Higher-order super-compact scheme for three-dimensional heat transfer with nanofluid and conducting fins

Abstract

This study presents a new higher-order super-compact (HOSC) finite difference scheme for analyzing enhanced heat transfer of three-dimensional (3D) nanofluid natural convection in a cubic cavity. The problem is motivated by the need for efficient numerical methods to analyze heat transfer enhancement in nanofluid-based systems. The novelty of this work lies in the extension of the higher-order super-compact finite difference scheme to examine the natural convection of nanofluid in the 3D cavity. This numerical approach achieves fourth-order spatial accuracy and second-order temporal accuracy. ‘Super-compact’ term signifies its efficiency, utilizing 19 grid points at the current time level $(n^{th}$ time level) and just seven grid points at the subsequent time level $({(n+1)}^{th}$ time level) around which the finite difference discretization is made. The nanoparticle volume fraction is maintained up to 0.04 (4%) to ensure the mixture exhibits Newtonian behavior. The newly developed numerical scheme is validated by qualitative and quantitative comparisons with existing benchmark results. The scheme is then applied to investigate fluid flow and heat transfer phenomena in a Cu-water nanofluid-filled cavity over a range of Rayleigh numbers (${10}^2\le Ra\le {10}^5$), considering $Ra={10}^2,{10}^3,{10}^4$, and 10⁵, and nanoparticle volume fractions of $\varphi =0.0,0.02$, and 0.04. In addition to introducing the new HOSC scheme for the convection of nanofluids, we examine two cases: the natural convection of nanofluid in a simple 3D cavity and a configuration incorporating two aluminum conducting fins on the heated wall to further enhance the heat transfer rate. Results are presented through isotherms, streamlines, local Nusselt numbers, and average Nusselt numbers for both the considered cases and compared their results. Present computed results reveal significant modifications in thermal performance due to the dual fin configuration. The incorporation of two conducting fins enhances the heat transfer rate by up to 88.9% at $Ra={10}^2$. However, the study also demonstrates that the addition of nanoparticles or conducting fins does not always lead to enhanced heat transfer. Notably, at $Ra={10}^5$, the combination of conducting fins and nanofluids can result in a counterintuitive reduction in heat transfer efficiency, deviating from conventional expectations. These findings provide new insights into the interplay between fin geometry, nanoparticle concentration, and convective heat transfer mechanisms in complex 3D systems.