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 = 104–107), Prandtl (Pr = 0.71–7) and undulation (n = 3) numbers, in addition to wave amplitudes (A = 0.025–0.1) and particle volume concentration ( $$\phi$$ = 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 > 105 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 = 105 is observed whereby the mean Nusselt number decreases despite particle volume concentration, particularly at high Hartmann values.
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