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<p>The present study examines the behavior of nanofluid over an infinite permeable plate with a heat source sink, viscous dissipation, and mixed convection, focusing on thermophoretic particle deposition by using the response surface methodology and sensitivity analysis. The nanofluid is moving on one side of the plate, which is infinite in length along a vertical direction. The governing equations are reduced to nondimensional partial differential equations and solved with the Crank–Nicolson scheme. The solutions obtained for various dimensionless constraints are visualized with the help of graphs. The important engineering factors, such as skin friction and Nusselt number variations over different parameters, are discussed in detail. The concentration profile decreases for increasing values of the thermophoretic parameter. The rising values of the Eckert number will enhance the thermal profile. The sensitivity analysis is carried out by implementing response surface methodology (RSM) to obtain the connection between the parameters, such as porous parameter, Grashof number, and heat source-sink parameter, with the output response Nusselt number. With the help of the analysis of variance (ANOVA) table, the correlation among input and output variables is developed. The validity of correlated equations is checked with the help of residual graphs. The sensitivity analysis is carried out to find the prior influential inputs on the response, and it is found that the rate of heat transfer exhibits a strong correlation with <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14816_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\({\text{Gr}}_{{1}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>Gr</mtext> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>.</p>

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Crank Nicolson and response surface methodology-based simulation to analyze the thermophoretic particle deposition of nanofluids over an infinite porous plate under mixed convection: a sensitivity analysis

  • 期刊论文

  • 发表日期：

    2025年10月3日

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  • J. K. Madhukesh,
  • B. C. Prasannakumara,
  • Marouan Kouki,
  • Nehad Ali Shah

摘要

The present study examines the behavior of nanofluid over an infinite permeable plate with a heat source sink, viscous dissipation, and mixed convection, focusing on thermophoretic particle deposition by using the response surface methodology and sensitivity analysis. The nanofluid is moving on one side of the plate, which is infinite in length along a vertical direction. The governing equations are reduced to nondimensional partial differential equations and solved with the Crank–Nicolson scheme. The solutions obtained for various dimensionless constraints are visualized with the help of graphs. The important engineering factors, such as skin friction and Nusselt number variations over different parameters, are discussed in detail. The concentration profile decreases for increasing values of the thermophoretic parameter. The rising values of the Eckert number will enhance the thermal profile. The sensitivity analysis is carried out by implementing response surface methodology (RSM) to obtain the connection between the parameters, such as porous parameter, Grashof number, and heat source-sink parameter, with the output response Nusselt number. With the help of the analysis of variance (ANOVA) table, the correlation among input and output variables is developed. The validity of correlated equations is checked with the help of residual graphs. The sensitivity analysis is carried out to find the prior influential inputs on the response, and it is found that the rate of heat transfer exhibits a strong correlation with \({\text{Gr}}_{{1}}\) Gr 1 .