Quantitative analysis of Maxwell fluid flow with dual diffusion through the variable porous canonical gap using artificial neural network approach

Abstract

This work investigates the Maxwell fluid flow in the variable porous space of cone and disc influenced by double diffusion on a variable porous space. In this study, the heat and mass transfer is influenced by the combined effects of Fourier’s and Fick’s laws, leading to heat and mass flux assumptions proposed by Cattaneo-Christov to characterize these transfer phenomena. The modeled equations have been converted to dimensionless form by using a suitable set of appropriate variables. This set of dimensionless equations was then solved by using artificial neural networks (ANNs). For this, initially, HAM (homotopy analysis method) has been used for the evaluation of modeled equations, and then, to analyze the dynamics of flow, Levenberg Marquardt Scheme through Neural Network Algorithm (LMS-NNA) has been employed. The optimal performance of the fluid model is observed at the epoch 10, 08, 427, 164, 203, 146, 101, 130, 255, 298, 166, and 222. The proximity to unity is a pivotal observation in this work that has been signifying a high degree of precision in the LMS-NNA design for the proposed model. The porosity factor has opposed the primary velocity profiles and has supported the secondary velocity profiles. Moreover, primary velocity profiles have declined with growth in Maxwell factor while secondary velocity panels have retarded by the upsurge in the retardation time factor. Thermal distribution has been supported by progression in thermophoresis and Brownian motion factors and has been opposed by escalation in the Prandtl number. Concentration distribution has augmented with the upsurge in thermophoresis factor and has declined with the escalation in factor, Schmidt number, and concentration relaxation time factor. It has been also observed in this work that the variable porous space controls the fluid flow and maintains the stability of Maxwell fluid flow between the cone and disc apparatus. The maximum error for testing, training, and validation of the proposed model is achieved for all 12 cases and discussed numerically in tabular form.