# Sensitivity analysis of natural convection in a porous cavity filled with nanofluid and equipped with horizontal fins using various optimization methods and MRT-LB

## TL;DR

This study optimizes heat transfer in a porous cavity with nanofluid and fins using various methods, finding the best configuration for maximum efficiency.

## Contribution

The paper introduces a novel combination of optimization methods and MRT-LB simulation for natural convection in porous nanofluid cavities with fins.

## Key findings

- The optimal configuration achieved an average Nusselt number of 5.56 with specific fin and nanofluid parameters.
- The Darcy number had the most significant impact on maximizing heat transfer, while the number of fins had the least.
- Optimal parameters included fin length L/2, two fins spaced L/12 apart, porosity 0.8, Darcy number 0.1, and nanoparticle fraction 0.02.

## Abstract

In the present study, natural convection heat transfer is investigated in a porous cavity filled with Cu/water nanofluid and equipped with horizontal fins. Optimization and sensitivity analysis of the fin’s geometry, porous medium and nanofluid properties to maximize heat transfer rate is the aim of this work. To achieve this purpose, a design space is created by input parameters which include length, number of fins, distance between fins, porosity, Darcy number and volumetric fraction of the nanoparticles. Several tools have been used to implement optimization methods including the Taguchi method (TM) for design points generation, sensitivity analysis of design variables by using signal-to-noise ratio (SNR) and analysis of variance (ANOVA), response surface method (RSM) for interpolation and regression by using nonparametric regression, and genetic algorithm (GA) for finding optimum design point. The double multi-relaxation time lattice Boltzmann method (MRT-LBM) is used to analyze and simulate the flow field and heat transfer in each design point. The results show that the optimal configuration leads to an average Nusselt number of 5.56. This optimal configuration is at the length of fins L/2, the number of fins 2, the distance between fins L/12, porosity 0.8, Darcy number 0.1, and the volumetric fraction of the nanoparticles 0.02. By using the SNR results, the Darcy number and the number of fins have the most and the least effect in maximizing the average Nusselt number, respectively. The ANOVA results and global sensitivity analysis (GSA) findings further validated this conclusion.