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<p>The main purpose of the Levenberg–Marquardt Scheme to analyze flow behvaiour of on non-Newtonian fluid models influenced by gyrotactic microorganisms. The research addresses the complexities of fluid behavior in the presence of biological entities and thermal effects. The study begins by establishing the governing equations for fluid flow as partial differential equations, which are transformed into ordinary differential equations. The numerical solution are obtained with MATLAB ODEs solver bbvp4c. The Levenberg–Marquardt Scheme (LMS) is integrated with a Backpropagation Neural Network (BPNN) to enhance the accuracy of predictions. The efficacy of the proposed LMS-BPNN model is assessed using various statistical metrics, i.e. correlation index, linear regression, and mean squared error. These metrics confirm that LMS-BPNN model provides reliable predictions for fluid dynamics in this context. The study graphically illustrates the effects of various parameters on the momentum boundary layer, thermal boundary layer, species concentration, and motile microorganism behavior. The results show a strong correlation between numerical and predicted results, validating the effectiveness of the LMS-BPNN approach for modeling complex fluid behaviors involving non-Newtonian fluids and gyrotactic microorganisms. The thermal boundary layer grow as there is an increment in the values hybrid nanoparticles (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_817_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="57" /> </InlineMediaObject> <EquationSource Format="TEX">\({\phi }_{1}={\phi }_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>ϕ</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>ϕ</mi> <mn>2</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>). The study contributes valuable insights into how various parameters affect momentum, thermal dynamics, and concentration distributions in fluid mechanics, paving the way for future research in this domain.</p>

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Thermal energy in electro-permeable eyring-powell hybrid nano-fluid: an advanced thermo-biological computational modeling approach

  • 期刊论文

  • 发表日期：

    2025年3月25日

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  • Zheng Mingliang,
  • Refka Ghodhbani,
  • Arslan Bin Amjad,
  • Muhammad Imran Khan,
  • Ahmed Zeeshan,
  • Najma Saleem,
  • Nouman Ijaz

摘要

The main purpose of the Levenberg–Marquardt Scheme to analyze flow behvaiour of on non-Newtonian fluid models influenced by gyrotactic microorganisms. The research addresses the complexities of fluid behavior in the presence of biological entities and thermal effects. The study begins by establishing the governing equations for fluid flow as partial differential equations, which are transformed into ordinary differential equations. The numerical solution are obtained with MATLAB ODEs solver bbvp4c. The Levenberg–Marquardt Scheme (LMS) is integrated with a Backpropagation Neural Network (BPNN) to enhance the accuracy of predictions. The efficacy of the proposed LMS-BPNN model is assessed using various statistical metrics, i.e. correlation index, linear regression, and mean squared error. These metrics confirm that LMS-BPNN model provides reliable predictions for fluid dynamics in this context. The study graphically illustrates the effects of various parameters on the momentum boundary layer, thermal boundary layer, species concentration, and motile microorganism behavior. The results show a strong correlation between numerical and predicted results, validating the effectiveness of the LMS-BPNN approach for modeling complex fluid behaviors involving non-Newtonian fluids and gyrotactic microorganisms. The thermal boundary layer grow as there is an increment in the values hybrid nanoparticles ( \({\phi }_{1}={\phi }_{2}\) ϕ 1 = ϕ 2 ). The study contributes valuable insights into how various parameters affect momentum, thermal dynamics, and concentration distributions in fluid mechanics, paving the way for future research in this domain.