Effect of fractional derivatives on natural convection in a complex-wavy-wall surrounded enclosure filled with porous media using nanofluids

In this paper, the heat transfer by the natural convection flow in wavy-walls enclosures filled with porous media using nanofluids is represented by the fractional differential equations. Conformable fractional derivatives are applied on both the time and space of the governing equations. The geometry is considered as enclosures with horizontal wavy walls. The Buongiorno's model is used to simulate the nanofluids while the Darcy model is used for the porous medium. The governing equations are mapped to a rectangular domain using suitable grid transformations based on the chain rule in the fractional approaches then they are solved numerically using an implicit finite difference method. The obtained numerical results are presented in terms of the streamlines, the isotherms and the nanoparticles volume fraction contours as well as the local Nusselt number for wide ranges of the governing parameters. It is found that the decrease in order of the fractional derivatives enhances rate of the fluid flow and the local Nusselt number, particularly, at the middle part of the bottom wall. Also, an increase in the surface waviness parameter increases both of the nanofluid flow and rate of the heat transfer.