New Higher-Order Super-Compact Scheme for Enhanced Three-Dimensional Heat Transfer with Nanofluid and Conducting Fins

TL;DR

This paper introduces a novel higher-order super-compact finite difference scheme for 3D nanofluid heat transfer analysis, achieving high accuracy with minimal grid points, validated against benchmarks, and applied to optimize heat transfer with fins and nanoparticles.

Contribution

The work extends a higher-order super-compact finite difference scheme to 3D nanofluid convection, achieving fourth-order spatial accuracy with minimal grid points, and explores heat transfer enhancement strategies.

Findings

Nanoparticles and fins do not always improve heat transfer.

The scheme accurately predicts natural convection phenomena.

Heat transfer effectiveness depends on multiple parameters.

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 unique contribution of the present 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 ($10^2 \leq Ra \leq 10^5$). 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. It is found that the addition of nanoparticles or conducting fins does not always lead to enhanced heat transfer rates. Instead, the effectiveness of these enhancements is highly dependent on a range of parameters, which are thoroughly examined and discussed in this work.