LAUSR

Thermal transport of nanofluid natural convection in a wavy porous enclosure exposed to an external and uniform magnetic source is investigated numerically. Numerous pertinent factors in terms of Darcy ( Da  = 10 −4 –10 −2 ), Hartmann ( Ha  = 0–40), Rayleigh ( Ra  = 10 4 –10 7 ), Prandtl ( Pr  = 0.71–7) and undulation ( n  = 3) numbers, in addition to wave amplitudes ( A  = 0.025–0.1) and particle volume concentration ( $$\phi$$ ϕ  = 0, 2 and 4%) have been investigated. The Brinkmann–Forchheimer extended Darcy model is utilized, and the governing equations are solved by employing our own finite difference ADI-based program. Code accuracy was successfully validated with the open literature. The results revealed that for Ra  > 10 5 and Da  < 10 −3 , the magnetic field does not play a substantial role in the convective thermal energy, while at high Ha and low  Ra , the intensity of conduction increases. The surface waviness and Darcy number both have significant effects on the heat transfer suppression if insulation is desired. Furthermore, a critical value of Ra  = 10 5 is observed whereby the mean Nusselt number decreases despite particle volume concentration, particularly at high Hartmann values.