Exploring double-diffusive nanofluid flow in divergent/convergent nondarcy porous space: A machine learning numerical approach with zero mass flux

Abstract

In this study, authors address the problem of analyzing the Jeffrey–Hamel nanofluid flow within a nonparallel channel under the influence of a thermally balanced non-Darcy permeable medium. Our objective is to explore the behavior of the nanofluid, employing the Buongiorno nanofluid model, and considering factors such as zero mass flux conditions, variable rheological fluid properties, and the presence of temperature jump phenomena through ANN-PSO-NNA. To tackle this intricate issue, propose a novel approach using Artificial Neural Networks (ANN) integrated with particle swarm optimization (PSO) hybrid with neural network algorithm (NNA). This combined technique is referred to as ANN-PSO-NNA. The governing flow equations based on the Jeffrey–Hamel analysis are first transformed into dimensionless forms. To establish the efficacy of our approach compare it with the widely used NDSolve method. Furthermore, the study presents the absolute error analysis for four distinct cases offering a quantitative assessment of the accuracy of ANN-PSO-NNA. The absolute error between the NDsolve and the proposed ANN-PSO-NNA is given for four different cases, ranging from 1.95E-06 to 1.18E-08. The biases and weights obtained through proposed method range from −10 to 10. This enables us to gauge the performance of the ANN-PSO-NNA minimum values of the fitness function 2.37E-08, 2.30E-08, 3.92E-08, and 1.22E-08 from multiple independent runs, which are showcased to be convergent, underscoring the robustness of the ANN-PSO-NNA approach. Employing graphical representations, explores the influence of various parameters on the velocity and temperature profiles. Our integrated approach offers a comprehensive understanding of the underlying dynamics, paving the way for optimized designs and enhanced efficiency across these diverse engineering applications.

Keywords:

• Artificial neural networks (ANN)
• double diffusion convection
• nanofluid
• neural network algorithm (NNA)
• particle swarm optimization (PSO)

Data availability statement

The manuscript has no associated data.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Table 1. Comparison velocity between NDSolve and ANN-PSO-NNA for $\mathit{\text{Re}}=1,\lambda =0.1,{\lambda }_1=0.1,\beta =0.$

Table 2. Comparison velocity between NDSolve and ANN-PSO-NNA for $\mathit{\text{Re}}=1,\lambda =0.1,{\lambda }_1=0.1,\beta =0.$