<p>This study presents a comprehensive thermal and momentum analysis of ferro-hybrid nanofluid thin film flow affected by radiation heat transfer and an angled magnetic field past an elongating surface. The mathematical model incorporates viscous and Joule dissipation effects within the framework of a two-phase hybrid nanofluid composed of ethylene glycol <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(({\text{EG}})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mtext>EG</mtext> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> suspended with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\text{Fe}}_{3} {\text{O}}_{4}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>Fe</mtext> <mn>3</mn> </msub> <msub> <mtext>O</mtext> <mn>4</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\text{CoFe}}_{2} {\text{O}}_{4}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>CoFe</mtext> <mn>2</mn> </msub> <msub> <mtext>O</mtext> <mn>4</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> nanoparticles, while comparative observations are made with a single-component ferrofluid (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({\text{EG}} + {\text{Fe}}_{3} {\text{O}}_{4}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>EG</mtext> <mo>+</mo> <msub> <mtext>Fe</mtext> <mn>3</mn> </msub> <msub> <mtext>O</mtext> <mn>4</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>). The governing nonlinear coupled ordinary differential equations, emerging from boundary layer approximations, are addressed through the differential transform method (DTM). Detailed parametric exploration is carried out for key dimensionless quantities, including the magnetic field strength, unsteadiness, film thickness, inclination angle, thermal radiation, Eckert number, and Biot number. Validation of the present methodology is established through agreement with numerical results obtained via the bvp5c solver in MATLAB. The study demonstrates that a stronger magnetic field generates Lorentz resistance, reducing ferrofluid velocity, while increased film thickness and flow unsteadiness dampen both momentum and thermal transport. In contrast, higher radiation intensity and viscous dissipation enrich the internal energy, thereby amplifying the thermal profile within the fluid domain. The ferro-hybrid nanofluid exhibits improved thermal behaviour in the thin film domain relative to its mono-nanofluid counterpart, primarily due to its elevated thermal conductivity and superior energy absorption capability, which together facilitate more efficient heat transport. The rise in <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(M\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>M</mi> </math></EquationSource> </InlineEquation> from 0.5 to 2.0, the <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\sqrt {{\text{Re}}_{{\text{x}}} } Cf_{{\text{x}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msqrt> <msub> <mtext>Re</mtext> <mtext>x</mtext> </msub> </msqrt> <mi>C</mi> <msub> <mi>f</mi> <mtext>x</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation> experiences a notable 47.6% decline, while <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\({{{\text{Nu}}_{{\text{x}}} } \mathord{\left/ {\vphantom {{{\text{Nu}}_{{\text{x}}} } {\sqrt {{\text{Re}}_{{\text{x}}} } }}} \right. \kern-0pt} {\sqrt {{\text{Re}}_{{\text{x}}} } }}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>Nu</mtext> <mtext>x</mtext> </msub> <mrow> <mfenced open="/"> <mphantom> <mpadded width="0pt"> <msub> <mtext>Nu</mtext> <mtext>x</mtext> </msub> <msqrt> <msub> <mtext>Re</mtext> <mtext>x</mtext> </msub> </msqrt> </mpadded> </mphantom> </mfenced> </mrow> <msqrt> <msub> <mtext>Re</mtext> <mtext>x</mtext> </msub> </msqrt> </mrow> </math></EquationSource> </InlineEquation> declines by approximately 0.83% as the <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\({\text{Ec}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>Ec</mtext> </math></EquationSource> </InlineEquation> rises from 0.01 to 0.04. A magnetic field’s impact, alignment radiation-induced stratification, and internal heating mechanisms distinctly sculpt the flow and temperature distributions, offering insights relevant to industrial coating, microfluidic cooling, and advanced material processing applications.</p>

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Hydromagnetic radiative heat transfer analysis of ferro-hybrid nanofluid thin film flow past an elongating surface with inclined magnetic field and viscous and joule dissipation: differential transform approach

  • Thirupathi Thumma,
  • Reshu Gupta,
  • R. Archana Reddy,
  • Ch. Achi Reddy

摘要

This study presents a comprehensive thermal and momentum analysis of ferro-hybrid nanofluid thin film flow affected by radiation heat transfer and an angled magnetic field past an elongating surface. The mathematical model incorporates viscous and Joule dissipation effects within the framework of a two-phase hybrid nanofluid composed of ethylene glycol \(({\text{EG}})\) ( EG ) suspended with \({\text{Fe}}_{3} {\text{O}}_{4}\) Fe 3 O 4 and \({\text{CoFe}}_{2} {\text{O}}_{4}\) CoFe 2 O 4 nanoparticles, while comparative observations are made with a single-component ferrofluid ( \({\text{EG}} + {\text{Fe}}_{3} {\text{O}}_{4}\) EG + Fe 3 O 4 ). The governing nonlinear coupled ordinary differential equations, emerging from boundary layer approximations, are addressed through the differential transform method (DTM). Detailed parametric exploration is carried out for key dimensionless quantities, including the magnetic field strength, unsteadiness, film thickness, inclination angle, thermal radiation, Eckert number, and Biot number. Validation of the present methodology is established through agreement with numerical results obtained via the bvp5c solver in MATLAB. The study demonstrates that a stronger magnetic field generates Lorentz resistance, reducing ferrofluid velocity, while increased film thickness and flow unsteadiness dampen both momentum and thermal transport. In contrast, higher radiation intensity and viscous dissipation enrich the internal energy, thereby amplifying the thermal profile within the fluid domain. The ferro-hybrid nanofluid exhibits improved thermal behaviour in the thin film domain relative to its mono-nanofluid counterpart, primarily due to its elevated thermal conductivity and superior energy absorption capability, which together facilitate more efficient heat transport. The rise in \(M\) M from 0.5 to 2.0, the \(\sqrt {{\text{Re}}_{{\text{x}}} } Cf_{{\text{x}}}\) Re x C f x experiences a notable 47.6% decline, while \({{{\text{Nu}}_{{\text{x}}} } \mathord{\left/ {\vphantom {{{\text{Nu}}_{{\text{x}}} } {\sqrt {{\text{Re}}_{{\text{x}}} } }}} \right. \kern-0pt} {\sqrt {{\text{Re}}_{{\text{x}}} } }}\) Nu x Nu x Re x Re x declines by approximately 0.83% as the \({\text{Ec}}\) Ec rises from 0.01 to 0.04. A magnetic field’s impact, alignment radiation-induced stratification, and internal heating mechanisms distinctly sculpt the flow and temperature distributions, offering insights relevant to industrial coating, microfluidic cooling, and advanced material processing applications.