Critical points and stability analysis in MHD radiative non‐Newtonian nanoliquid transport phenomena with artificial neural network prediction

Abstract

In the present framework, flow and thermal transport behavior of non-Newtonian viscoelastic fluid induced by stretching/shrinking of the horizontal sheet under the influence of Lorentz force, volumetric heat source/sink, and radiation (assuming optically thick medium) has been investigated. Multiple solutions (Branches) have been predicted numerically using Lie symmetry transformation and Runge Kutta Dormand Prince (RKDP) algorithm-based Shooting method for the different controlling parameters, stretching/shrinking (𝛾 c < −1 < 𝛾 < ∞), and suction (𝛼 c < 𝛼 < ∞) with substantial impact with UCM parameter, 𝛽 > 0. Some of the results have also been compared with MATLAB built-in solvers to validate our in-house code. The deviations in critical (turning) points (𝛽 c , 𝛾 c ) have been noticed for different values of M and 𝛼. The temporal stability analysis is performed for these parameters (𝛽, 𝛾), and the upper (lower) branch is only physically feasible (infeasible). The combined effect on Nusselt number and skin-friction coefficient is also depicted in the form of contour plots. The outcomes from artificial neural network (ANN) using Levenberg-Marquardt algorithm give a preferred estimate for current numerical simulation. In ANN prediction, the optimal number of neurons in the hidden layer is used, having minimum value of RMSE and RMRE with maximum R 2 for different cases of non Newtonian stretching/shrinking sheet. Finally, the results conclude that the applied ANN model can accurately predict the output results.

Multiple solutions and stability analysis in MHD non‐Newtonian nanofluid slip flow with convective and passive boundary condition: Heat transfer optimization using RSM‐CCD

“…The linear form of Rosseland approximation is implemented for radiative heat flux (𝑞 𝑟 ). The governing equation may be written by following [44,[57][58][59][60][61] as: (3)…”

“…The linear form of Rosseland approximation is implemented for radiative heat flux ($$q_r$$). The governing equation may be written by following [44, 57–61] as: $$$$\begin{equation} \frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0 \end{equation}$$$$ $$$$\begin{equation} \frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}=\nu \frac{{{\partial }^{2}}u}{\partial {{y}^{2}}} + \sqrt {2} \nu \Gamma \frac{\partial u}{\partial y} \frac{\partial ^2 u}{\partial y^2}-\frac{\sigma B^{2}}{\rho }u \end{equation}$$$$ …”

“…Heat and flow transportation of non-Newtonian fluids [39][40][41][42][43][44] are generally experienced in numerous mechanical and innovative applications, for example, glues, asphalts, paints, biological solutions, dissolved polymers, and so forth. Most particulate slurries like inks, sewage sludge, coal in water, China clay, and so forth and multi-phase blends like emulsions of oil and water, dispersion of gases and liquid like butter, froths and foams, and so forth are characterized under the category of non-Newtonian fluids.…”