Thermal management of the central processing unit cooling system using a cylindrical metal foam heat sink under the influence of magnetohydrodynamic nanofluid flow
Authors: Izadi Ali Akbar , Rasam Hamed 
Published: September 2023

Purpose
Efficient thermal management of central processing unit (CPU) cooling systems is vital in the context of advancing information technology and the demand for enhanced data processing speeds. This study aims to explore the thermal performance of a CPU cooling setup using a cylindrical porous metal foam heat sink.

Design/methodology/approach
Nanofluid flow through the metal foam is simulated using the Darcy–Brinkman–Forschheimer equation, accounting for magnetic field effects. The temperature distribution is modeled through the local thermal equilibrium equation, considering viscous dissipation. The problem’s governing partial differential equations are solved using the similarity method. The CPU’s hot surface serves as a solid wall, with nanofluid entering the heat sink as an impinging jet. Verification of the numerical results involves comparison with existing research, demonstrating strong agreement across numerical, analytical and experimental findings. Ansys Fluent® software is used to assess temperature, velocity and streamlines, yielding satisfactory results from an engineering standpoint.

Findings
Investigating critical parameters such as Darcy number (10−4 ≤ DaD ≤ 10−2), aspect ratio (0.5 ≤ H/D ≤ 1.5), Reynolds number (5 ≤ ReD,bf ≤ 3500), Eckert number (0 ≤ ECbf ≤ 0.1) , porosity (0.85 ≤ ε ≤ 0.95), Hartmann number (0 ≤ HaD,bf ≤ 300) and the volume fraction of nanofluid (0 ≤ φ ≤ 0.1) reveals their impact on fluid flow and heat sink performance. Notably, Nusselt number will reduce 45%, rise 19.2%, decrease 14.1%, and decrease 0.15% for Reynolds numbers of 600, with rising porosity from 0.85 to 0.95, Darcy numbers from 10−4 to 10−2, Eckert numbers from 0 to 0.1, and Hartman numbers from 0 to 300.

Originality/value
Despite notable progress in studying thermal management in CPU cooling systems using porous media and nanofluids, there are still significant gaps in the existing literature. First, few studies have considered the Darcy–Brinkman–Forchheimer equation, which accounts for non-Darcy effects and the flow and geometric interactions between coolant and porous medium. The influence of viscous dissipation on heat transfer in this specific geometry has also been largely overlooked. Additionally, while nanofluids and impinging jets have demonstrated potential in enhancing thermal performance, their utilization within porous media remains underexplored. Furthermore, the unique thermal and structural characteristics of porous media, along with the incorporation of a magnetic field, have not been fully investigated in this particular configuration. Consequently, this study aims to address these literature gaps and introduce novel advancements in analytical modeling, non-Darcy flow, viscous dissipation, nanofluid utilization, impinging jets, porous media characteristics and the impact of a magnetic field. These contributions hold promising prospects for improving CPU cooling system thermal management and have broader implications across various applications in the field.