Lattice Boltzmann Modeling of natural convection in electronic cooling: Analysis of partially bottom-heated square enclosures

The Lattice Boltzmann Method (LBM) is used to analyze the flow with heat transfer in a two-dimensional closed enclosure filled with air (Pr = 0.71). The enclosure has a partially heated bottom wall segment, whose length varies from 0.2 to 0.8 times the total width, subjected to a hot temperature T<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</inf>. This segment can represent an electronic component, with insulated top and bottom walls, the side-walls are kept at cold temperature T<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</inf>. To analyze the effect of heat source length variations on the thermal convection flow, characterized by a Rayleigh number between 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> and 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup>, we used a mesoscopic D2Q9 lattice configuration with the BGK (Bhatnagar-Gross-Krook) collision model. The results show a positive correlation between heated segment length and the Rayleigh number. Isotherms and streamlines agree well with the literature results. In this study, we extended previous investigations by examining the interaction between the heat source width and the Rayleigh number over several orders of magnitude, through a systematic approach to thermal parameters. We analyzed the transition from a conduction-dominated regime to a convection*-dominated regime. Furthermore, we believe that the results provide valuable guidelines for the design of electronic cooling applications, where optimization of component size and thermal management is very important.