhouse structure. The numerical simulation employs the Galerkin finite element method. The cavity is subjected to a hot isothermal temperature Th along the heated pipes and a cold isothermal temperature Tc on the top wall. Momentum transfer in the porous medium is modeled using the Darcy-Brinkman approach, incorporating non-Darcian flow effects. Key parameters explored include Rayleigh numbers (104<Ra<106), Darcy numbers (Da= 10-4 and 10-2), and porosities (ε=0.2 to 0.5). Results reveal that heat transfer significantly increases with higher Rayleigh numbers, while the effect of porosity is minimal. However, increased permeability and higher Darcy numbers substantially enhance heat transfer, particularly at elevated Rayleigh values.