<p>This study develops a Python-Based Supervised Artificial Intelligence (PB-SAI) framework to examine the nonlinear thermofluidic performance of a kerosene-bound single- and multi-walled carbon nanotube (SWCNT–MWCNT) hybrid nanofluid over a stretchable porous surface subjecting to solar radiation and Darcy–Forchheimer resistance. The proposed framework develops a magnetohydrodynamic (MHD) model with critical transport phenomena involving Joule heating, thermal radiation, and viscous dissipation. The governing partial differential equations (PDEs) will be reduced to a coupled set of ordinary differential equations (ODEs) via similarity transformations, using <i>solve_bvp</i> in <i>SciPy</i> to numerically solve the system. The high-fidelity numerical solutions for the velocity and temperature profiles from the governing PDEs will be used as training data for a deep feedforward neural network (DFNN) built in PyTorch, utilizing <i>Swish</i> activation function and Adam optimizer. The trained artificial intelligence (AI) realizes high competency with MSE up to 10<sup>–6</sup>, along with regression accuracy around 0.9966, in confidence across nonlinear regimes. There are five dimensionless parameters on the performance metrics which were examined: magnetic parameter (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14852_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(M\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>M</mi> </math></EquationSource> </InlineEquation>), porosity parameter (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14852_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>), Forchheimer number (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14852_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(Fr\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">Fr</mi> </mrow> </math></EquationSource> </InlineEquation>), thermal radiation parameter (<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14852_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\(Rd\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">Rd</mi> </mrow> </math></EquationSource> </InlineEquation>), and Eckert number (<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14852_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\(Ec)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>E</mi> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. All results showed that increasing <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14852_Article_IEq6.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(M, \lambda\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>M</mi> <mo>,</mo> <mi>λ</mi> </mrow> </math></EquationSource> </InlineEquation>, and Fr significantly reduces velocity magnitude, whereas Rd, M, and Ec increase temperature distribution. This integrated PB-SAI modeling approach provided a robust and accurate solution method for simulating hybrid nanofluid transport modeling for solar energy, smart cooling systems, and next-generation aerospace energy applications. These outcomes can be directly applied to improve solar aircraft performance and contribute to sustainable aerospace energy solutions.</p>

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Hybrid computational modeling of solar aircraft efficiency in magnetohydrodynamics Darcy–Forchheimer flow using kerosene-based SWCNT and MWCNT nanofluids

  • Hanen Louati,
  • Zahoor Shah,
  • Muhammad Talha,
  • Mohammed M. A. Almazah

摘要

This study develops a Python-Based Supervised Artificial Intelligence (PB-SAI) framework to examine the nonlinear thermofluidic performance of a kerosene-bound single- and multi-walled carbon nanotube (SWCNT–MWCNT) hybrid nanofluid over a stretchable porous surface subjecting to solar radiation and Darcy–Forchheimer resistance. The proposed framework develops a magnetohydrodynamic (MHD) model with critical transport phenomena involving Joule heating, thermal radiation, and viscous dissipation. The governing partial differential equations (PDEs) will be reduced to a coupled set of ordinary differential equations (ODEs) via similarity transformations, using solve_bvp in SciPy to numerically solve the system. The high-fidelity numerical solutions for the velocity and temperature profiles from the governing PDEs will be used as training data for a deep feedforward neural network (DFNN) built in PyTorch, utilizing Swish activation function and Adam optimizer. The trained artificial intelligence (AI) realizes high competency with MSE up to 10–6, along with regression accuracy around 0.9966, in confidence across nonlinear regimes. There are five dimensionless parameters on the performance metrics which were examined: magnetic parameter ( \(M\) M ), porosity parameter ( \(\lambda\) λ ), Forchheimer number ( \(Fr\) Fr ), thermal radiation parameter ( \(Rd\) Rd ), and Eckert number ( \(Ec)\) E c ) . All results showed that increasing \(M, \lambda\) M , λ , and Fr significantly reduces velocity magnitude, whereas Rd, M, and Ec increase temperature distribution. This integrated PB-SAI modeling approach provided a robust and accurate solution method for simulating hybrid nanofluid transport modeling for solar energy, smart cooling systems, and next-generation aerospace energy applications. These outcomes can be directly applied to improve solar aircraft performance and contribute to sustainable aerospace energy solutions.