Optimal arrangements of a heat sink partially filled with multilayered porous media employing hybrid nanofluid Hossein Arasteh 1 • Ramin Mashayekhi 2 • Davood Toghraie 3 • Arash Karimipour 4 • Mehdi Bahiraei 5 • Alireza Rahbari 6 Received: 7 December 2018 / Accepted: 3 January 2019 Ó Akade ´miai Kiado ´, Budapest, Hungary 2019 Abstract Although many studies have addressed the urge of exploring the porous media partially embedded in a channel due to its wide engineering applications, the heat transfer and fluid flow of a channel consisting of multilayered metal foam are relatively untouched. To tackle this research gap, a numerical study is conducted to analyze a channel partially filled with a three-layered porous medium—occupying sixty percent of a heat sink—over the Reynolds numbers ranging from 50 to 150 and water base fluid. To this aim, two configuration models of porous media are evaluated here: metal foam with (A) similar particle diameters (2 mm) and different porosities (0.75, 0.85, 0.95) and (B) similar porosities (0.88) and different particle diameters (1, 2, 3 mm). Darcy–Brinkman–Forchheimer and local thermal non-equilibrium methods are used to solve the momentum and energy equations in the porous region, respectively. The validity assessment of the local thermal equilibrium method elucidates that its accuracy is questionable at higher porosities and particle diameters of the metal foam—highlighting the necessity of incorporating the LTNE method under the mentioned circumstances. Among the considered geometries, the optimal arrangements of metal foam at both models are selected according to the performance evaluation criteria value. Keywords Porous media  Copper metal foam  Multilayered  Local thermal non-equilibrium  Optimal arrangement  Nanofluid  Heat sink List of symbols A Area (m 2 ) a sf Fluid to solid specific area C Specific heat capacity (J kg -1 K -1 ) d p Particle diameter (m) Da Darcy number f Friction coefficient f p Friction coefficient of plain channel h Heat transfer coefficient (W m -2 K -1 ) h c Channel height (m) h p Porous thickness (m) h sf Fluid to solid heat transfer coefficient K Permeability (m 2 ) k Thermal conductivity (W m -1 K -1 ) k eff Effective thermal conductivity (W m -1 K -1 ) k ef Effective thermal conductivity of porous region solid phase (W m -1 K -1 ) k es Effective thermal conductivity of porous region fluid phase (W m -1 K -1 ) k er Ratio of effective solid thermal conductivity to that of fluid l Length of the channel (m) Nu Nusselt number Nu p Nusselt number of plain channel Nu x Local Nusselt number Nu avg Average Nusselt number & Davood Toghraie davoodtoghraie@gmail.com 1 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran 2 Young Researchers and Elite Club, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran 3 Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran 4 Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran 5 Department of Mechanical Engineering, Kermanshah University of Technology, Kermanshah, Iran 6 Research School of Engineering, The Australian National University, Canberra 2601, Australia 123 Journal of Thermal Analysis and Calorimetry https://doi.org/10.1007/s10973-019-08007-z