<p>The present study aims to implement regression modeling using Response Surface Methodology (RSM) for analyzing the heat transfer and prediction of skin-friction coefficients of a magnetohydrodynamic (MHD) nanofluid flow across a vertical wedge along with its applications in data prediction and response optimization. The differential equations arising after the similarity transformations were solved using bvp4c in MATLAB. The importance of the present study lies in its application in forging of hot exhaust-valve heads, manufacture of water heaters, extrusion processes, cooling processes, turbine blades, and medical industries, etc. Some of the insightful results noted were increasing heat-transfer rates by <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11043_2025_9808_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mn>0.74</mn> <mi mathvariant="normal">%</mi> </math></EquationSource> <EquationSource Format="TEX">$0.74\%$</EquationSource> </InlineEquation> for nonaggregation modeling and by <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11043_2025_9808_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mn>0.78</mn> <mi mathvariant="normal">%</mi> </math></EquationSource> <EquationSource Format="TEX">$0.78\%$</EquationSource> </InlineEquation> for aggregated model with increase in the magnetic parameter from 0.2 to 0.8 followed by the increase in skin-friction coefficient for transition from nonaggregation to the aggregation model. Augmented velocity profiles by <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11043_2025_9808_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mn>2.08</mn> <mi mathvariant="normal">%</mi> </math></EquationSource> <EquationSource Format="TEX">$2.08\%$</EquationSource> </InlineEquation> were observed for the nonaggregation as compared to the aggregation model. A face-centerd central composite design was implemented in RSM for determining the Analysis of Variance (ANOVA) for our results using a quadratic fitting model with <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11043_2025_9808_Article_IEq4.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="149" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>=</mo> <mi>A</mi> <mi>d</mi> <mi>j</mi> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>=</mo> <mn>100</mn> <mi mathvariant="normal">%</mi> </math></EquationSource> <EquationSource Format="TEX">$R_{1}^{2}=Adj R_{1}^{2}=100\%$</EquationSource> </InlineEquation> for both the aggregation and nonaggregation models. The velocity-ratio parameter showed negative sensitivity to the response parameter. <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11043_2025_9808_Article_IEq5.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="130" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>P</mi> <mi>r</mi> <mi>e</mi> <mi>d</mi> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>=</mo> <mn>99.99</mn> <mi mathvariant="normal">%</mi> </math></EquationSource> <EquationSource Format="TEX">$Pred R_{1}^{2}=99.99\%$</EquationSource> </InlineEquation> represented very high predictability rate for new observations. The predicted values recorded a maximum absolute error of the order <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11043_2025_9808_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </math></EquationSource> <EquationSource Format="TEX">$10^{-4}$</EquationSource> </InlineEquation> when compared to the actual numerical data along with a desirability of <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11043_2025_9808_Article_IEq7.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mn>100</mn> <mi mathvariant="normal">%</mi> </math></EquationSource> <EquationSource Format="TEX">$100\%$</EquationSource> </InlineEquation> to attain the extremum values for both models.</p>

Flow optimization for a MHD radiative nanofluid across a moving vertical wedge with nanoparticle-aggregation effect: data prediction and response optimization

期刊论文
发表日期：

2025年7月29日

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Anomitra Chakraborty,
Pranitha Janapatla

摘要

The present study aims to implement regression modeling using Response Surface Methodology (RSM) for analyzing the heat transfer and prediction of skin-friction coefficients of a magnetohydrodynamic (MHD) nanofluid flow across a vertical wedge along with its applications in data prediction and response optimization. The differential equations arising after the similarity transformations were solved using bvp4c in MATLAB. The importance of the present study lies in its application in forging of hot exhaust-valve heads, manufacture of water heaters, extrusion processes, cooling processes, turbine blades, and medical industries, etc. Some of the insightful results noted were increasing heat-transfer rates by $0.74 %$ $0.74\%$ for nonaggregation modeling and by $0.78 %$ $0.78\%$ for aggregated model with increase in the magnetic parameter from 0.2 to 0.8 followed by the increase in skin-friction coefficient for transition from nonaggregation to the aggregation model. Augmented velocity profiles by $2.08 %$ $2.08\%$ were observed for the nonaggregation as compared to the aggregation model. A face-centerd central composite design was implemented in RSM for determining the Analysis of Variance (ANOVA) for our results using a quadratic fitting model with $R_{1}^{2} = A d j R_{1}^{2} = 100 %$ $R_{1}^{2}=Adj R_{1}^{2}=100\%$ for both the aggregation and nonaggregation models. The velocity-ratio parameter showed negative sensitivity to the response parameter. $P r e d R_{1}^{2} = 99.99 %$ $Pred R_{1}^{2}=99.99\%$ represented very high predictability rate for new observations. The predicted values recorded a maximum absolute error of the order $10^{- 4}$ $10^{-4}$ when compared to the actual numerical data along with a desirability of $100 %$ $100\%$ to attain the extremum values for both models.