The spike in micro-thermal gadgets emphasizes the global need for novel thermal management solutions for ensuring optimal efficiency and long-term durability. Therefore, this work deals with the effects of location of heat flux and the embraced heated rectangular cavity in porous stratum on the convective heat enhancement of micropolar hybrid nanofluid (Al2O3-Cu/H2O) within a square enclosure. This study examines cases with single heat flux applied at different locations and discrete heat fluxes of equal net length to compare their effects on heat convection enhancement. The non-dimensional partial differential equations (PDEs) governing fluid flow and heat transfer are transformed into algebraic equations through discretization via the finite difference method (FDM) and are solved iteratively using efficient computational techniques employed through custom MATLAB codes. These codes utilize the Gauss–Seidel method in combination with successive over-relaxation (SOR) and successive under-relaxation (SUR) techniques for computational efficiency. The influence of determined physical factors, including the vortex viscosity parameter (2 ≤ K0 ≤ 7), Rayleigh number (103 ≤ Ra ≤ 105), volume concentration of hybrid nanoparticles (0.0 ≤ <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14283_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">${{{\phi}}}_{\text{hnf}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ϕ</mi> <mtext>hnf</mtext> </msub> </math></EquationSource> </InlineEquation> ≤ 0.10), Darcy number (10−5 ≤ Da ≤ 10−3), and Kirpichev heat number (1 ≤ Ki ≤ 3) on flow, temperature and both local and average Nusselt numbers is examined through graphical representations. It has been observed that when the heat flux acting either at vertical or bottom walls, “average Nusselt number” at the heated inner rectangular cavity remains higher when its larger portion was exposed in the purely nanofluid region than the porous stratum. The outcomes indicates that when the heat flux was applied to bottom, top, and vertical walls, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14283_Article_IEq2.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">${\text{Nu}}_{{\text{avg}}_{{\text{hb}}^{\text{f}}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>Nu</mtext> <msub> <mtext>avg</mtext> <msup> <mrow> <mtext>hb</mtext> </mrow> <mtext>f</mtext> </msup> </msub> </msub> </math></EquationSource> </InlineEquation> increases by 32.15, 11.92, and 32.86%, respectively; <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14283_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="57" /> </InlineMediaObject> <EquationSource Format="TEX">${\text{Nu}}_{{\text{avg}}_{{\text{hb}}^{\text{p}}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>Nu</mtext> <msub> <mtext>avg</mtext> <msup> <mrow> <mtext>hb</mtext> </mrow> <mtext>p</mtext> </msup> </msub> </msub> </math></EquationSource> </InlineEquation> upsurges by 5.60, 7.88, and 3.09%, respectively, and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14283_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="TEX">${\text{Nu}}_{{\text{avg}}_{\text{hf}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>Nu</mtext> <msub> <mtext>avg</mtext> <mtext>hf</mtext> </msub> </msub> </math></EquationSource> </InlineEquation> increases by 10.47, 37.91, and 30.06%, respectively, with an increase in <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14283_Article_IEq5.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">${\phi }_{\text{hnf}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ϕ</mi> <mtext>hnf</mtext> </msub> </math></EquationSource> </InlineEquation> =0.0 to 0.10.

Analysis of thermal efficiency of micropolar hybrid nanofluids in a partially porous enclosure with heat flux

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发表日期：

2025年7月1日

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Anil Ahlawat,
Mukesh Kumar Sharma,
Lioua Kolsi

摘要

The spike in micro-thermal gadgets emphasizes the global need for novel thermal management solutions for ensuring optimal efficiency and long-term durability. Therefore, this work deals with the effects of location of heat flux and the embraced heated rectangular cavity in porous stratum on the convective heat enhancement of micropolar hybrid nanofluid (Al₂O₃-Cu/H₂O) within a square enclosure. This study examines cases with single heat flux applied at different locations and discrete heat fluxes of equal net length to compare their effects on heat convection enhancement. The non-dimensional partial differential equations (PDEs) governing fluid flow and heat transfer are transformed into algebraic equations through discretization via the finite difference method (FDM) and are solved iteratively using efficient computational techniques employed through custom MATLAB codes. These codes utilize the Gauss–Seidel method in combination with successive over-relaxation (SOR) and successive under-relaxation (SUR) techniques for computational efficiency. The influence of determined physical factors, including the vortex viscosity parameter (2 ≤ K₀ ≤ 7), Rayleigh number (10³ ≤ Ra ≤ 10⁵), volume concentration of hybrid nanoparticles (0.0 ≤ ${{{\phi}}}_{\text{hnf}}$ $ϕ_{hnf}$ ≤ 0.10), Darcy number (10⁻⁵ ≤ Da ≤ 10⁻³), and Kirpichev heat number (1 ≤ K_i ≤ 3) on flow, temperature and both local and average Nusselt numbers is examined through graphical representations. It has been observed that when the heat flux acting either at vertical or bottom walls, “average Nusselt number” at the heated inner rectangular cavity remains higher when its larger portion was exposed in the purely nanofluid region than the porous stratum. The outcomes indicates that when the heat flux was applied to bottom, top, and vertical walls, ${\text{Nu}}_{{\text{avg}}_{{\text{hb}}^{\text{f}}}}$ ${Nu}_{{avg}_{{hb}^{f}}}$ increases by 32.15, 11.92, and 32.86%, respectively; ${\text{Nu}}_{{\text{avg}}_{{\text{hb}}^{\text{p}}}}$ ${Nu}_{{avg}_{{hb}^{p}}}$ upsurges by 5.60, 7.88, and 3.09%, respectively, and ${\text{Nu}}_{{\text{avg}}_{\text{hf}}}$ ${Nu}_{{avg}_{hf}}$ increases by 10.47, 37.91, and 30.06%, respectively, with an increase in ${\phi }_{\text{hnf}}$ $ϕ_{hnf}$ =0.0 to 0.10.