Efficient thermal management in compact engineering systems requires enhanced heat transfer with minimal hydraulic penalties. This study investigates the magnetohydrodynamics (MHD) of forced convection of a Cu–CuO–Al2O3/water ternary hybrid nanofluid in a corrugated channel equipped with porous baffles. Unlike previous studies primarily using impermeable baffles, the present work combines corrugated heated walls, permeability-controlled porous baffles, ternary hybrid nanofluid transport, and artificial neural network (ANN)-based surrogate modeling within a unified framework. The governing equations are discretized and solved using the finite element method (FEM), where the clear fluid region is modeled using the Navier–Stokes equations and the porous baffle's region is modeled using the Darcy–Brinkman–Forchheimer formulation under local thermal equilibrium (LTE). The effects of the Reynolds number (Re), Darcy number (Da), Hartmann number (Ha), and nanoparticle volume fraction ($ \varphi $) are analyzed in terms of streamlines, isotherms' contours, Nusselt numbers, pressure drop, and the thermo-hydraulic performance index. The results show that replacing solid baffles with porous baffles increases the mean Nusselt number by approximately 5.55% while reducing the pressure drop by 13.22%. Furthermore, increasing the Da from 10–6 to 10–2 enhance the mean Nusselt number by approximately 13.14% and decrease the pressure drop by 9.36%, demonstrating the importance of permeability-controlled flow penetration. The performance index remains above unity, conforming a favorable balance between thermal enhancement and hydraulic resistance. To complement the mathematical simulations, feedforward ANNs using hyperbolic tangent sigmoid function and Levenberg–Marquart taring are developed to predict the U-velocity, V-velocity, temperature, and Nusselt number from the FEM-generated datasets. Regression, error, residual, and FEM-ANN comparisons demonstrate strong predictive agreement, conforming the capability of the ANN models to reproduce the nonlinear thermo-hydrodynamic responses. The combined FEM-ANN framework provides an effective approach for analyzing and predicting coupled MHD transport in porous flow systems.
Citation: Talal Ali Alzahrani, Saleh Mousa Alzahrani. Mathematical and machine learning analysis of MHD ternary hybrid nanofluid flow through a porous-baffled corrugated channel[J]. AIMS Mathematics, 2026, 11(10): 34730-34762. doi: 10.3934/math.20261353
Efficient thermal management in compact engineering systems requires enhanced heat transfer with minimal hydraulic penalties. This study investigates the magnetohydrodynamics (MHD) of forced convection of a Cu–CuO–Al2O3/water ternary hybrid nanofluid in a corrugated channel equipped with porous baffles. Unlike previous studies primarily using impermeable baffles, the present work combines corrugated heated walls, permeability-controlled porous baffles, ternary hybrid nanofluid transport, and artificial neural network (ANN)-based surrogate modeling within a unified framework. The governing equations are discretized and solved using the finite element method (FEM), where the clear fluid region is modeled using the Navier–Stokes equations and the porous baffle's region is modeled using the Darcy–Brinkman–Forchheimer formulation under local thermal equilibrium (LTE). The effects of the Reynolds number (Re), Darcy number (Da), Hartmann number (Ha), and nanoparticle volume fraction ($ \varphi $) are analyzed in terms of streamlines, isotherms' contours, Nusselt numbers, pressure drop, and the thermo-hydraulic performance index. The results show that replacing solid baffles with porous baffles increases the mean Nusselt number by approximately 5.55% while reducing the pressure drop by 13.22%. Furthermore, increasing the Da from 10–6 to 10–2 enhance the mean Nusselt number by approximately 13.14% and decrease the pressure drop by 9.36%, demonstrating the importance of permeability-controlled flow penetration. The performance index remains above unity, conforming a favorable balance between thermal enhancement and hydraulic resistance. To complement the mathematical simulations, feedforward ANNs using hyperbolic tangent sigmoid function and Levenberg–Marquart taring are developed to predict the U-velocity, V-velocity, temperature, and Nusselt number from the FEM-generated datasets. Regression, error, residual, and FEM-ANN comparisons demonstrate strong predictive agreement, conforming the capability of the ANN models to reproduce the nonlinear thermo-hydrodynamic responses. The combined FEM-ANN framework provides an effective approach for analyzing and predicting coupled MHD transport in porous flow systems.
