<p>Artificial neural networks play a vital role in predicting and analyzing magnetohydrodynamic natural convection of Boger nanofluids around a semi-circular obstacle inside a triangular cavity, providing key insights for enhancing thermal performance. This study conducts a detailed numerical investigation of Boger nanofluid flow within a triangular cavity, governed by the Cattaneo–Christov heat flux model and influenced by non-uniform internal heat sources/sinks, thermal radiation, and Lorentz forces. A semi-circular obstacle with distinct thermal boundary conditions is placed inside the cavity, which features adiabatic bottom-left and bottom-right inclined walls, while the central segments of the top, left, and right walls are maintained at a high temperature. Heat transfer arises due to the movement of these heated regions and temperature gradients within the cavity, leading to complex convection behavior. The dimensionless nonlinear partial differential equations are solved using the finite element method, accompanied by a comprehensive parametric analysis. The effects of critical parameters such as solvent fraction (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$200 \le \beta _1 \le 300$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>200</mn> <mo>≤</mo> <msub> <mi>β</mi> <mn>1</mn> </msub> <mo>≤</mo> <mn>300</mn> </mrow> </math></EquationSource> </InlineEquation>), time relaxation ratio (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$7 \le \beta _2 \le 11$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>7</mn> <mo>≤</mo> <msub> <mi>β</mi> <mn>2</mn> </msub> <mo>≤</mo> <mn>11</mn> </mrow> </math></EquationSource> </InlineEquation>), Darcy number (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$10^{-2} \le Da \le 10$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> <mo>≤</mo> <mi>D</mi> <mi>a</mi> <mo>≤</mo> <mn>10</mn> </mrow> </math></EquationSource> </InlineEquation>), Rayleigh number (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$10^{1.5} \le Ra \le 10^{2.5}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mn>10</mn> <mrow> <mn>1.5</mn> </mrow> </msup> <mo>≤</mo> <mi>R</mi> <mi>a</mi> <mo>≤</mo> <msup> <mn>10</mn> <mrow> <mn>2.5</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>), time (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">$0.05 \le Ra \le 0.5$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0.05</mn> <mo>≤</mo> <mi>R</mi> <mi>a</mi> <mo>≤</mo> <mn>0.5</mn> </mrow> </math></EquationSource> </InlineEquation>), and thermal relaxation parameter (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">$10 \le \gamma \le 50$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>10</mn> <mo>≤</mo> <mi>γ</mi> <mo>≤</mo> <mn>50</mn> </mrow> </math></EquationSource> </InlineEquation>) are evaluated through changes in isotherms and streamlines. Results indicate that increasing the solvent fraction enhances vertical velocity and temperature distribution but reduces the Nusselt number along the heated surfaces and semi-circular region. Moreover, higher values of thermal relaxation and radiation parameters tend to suppress the temperature field. The analysis concludes that heat transfer, as reflected by the Nusselt number, is more efficient on the cold semi-circular boundary compared to the heated semi-circular. The ANN predictions exhibit excellent consistency with FEM simulations, lending credibility to the ANN framework as a surrogate modeling strategy for estimating local Nusselt numbers in complex thermal systems.</p>

Artificial neural network analysis of Boger nanofluid natural convection with thermal radiation in a triangular cavity containing a semi-circular obstacle

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发表日期：

2026年2月2日

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Shuke Li,
Qadeer Raza,
Xiaodong Wang,
Tahir Mushtaq,
Bagh Ali

摘要

Artificial neural networks play a vital role in predicting and analyzing magnetohydrodynamic natural convection of Boger nanofluids around a semi-circular obstacle inside a triangular cavity, providing key insights for enhancing thermal performance. This study conducts a detailed numerical investigation of Boger nanofluid flow within a triangular cavity, governed by the Cattaneo–Christov heat flux model and influenced by non-uniform internal heat sources/sinks, thermal radiation, and Lorentz forces. A semi-circular obstacle with distinct thermal boundary conditions is placed inside the cavity, which features adiabatic bottom-left and bottom-right inclined walls, while the central segments of the top, left, and right walls are maintained at a high temperature. Heat transfer arises due to the movement of these heated regions and temperature gradients within the cavity, leading to complex convection behavior. The dimensionless nonlinear partial differential equations are solved using the finite element method, accompanied by a comprehensive parametric analysis. The effects of critical parameters such as solvent fraction ( $200 \le \beta _1 \le 300$ $200 \leq β_{1} \leq 300$ ), time relaxation ratio ( $7 \le \beta _2 \le 11$ $7 \leq β_{2} \leq 11$ ), Darcy number ( $10^{-2} \le Da \le 10$ $10^{- 2} \leq D a \leq 10$ ), Rayleigh number ( $10^{1.5} \le Ra \le 10^{2.5}$ $10^{1.5} \leq R a \leq 10^{2.5}$ ), time ( $0.05 \le Ra \le 0.5$ $0.05 \leq R a \leq 0.5$ ), and thermal relaxation parameter ( $10 \le \gamma \le 50$ $10 \leq γ \leq 50$ ) are evaluated through changes in isotherms and streamlines. Results indicate that increasing the solvent fraction enhances vertical velocity and temperature distribution but reduces the Nusselt number along the heated surfaces and semi-circular region. Moreover, higher values of thermal relaxation and radiation parameters tend to suppress the temperature field. The analysis concludes that heat transfer, as reflected by the Nusselt number, is more efficient on the cold semi-circular boundary compared to the heated semi-circular. The ANN predictions exhibit excellent consistency with FEM simulations, lending credibility to the ANN framework as a surrogate modeling strategy for estimating local Nusselt numbers in complex thermal systems.