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<p>Williamson fluid has been utilized to explore the aligned magnetic field in the presence of thermal radiation and heat source/sink utilizing Newtonian heating on a stretched sheet soaked in porous medium. The governing partial differential equations are transformed into nonlinear ordinary differential equations by applying similarity transformations. These equations are then solved using MATLAB and the Runge-Kutta fourth-order technique with a shooting technique. Graphs were used to investigate the effects of different factors on dimensionless velocity and temperature. A decrease in the velocity field and an improvement in the distribution of temperature are caused by an enhancement in the Non-Newtonian Williamson fluid parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2024_258_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:\xi\:\)</EquationSource> </InlineEquation> and permeability restriction K, whereas the opposite effect is evident when the Aligned angle parameter <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2024_258_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:\varphi\:,\)</EquationSource> </InlineEquation> is increased. When the conjugate factor for Newtonian heating parameter <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2024_258_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:\varUpsilon\:,\)</EquationSource> </InlineEquation> is increased, temperature rises, even as the reverse effect is seen in Prandtl number <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2024_258_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:Pr.\)</EquationSource> </InlineEquation> The coefficient of skin friction is an decreasing function and the Nusselt number is increasing function of Non-Newtonian Williamson fluid parameter<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2024_258_Article_IEq5.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:\:\xi\:\)</EquationSource> </InlineEquation> and permeability restriction K. while the reverse effect is seen in Aligned angle parameter <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2024_258_Article_IEq6.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:\phi\:\)</EquationSource> </InlineEquation>. The Nusselt number is increased function of heat source/sink parameter <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2024_258_Article_IEq7.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:\delta\:\)</EquationSource> </InlineEquation>, and Newtonian heating parameter <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2024_258_Article_IEq8.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:\varUpsilon\:\)</EquationSource> </InlineEquation>. While the reverse effect is seen in Prandtl number <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2024_258_Article_IEq9.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:Pr\)</EquationSource> </InlineEquation>.</p>

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Numerical Study of Williamson Fluid Flow over a Stretching Sheet with Newtonian Heating Embedded in a Porous Medium in Presence of Thermal Radiation and Heat Source/Sink

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  • 发表日期：

    2025年1月16日

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  • Ravindra Kumar,
  • Ruchika Mehta,
  • Anurag Bhatnagar,
  • Ilker Ozsahin,
  • Berna Uzun,
  • Bandar Almohsen,
  • Hijaz Ahmad

摘要

Williamson fluid has been utilized to explore the aligned magnetic field in the presence of thermal radiation and heat source/sink utilizing Newtonian heating on a stretched sheet soaked in porous medium. The governing partial differential equations are transformed into nonlinear ordinary differential equations by applying similarity transformations. These equations are then solved using MATLAB and the Runge-Kutta fourth-order technique with a shooting technique. Graphs were used to investigate the effects of different factors on dimensionless velocity and temperature. A decrease in the velocity field and an improvement in the distribution of temperature are caused by an enhancement in the Non-Newtonian Williamson fluid parameter \(\:\xi\:\) and permeability restriction K, whereas the opposite effect is evident when the Aligned angle parameter \(\:\varphi\:,\) is increased. When the conjugate factor for Newtonian heating parameter \(\:\varUpsilon\:,\) is increased, temperature rises, even as the reverse effect is seen in Prandtl number \(\:Pr.\) The coefficient of skin friction is an decreasing function and the Nusselt number is increasing function of Non-Newtonian Williamson fluid parameter \(\:\:\xi\:\) and permeability restriction K. while the reverse effect is seen in Aligned angle parameter \(\:\phi\:\) . The Nusselt number is increased function of heat source/sink parameter \(\:\delta\:\) , and Newtonian heating parameter \(\:\varUpsilon\:\) . While the reverse effect is seen in Prandtl number \(\:Pr\) .