<p>This work proposes an innovative approach utilizing Gegenbauer wavelet derivative operational matrix (GWDM) to address system of nonlinear differential equation which models the magnetohydrodynamic squeezing nanofluid flow and heat transfer between parallel porous disk. To establish the applicability of the novel approach, a system of nonlinear boundary value problems with exact solutions is utilized as a test problem. Outcomes of the test problem are compared with exact solution, Haar wavelet-based method (HWM), and RK-45 method and has been displayed in figures. For <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_936_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">$N = 13$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>=</mo> <mn>13</mn> </mrow> </math></EquationSource> </InlineEquation>, GWDM achieves an error accuracy of up to E−10 and E−11 for the test problem. Through the application of similarity transformation, the fundamental governing equations of the flow problem were subsequently transformed into a collection of coupled nonlinear ordinary differential equations and are solved by the proposed method. The influence of physical parameters, including the squeezing number, magnetic number, suction parameter, Eckert number, and Prandtl number on velocity and temperature profile is illustrated effectively. As <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_936_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">$Ec$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">Ec</mi> </mrow> </math></EquationSource> </InlineEquation> increases from 0.4 to 0.7, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_936_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$\Pr$</EquationSource> <EquationSource Format="MATHML"><math> <mo>Pr</mo> </math></EquationSource> </InlineEquation> from 3.3 to 3.9 and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_936_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">$\delta$</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation> from 0.3 to 0.6 the temperature between the middle of the disk rises by 15.99%, 3.28% and 10.15% respectively. Out of the four distinct shapes and three nanoparticles, the spherical <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_936_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">$Al_{2} O_{3}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>A</mi> <msub> <mi>l</mi> <mn>2</mn> </msub> <msub> <mi>O</mi> <mn>3</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> nanoparticle performs better in heat transmission about 0.37% than the others. The local heat transfer rate and skin friction coefficient are quantified using physical parameters.</p>

Gegenbauer wavelet operational derivative method for the numerical solution of squeezing nanofluid flow and heat transfer between parallel disk with shape factor effect

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发表日期：

2025年6月16日

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

摘要

This work proposes an innovative approach utilizing Gegenbauer wavelet derivative operational matrix (GWDM) to address system of nonlinear differential equation which models the magnetohydrodynamic squeezing nanofluid flow and heat transfer between parallel porous disk. To establish the applicability of the novel approach, a system of nonlinear boundary value problems with exact solutions is utilized as a test problem. Outcomes of the test problem are compared with exact solution, Haar wavelet-based method (HWM), and RK-45 method and has been displayed in figures. For $N = 13$ $N = 13$ , GWDM achieves an error accuracy of up to E−10 and E−11 for the test problem. Through the application of similarity transformation, the fundamental governing equations of the flow problem were subsequently transformed into a collection of coupled nonlinear ordinary differential equations and are solved by the proposed method. The influence of physical parameters, including the squeezing number, magnetic number, suction parameter, Eckert number, and Prandtl number on velocity and temperature profile is illustrated effectively. As $Ec$ $Ec$ increases from 0.4 to 0.7, $\Pr$ $Pr$ from 3.3 to 3.9 and $\delta$ $δ$ from 0.3 to 0.6 the temperature between the middle of the disk rises by 15.99%, 3.28% and 10.15% respectively. Out of the four distinct shapes and three nanoparticles, the spherical $Al_{2} O_{3}$ $A l_{2} O_{3}$ nanoparticle performs better in heat transmission about 0.37% than the others. The local heat transfer rate and skin friction coefficient are quantified using physical parameters.