<p>This study numerically investigates mixed convective flow and heat transfer of a non-Newtonian nanofluid over a rotating disk using MATLAB bvp4c solver (Finite Difference Lobatto IIIa collocation method). High-thermal effects are considered by taking a nonlinear (quadratic form) Boussinesq approximation to accurately model buoyancy-driven nanofluid multi-slip flow problems. The impact of various controlling parameters, such as Grashof number containing the rotation term, nonlinear convection parameter, viscoelastic (non-Newtonian) parameter, and Stefan parameter, along with radiation and chemical reaction, is studied. Moreover, a non-homogeneous Buongiorno’s approach is adopted, in which two dominant slip mechanisms are used to analyse the influence of nanoparticle volume fraction (NVF) in the current rotating disk problem. We observed a reduction of approximately 12% in the Nusselt number and 71% in the Sherwood number when the combined slip parameters were set to 1.0, compared to the no-slip condition (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">${s}_{V}={s}_{T}={s}_{C}=0)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>s</mi> <mi>V</mi> </msub> <mo>=</mo> <msub> <mi>s</mi> <mi>T</mi> </msub> <mo>=</mo> <msub> <mi>s</mi> <mi>C</mi> </msub> <mrow> <mo>=</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for the default set of other parameters. The highest considered value of the exponential heat source <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$(Q=0.5)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>Q</mi> <mo>=</mo> <mn>0.5</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> under non-radiative conditions (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">${N}_{r}=0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>N</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>) yields the maximum heat transfer, showing an <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$93\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>93</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> increase compared to the lowest heat transfer case, while exhibiting the minimum mass transfer. In addition, the smallest considered value of thermophoresis and Brownian motion promotes the heat transfer rate. Response Surface Methodology (RSM) was implemented to generate quadratic correlations and optimize parameters, yielding maximum <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$Nur=0.54476$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mi>u</mi> <mi>r</mi> <mo>=</mo> <mn>0.54476</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$Shr=1.35652$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>h</mi> <mi>r</mi> <mo>=</mo> <mn>1.35652</mn> </mrow> </math></EquationSource> </InlineEquation> at <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\Gamma =0.7343$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Γ</mi> <mo>=</mo> <mn>0.7343</mn> </mrow> </math></EquationSource> </InlineEquation>, <i>SV</i> = 0.1, and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$Q=0.5$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>Q</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </math></EquationSource> </InlineEquation>, with a composite desirability of 0.79685, demonstrating effective control over thermal transport in non-Newtonian (viscoelastic type) rotating disk flows.</p>

Swirling multiple slip flow of a viscoelastic non-Newtonian nanofluid over a spinning disk with Arrhenius activation energy: RSM optimization

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发表日期：

2025年12月6日

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Anjali Rawal,
Chinta Mani Tiwari

摘要

This study numerically investigates mixed convective flow and heat transfer of a non-Newtonian nanofluid over a rotating disk using MATLAB bvp4c solver (Finite Difference Lobatto IIIa collocation method). High-thermal effects are considered by taking a nonlinear (quadratic form) Boussinesq approximation to accurately model buoyancy-driven nanofluid multi-slip flow problems. The impact of various controlling parameters, such as Grashof number containing the rotation term, nonlinear convection parameter, viscoelastic (non-Newtonian) parameter, and Stefan parameter, along with radiation and chemical reaction, is studied. Moreover, a non-homogeneous Buongiorno’s approach is adopted, in which two dominant slip mechanisms are used to analyse the influence of nanoparticle volume fraction (NVF) in the current rotating disk problem. We observed a reduction of approximately 12% in the Nusselt number and 71% in the Sherwood number when the combined slip parameters were set to 1.0, compared to the no-slip condition ( ${s}_{V}={s}_{T}={s}_{C}=0)$ $s_{V} = s_{T} = s_{C} = 0)$ for the default set of other parameters. The highest considered value of the exponential heat source $(Q=0.5)$ $(Q = 0.5)$ under non-radiative conditions ( ${N}_{r}=0$ $N_{r} = 0$ ) yields the maximum heat transfer, showing an $93\%$ $93 %$ increase compared to the lowest heat transfer case, while exhibiting the minimum mass transfer. In addition, the smallest considered value of thermophoresis and Brownian motion promotes the heat transfer rate. Response Surface Methodology (RSM) was implemented to generate quadratic correlations and optimize parameters, yielding maximum $Nur=0.54476$ $N u r = 0.54476$ and $Shr=1.35652$ $S h r = 1.35652$ at $\Gamma =0.7343$ $Γ = 0.7343$ , SV = 0.1, and $Q=0.5$ $Q = 0.5$ , with a composite desirability of 0.79685, demonstrating effective control over thermal transport in non-Newtonian (viscoelastic type) rotating disk flows.