<p>Recently nanofluids, which are nanoparticle postponements in a base fluid, pointedly impact tribological performances by&#xa0;increasing lubrication and dipping resistance and wear.&#xa0;These enrichments are attained through tools like the materialization of greasing layers, amplified thermal conductivity, and the facility of nanoparticles to adjust the resistance and wear features of the contacting surfaces. The study of microorganisms is noteworthy in farming microbiology, as they can produce surface-active and bio-surfactants elements. Many uses, comprising enriched oil retrieval and biological bioremediation, are subject to these bio-surfactants. Furthermore, the collective influence of microorganisms and nanofluids deals a multitude of cost-effective prospects, mostly in the design of micro-fluidic products, for instance, microvessels and microscopic networks. This article explores the phenomenon of bioconvection Maxwell nanofluid with nanoparticles over a rotating disk. The suction phenomenon that is Forchheimer–Darcy porous media, mixed convection, chemical reactions and thermal radiation are incorporated. The convective and new mass flux conditions are also incorporated. The formulated flow equations under heat and mass transport are constructed and transfigured into a system of non-dimensional ordinary differential equations (ODEs) via suitable transformations. The obtained equations are sorted into numerical solutions by implementing Runge–Kutta–Fehlberg (RKF45) method combined with the shooting scheme. The flow analysis with significance of heat transfer and various dimensionless parameters like the Deborah number, Darcy–Forchheimer, radiation, Prandtl number, thermophoresis, Brownian motion, Schmidt factor, Biot factor, and Peclet number is discussed. The key results are obtained and compared in terms of surface drag force, Nusselt number, and microorganism density factor, providing insights into the behavior of the nanofluid under different physical conditions. The major findings of the study reveal the interplay of physical forces (Lorentz) porous resistance, radiation, and microbial motion in thermo-mass transport. Such as, Deborah number, Darcy–Forchheimer, and stretching parameters reduce fluid velocity, while the radiation and Biot factors increase the temperature field; however, they decay for Prandtl number. The Peclet number and gyrotactic difference reduce microorganism density, whereas the concentration field declines for Peclet and Schmidt number. The numerical values of skin friction in table shape are presented which exhibit validation of the code and are compared with former literature, showing minimal deviations (0.0150% and 0.0141% for&#xa0;<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14761_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(M\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>M</mi> </math></EquationSource> </InlineEquation> = 0, and 0.0002% and 0.0009% for&#xa0;<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14761_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(M\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>M</mi> </math></EquationSource> </InlineEquation> = 0.5). These negligible differences (&lt; 0.02%) validate the accuracy of the current results, confirming strong agreement with established literature under varying magnetic parameters.</p>

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Darcy–Forchheimer MHD Maxwell Bioconvection Nanofluid with Angular Velocity and Solar–Thermal Energy Effects: Thermal Engineering Applications

  • Usman Ali,
  • Abdulaziz Alasiri,
  • Muhammad Irfan

摘要

Recently nanofluids, which are nanoparticle postponements in a base fluid, pointedly impact tribological performances by increasing lubrication and dipping resistance and wear. These enrichments are attained through tools like the materialization of greasing layers, amplified thermal conductivity, and the facility of nanoparticles to adjust the resistance and wear features of the contacting surfaces. The study of microorganisms is noteworthy in farming microbiology, as they can produce surface-active and bio-surfactants elements. Many uses, comprising enriched oil retrieval and biological bioremediation, are subject to these bio-surfactants. Furthermore, the collective influence of microorganisms and nanofluids deals a multitude of cost-effective prospects, mostly in the design of micro-fluidic products, for instance, microvessels and microscopic networks. This article explores the phenomenon of bioconvection Maxwell nanofluid with nanoparticles over a rotating disk. The suction phenomenon that is Forchheimer–Darcy porous media, mixed convection, chemical reactions and thermal radiation are incorporated. The convective and new mass flux conditions are also incorporated. The formulated flow equations under heat and mass transport are constructed and transfigured into a system of non-dimensional ordinary differential equations (ODEs) via suitable transformations. The obtained equations are sorted into numerical solutions by implementing Runge–Kutta–Fehlberg (RKF45) method combined with the shooting scheme. The flow analysis with significance of heat transfer and various dimensionless parameters like the Deborah number, Darcy–Forchheimer, radiation, Prandtl number, thermophoresis, Brownian motion, Schmidt factor, Biot factor, and Peclet number is discussed. The key results are obtained and compared in terms of surface drag force, Nusselt number, and microorganism density factor, providing insights into the behavior of the nanofluid under different physical conditions. The major findings of the study reveal the interplay of physical forces (Lorentz) porous resistance, radiation, and microbial motion in thermo-mass transport. Such as, Deborah number, Darcy–Forchheimer, and stretching parameters reduce fluid velocity, while the radiation and Biot factors increase the temperature field; however, they decay for Prandtl number. The Peclet number and gyrotactic difference reduce microorganism density, whereas the concentration field declines for Peclet and Schmidt number. The numerical values of skin friction in table shape are presented which exhibit validation of the code and are compared with former literature, showing minimal deviations (0.0150% and 0.0141% for  \(M\) M  = 0, and 0.0002% and 0.0009% for  \(M\) M  = 0.5). These negligible differences (< 0.02%) validate the accuracy of the current results, confirming strong agreement with established literature under varying magnetic parameters.