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Figures(20) / Tables(2)
Talal Ali Alzahrani, Saleh Mousa Alzahrani. Mathematical and machine learning analysis of MHD ternary hybrid nanofluid flow through a porous-baffled corrugated channel[J]. AIMS Mathematics, 2026, 11(10): 34730-34762. doi: 10.3934/math.20261353
Schematic of a corrugated channel with porous baffles arranged in the BCL configuration
Finite element mesh with 98,272 elements
Convergence history of the fully coupled nonlinear FEM solver
(a) Comparison of the streamlines' contours predicted by the present numerical model with the refernce results of Hamza et al. [36] for a corrugated channel with solid obstacles at $ Ha = 0 $ and $ \phi = 0.03. $ (b) Comparison of the average Nusselt number obtained from the present FEM model with the numerical results of Hamza et al. [36] for the MCL configuration at $ Ha = 0 $ and $ \phi = 0 $
Streamlines for the solid baffle channel (top row) and the porous baffle channel (bottom row) for $ Re\ \mathrm{a}\mathrm{t}, \phi = 0.03\ \mathrm{a}\mathrm{n}\mathrm{d}\ Ha = 0.0. $ For the porous fin case, $ Da = {10}^{-3}\ \mathrm{and}\ ϵ = 0.6 $
Isotherms contours for the solid baffle channel (top row) and the porous baffle channel (bottom row) for $ Re\ \mathrm{at}, \phi = 0.03\ \mathrm{and}\ Ha = 0.0.\mathrm{For}\ \ \mathrm{the}\ \ \mathrm{porous}\ \ \mathrm{fin}\ \ \mathrm{case}, Da = {10}^{-3}\ \mathrm{and}\ ϵ = 0.6 $
Variation of (a) $ {Nu}_{avg} $ and (b) $ \mathrm{\Delta }\mathrm{P} $ with Re for the solid baffle channel and the porous baffle channel
Streamlines (top row) and isotherm contours (bottom row) for selected Da values in the porous baffle channel at $ Re = 100, \phi = 0.03, Ha = 10, \ \mathrm{a}\mathrm{n}\mathrm{d}\ ϵ = 0.6 $
Variation in (a) $ {Nu}_{avg} $ and (b) $ \mathrm{\Delta }\mathrm{P} $ with Da for the porous baffled channel
Streamlines (top row) and isotherms contours (bottom row) for selected Ha values in the porous baffle channel at $ Re = 100, \phi = 0.03, Da = {10}^{-3}, \ \mathrm{a}\mathrm{n}\mathrm{d}\ ϵ = 0.6 $
Variation in (a) $ {Nu}_{avg} $ and (b) $ \mathrm{\Delta }\mathrm{P} $ with Ha and $ \phi $ for the porous baffle channel
Vertical cutline profiles of (a) $ U $-velocity, (b) $ V $-velocity, (c) temperature $ \left(\theta \right) $, and (d) variation in the local Nusselt number (Nu) along the upper wavy heated wall for different values of $ Da $ at $ Re = 100, ϵ = 0.6 $, and $ \phi = 0.03 $
Thermo-hydraulic performance index (PI) for (a) porous fins relative to solid fins at different values of $ Re $, and (b) the porous baffle $ Da $ using $ Da = {10}^{-6} $ as the reference case
Architecture of the feedforward ANN used separately used for predicting the U-velocity, V-velocity, temperature, and local Nusselt number
Training and validation MSE learning curves for (a) U, (b) V, (c) $ \theta $, and (d) Nusselt number
Regression analysis between numerical and ANN-predicted values for (a) U, (b) V, (c) $ \theta $ and (d) Nusselt number
Prediction error histogram for (a) U, (b) V, (c) $ \theta $, and (d) Nusselt number (Nu)
Actual and ANN predicted values over the sample index for (a) U, (b) V, (c) $ \theta $, and (d) Nusselt number (Nu)
Residual probability density distribution for ANN-based predictions of (a) U, (b) V, (c) $ \theta $, and (d) Nusselt number (Nu)
Comparison between the numerical simulation and ANN predictions for (a) U, (b) V, (c) $ \theta $ and (d) Nusselt number (Nu)
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