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<p>This study aims to present a numerical algorithm for solving a nonlinear system of differential equations arising in nanofluid dynamics. The Bernoulli wavelet operational matrix of integration (BWIOMM) together with dynamical constraints is used to approximate the control function directly as a function of the state function. Finally, these approximations were put in the system of differential equations and necessary boundary conditions under consideration in an algebraic system. The proposed method’s effectiveness is assessed by utilizing a test problem consisting a set of boundary value problems with exact solutions. The test problem outcomes are compared to the Haar wavelet integration operational matrix approach and the Range Kutta 45 method and are displayed in figures and tables. Later, nanofluid flow and heat transfer characteristics between two parallel plates were analysed using BWIOMM. The fluid within the channel consists of water that contains various nanoparticles<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40819_2025_1978_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="126" /> </InlineMediaObject> <EquationSource Format="TEX">\((Cu,\;Ag,\;A{l_2}{O_3})\)</EquationSource> </InlineEquation>. Investigations are conducted into the impacts of the power law index, Reynolds number, nanoparticle volume fraction, and expansion ratio on heat transfer and flow. The findings demonstrate that when the Reynolds number and nanoparticle volume fraction rise, so does the Nusselt number. Furthermore, copper should be employed as a nanoparticle to achieve the highest Nusselt number.</p>

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Bernoulli Wavelet Integration Operational Matrix Method for the Numerical Solution of Nanofluid Flow in an Asymmetric Porous Channel with Expanding or Contracting Wall

  • 期刊论文

  • 发表日期：

    2025年7月29日

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  • S. C. Shiralashetti,
  • V. R. Pala,
  • S. I. Hanaji

摘要

This study aims to present a numerical algorithm for solving a nonlinear system of differential equations arising in nanofluid dynamics. The Bernoulli wavelet operational matrix of integration (BWIOMM) together with dynamical constraints is used to approximate the control function directly as a function of the state function. Finally, these approximations were put in the system of differential equations and necessary boundary conditions under consideration in an algebraic system. The proposed method’s effectiveness is assessed by utilizing a test problem consisting a set of boundary value problems with exact solutions. The test problem outcomes are compared to the Haar wavelet integration operational matrix approach and the Range Kutta 45 method and are displayed in figures and tables. Later, nanofluid flow and heat transfer characteristics between two parallel plates were analysed using BWIOMM. The fluid within the channel consists of water that contains various nanoparticles \((Cu,\;Ag,\;A{l_2}{O_3})\) . Investigations are conducted into the impacts of the power law index, Reynolds number, nanoparticle volume fraction, and expansion ratio on heat transfer and flow. The findings demonstrate that when the Reynolds number and nanoparticle volume fraction rise, so does the Nusselt number. Furthermore, copper should be employed as a nanoparticle to achieve the highest Nusselt number.