<p>This study examines radiative Casson<b>–</b>Carreau nanofluid flow on a dual-directional stretchable sheet. The surface is immured by variable Darcy medium and exposed to thermal and space-dependent heat sources. The flow is also affected by magnetic field in inclined direction. Heat and mass diffusions are controlled by employing Brownian motion and thermophoresis in combination of Cattaneo<b>–</b>Christov theory. In this study, solutions obtained from Parametric Continuation Method (PCM) are used as reference data to train an artificial neural network (ANN) based on the Levenberg<b>–</b>Marquardt back-propagation algorithm (LMBP). The generated dataset is employed for training, testing, and validation over a wide range of fluid parameter values to assess the modeled equations. It has deduced in this work that the primary and secondary velocities declined with surge in concentration of nanoparticles, variable porous and magnetic factors. Thermal panels have declined with surge in thermal relaxation time factor while amplified with growth in radiation factor, and thermal dependent heat source factor and thermal Boit number. Concentration profiles have enlarged for surge in Brownian motion factor and concentration Biot number while reduced with surge in mass relaxation time factor and Schmidt number. For all the scenarios the gradient values <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(6 \cdot 79 \times 10^{ - 5}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>6</mn> <mo>·</mo> <mn>79</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>5</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation><sub>,</sub><InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(1 \cdot 01 \times 10^{ - 7}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>·</mo> <mn>01</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>7</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation><InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(9.95 \times 10^{ - 8}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>9.95</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>8</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation><InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(4 \cdot 47 \times 10^{ - 5}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>4</mn> <mo>·</mo> <mn>47</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>5</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation><InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(4.82 \times 10^{ - 3}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>4.82</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(1 \cdot 49 \times 10^{ - 4}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>·</mo> <mn>49</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> are associated at the corresponding epochs 406, 555, 731, 939, 1000 and 1000.</p>

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Thermal dynamics of radiative Casson–Carreau nanofluid flow on a stretching surface subject to Cattaneo–Christov flux theory with machine learning approach

  • Mounirah Areshi,
  • Ebrahem A. Algehyne,
  • Fahad Maqbul Alamrani,
  • Rabab Alzahrani,
  • Weam G. Alharbi,
  • Arshad Khan

摘要

This study examines radiative CassonCarreau nanofluid flow on a dual-directional stretchable sheet. The surface is immured by variable Darcy medium and exposed to thermal and space-dependent heat sources. The flow is also affected by magnetic field in inclined direction. Heat and mass diffusions are controlled by employing Brownian motion and thermophoresis in combination of CattaneoChristov theory. In this study, solutions obtained from Parametric Continuation Method (PCM) are used as reference data to train an artificial neural network (ANN) based on the LevenbergMarquardt back-propagation algorithm (LMBP). The generated dataset is employed for training, testing, and validation over a wide range of fluid parameter values to assess the modeled equations. It has deduced in this work that the primary and secondary velocities declined with surge in concentration of nanoparticles, variable porous and magnetic factors. Thermal panels have declined with surge in thermal relaxation time factor while amplified with growth in radiation factor, and thermal dependent heat source factor and thermal Boit number. Concentration profiles have enlarged for surge in Brownian motion factor and concentration Biot number while reduced with surge in mass relaxation time factor and Schmidt number. For all the scenarios the gradient values \(6 \cdot 79 \times 10^{ - 5}\) 6 · 79 × 10 - 5 , \(1 \cdot 01 \times 10^{ - 7}\) 1 · 01 × 10 - 7 \(9.95 \times 10^{ - 8}\) 9.95 × 10 - 8 \(4 \cdot 47 \times 10^{ - 5}\) 4 · 47 × 10 - 5 \(4.82 \times 10^{ - 3}\) 4.82 × 10 - 3 and \(1 \cdot 49 \times 10^{ - 4}\) 1 · 49 × 10 - 4 are associated at the corresponding epochs 406, 555, 731, 939, 1000 and 1000.