Transport in Porous Media https://doi.org/10.1007/s11242-018-1166-3 Multi-layered Porous Foam Effects on Heat Transfer and Entropy Generation of Nanofluid Mixed Convection Inside a Two-Sided Lid-Driven Enclosure with Internal Heating Sasan Asiaei 1,2 · Ali Zadehkafi 1 · Majid Siavashi 2,3 Received: 21 April 2018 / Accepted: 25 September 2018 © Springer Nature B.V. 2018 Abstract Mixed convection of Cu-water nanofluid inside a two-sided lid-driven enclosure with an internal heater, filled with multi-layered porous foams is studied numerically and its heat transfer and entropy generation number are evaluated. Use of multi-layered porous media instead of homogeneous ones is capable of heat transfer enhancement, by weakening flow where does not impose a pivotal role on heat transfer and amplifying the flow in regions where have more effects on the heat transfer. Eight different arrangements of porous layers are considered and the two-phase mixture model is implemented to simulate nanofluid mixed convection inside the cavity. Results are presented in terms of stream functions, isotherms, Nusselt and entropy generation number for the eight cases considering various Richardson numbers (Ri = 10 −4 to 10 3 ) and nanofluid concentrations (ϕ  0 to 0.04). Results indicate that using the multi-layered porous material can confine flow vortices in the vicinity of the moving walls and could enhance the heat transfer up to 17 percent (with respect to the case using homogeneous porous material with the highest permeability), such that this enhancement is more in lower Ri values (stronger convective effects). Entropy generation number also increases by nanofluid volume fraction increment and Ri decrement. Cases with a higher heat transfer rate also have the higher entropy generation number. In addition, an increase of volume fraction decreases the relative entropy generation number (S*) for low Ri number, while contrary fact observed for high Ri values. Keywords Nanofluid · mixed convection · porous media · multi-layered · entropy generation List of symbols a Acceleration (m s −2 ) C d Drag coefficient B Majid Siavashi msiavashi@iust.ac.ir Extended author information available on the last page of the article 123