Alumina–magnetite (Al2O3-Fe3O4) nanoparticles have demonstrated significant potential in numerous biomedical uses comprising drug delivery systems, magnetic resonance imaging (MRI), and hyperthermia treatment modalities. Furthermore, this composite material is employed as a catalyst in numerous chemical reactions. This study aims to investigate the 2D alumina–magnetite boundary layer (BL) movement above a stretched surface in a permeable medium including heat generation/absorption, multiple slips, and solar radiation, emphasizing the novel applications of hybrid nanofluid (H-N-Fs). The phenomenon of dual solutions arises as a consequence of suction, thus necessitating the execution of a stability assessment to identify the stable solution. Alumina–magnetite hybrid nanoparticles are floating in a 50:50 mixture of water and ethylene glycol (WEG) to form the H-N-F. The fluid is classified as a Maxwell fluid. A numerical solution is obtained via Runge–Kutta integration technique in MATLAB. The influence of evolving aspects on the flow features is described via graphs and tables. The critical values for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\lambda_{1} = 0.4, 0.8,$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.4</mn> <mo>,</mo> <mn>0.8</mn> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$1.2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1.2</mn> </mrow> </math></EquationSource> </InlineEquation> are <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$S_{{{\text{c}}1}} = 2.4461$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>S</mi> <mrow> <mtext>c</mtext> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>2.4461</mn> </mrow> </math></EquationSource> </InlineEquation>,<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$S_{{{\text{c}}2}} = 2.3502$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>S</mi> <mrow> <mtext>c</mtext> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>2.3502</mn> </mrow> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$S_{{{\text{c}}3}} = 2.4511,$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>S</mi> <mrow> <mtext>c</mtext> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mn>2.4511</mn> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> respectively. In the domain <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$Ec$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">Ec</mi> </mrow> </math></EquationSource> </InlineEquation>, i.e., 0.4 <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\le Ec \le 1.2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>≤</mo> <mi>E</mi> <mi>c</mi> <mo>≤</mo> <mn>1.2</mn> </mrow> </math></EquationSource> </InlineEquation>, the critical values, regarding <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$R$</EquationSource> <EquationSource Format="MATHML"><math> <mi>R</mi> </math></EquationSource> </InlineEquation>, are <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$R_{{{\text{c}}1}} = 1.891220$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mrow> <mtext>c</mtext> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>1.891220</mn> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$R_{{{\text{c}}2}} = 1.544211$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mrow> <mtext>c</mtext> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>1.544211</mn> </mrow> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$R_{{{\text{c}}3}} = 1.487013$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mrow> <mtext>c</mtext> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mn>1.487013</mn> </mrow> </math></EquationSource> </InlineEquation>, while the critical values regarding <InlineEquation ID="IEq12"> <EquationSource Format="TEX">$M$</EquationSource> <EquationSource Format="MATHML"><math> <mi>M</mi> </math></EquationSource> </InlineEquation> are <InlineEquation ID="IEq13"> <EquationSource Format="TEX">$M_{{{\text{c}}1}} = 0.410035$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>M</mi> <mrow> <mtext>c</mtext> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0.410035</mn> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq14"> <EquationSource Format="TEX">$M_{{{\text{c}}2}} = 0.32710$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>M</mi> <mrow> <mtext>c</mtext> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>0.32710</mn> </mrow> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq15"> <EquationSource Format="TEX">$M_{{{\text{c}}3}} = 0.33502$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>M</mi> <mrow> <mtext>c</mtext> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mn>0.33502</mn> </mrow> </math></EquationSource> </InlineEquation>, respectively. For the code validation, it is equated with available investigation.

Dual solutions of alumina–magnetite MHD hybrid nanofluid flow over stretched sheet with thermal effect: multilinear regression analysis

期刊论文
发表日期：

2026年2月28日

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Zeeshan,
Waris Khan,
Nehad Ali Shah

摘要

Alumina–magnetite (Al₂O₃-Fe₃O₄) nanoparticles have demonstrated significant potential in numerous biomedical uses comprising drug delivery systems, magnetic resonance imaging (MRI), and hyperthermia treatment modalities. Furthermore, this composite material is employed as a catalyst in numerous chemical reactions. This study aims to investigate the 2D alumina–magnetite boundary layer (BL) movement above a stretched surface in a permeable medium including heat generation/absorption, multiple slips, and solar radiation, emphasizing the novel applications of hybrid nanofluid (H-N-Fs). The phenomenon of dual solutions arises as a consequence of suction, thus necessitating the execution of a stability assessment to identify the stable solution. Alumina–magnetite hybrid nanoparticles are floating in a 50:50 mixture of water and ethylene glycol (WEG) to form the H-N-F. The fluid is classified as a Maxwell fluid. A numerical solution is obtained via Runge–Kutta integration technique in MATLAB. The influence of evolving aspects on the flow features is described via graphs and tables. The critical values for $\lambda_{1} = 0.4, 0.8,$ $λ_{1} = 0.4, 0.8,$ and $1.2$ $1.2$ are $S_{{{\text{c}}1}} = 2.4461$ $S_{c 1} = 2.4461$ , $S_{{{\text{c}}2}} = 2.3502$ $S_{c 2} = 2.3502$ , and $S_{{{\text{c}}3}} = 2.4511,$ $S_{c 3} = 2.4511,$ respectively. In the domain $Ec$ $Ec$ , i.e., 0.4 $\le Ec \le 1.2$ $\leq E c \leq 1.2$ , the critical values, regarding $R$ $R$ , are $R_{{{\text{c}}1}} = 1.891220$ $R_{c 1} = 1.891220$ , $R_{{{\text{c}}2}} = 1.544211$ $R_{c 2} = 1.544211$ , and $R_{{{\text{c}}3}} = 1.487013$ $R_{c 3} = 1.487013$ , while the critical values regarding $M$ $M$ are $M_{{{\text{c}}1}} = 0.410035$ $M_{c 1} = 0.410035$ , $M_{{{\text{c}}2}} = 0.32710$ $M_{c 2} = 0.32710$ , and $M_{{{\text{c}}3}} = 0.33502$ $M_{c 3} = 0.33502$ , respectively. For the code validation, it is equated with available investigation.