<p>Nanofluids, consisting of suspended nanoparticles, offer significant potential for enhancing heat transfer in thermal systems. However, predicting heat transfer rates remains challenging, particularly under varying temperatures, due to the common assumption of constant thermophysical properties. This study addresses this limitation by incorporating temperature-dependent properties into a numerical analysis of natural convection in water-based nanofluids inside a rectangular enclosure. A single-phase model evaluates the effects of nanoparticle material, volume fraction, and enclosure aspect ratio on heat transfer. Three nanoparticle materials (TiO<sub>2</sub>, <i>C</i><sub>Diamond</sub>, Ag) are considered over Rayleigh numbers <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14197_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="TEX">\(\left(\text{Ra}\right)\)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mtext>Ra</mtext> </mfenced> </math></EquationSource> </InlineEquation> from <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14197_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\({10}^{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mn>10</mn> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14197_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\({10}^{6}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mn>10</mn> </mrow> <mn>6</mn> </msup> </math></EquationSource> </InlineEquation>. The findings reveal that incorporating variable properties improves Nusselt number predictions, particularly at lower <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14197_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{Ra}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>Ra</mtext> </math></EquationSource> </InlineEquation> and nanoparticle concentrations. The variable properties model corrects Nu underprediction by up to <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14197_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(39\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>39</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> at low <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14197_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{Ra}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>Ra</mtext> </math></EquationSource> </InlineEquation> and reduces overpredictions at high <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14197_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{Ra}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>Ra</mtext> </math></EquationSource> </InlineEquation> by up to <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14197_Article_IEq8.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(7\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>7</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> compared to constant property models. The effect of nanoparticle concentration varies with <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14197_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{Ra}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>Ra</mtext> </math></EquationSource> </InlineEquation>, influencing heat transfer trends. Silver nanoparticles achieve the highest heat transfer performance, with enhancements up to <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14197_Article_IEq10.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(43\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>43</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>, while TiO<sub>2</sub> shows the lowest. Aspect ratio <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14197_Article_IEq11.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">\((\text{AR}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mtext>AR</mtext> </mrow> </math></EquationSource> </InlineEquation>) also significantly impacts heat transfer, with <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14197_Article_IEq12.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{AR}=1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>AR</mtext> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> yielding the greatest enhancement with TiO<sub>2</sub> compared to <InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14197_Article_IEq13.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="68" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{AR}=1.5\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>AR</mtext> <mo>=</mo> <mn>1.5</mn> </mrow> </math></EquationSource> </InlineEquation> or <InlineEquation ID="IEq14"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14197_Article_IEq14.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation>. These results highlight the limitations of assuming constant properties and demonstrate the interplay of nanoparticle concentration, <InlineEquation ID="IEq15"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14197_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{Ra}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>Ra</mtext> </math></EquationSource> </InlineEquation>, material, and <InlineEquation ID="IEq16"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14197_Article_IEq16.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{AR}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>AR</mtext> </math></EquationSource> </InlineEquation> in nanofluid convection. Thus, incorporating temperature-dependent models is essential for accurately predicting nanofluid heat transfer rates, particularly in applications such as electronics cooling and advanced heat exchangers.</p>

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Numerical investigation of nanofluid free convection in a rectangular cavity using variable properties

  • Adel Alshayji,
  • Mohammad K. Alzuabi,
  • Nawaf F. Aljuwayhel

摘要

Nanofluids, consisting of suspended nanoparticles, offer significant potential for enhancing heat transfer in thermal systems. However, predicting heat transfer rates remains challenging, particularly under varying temperatures, due to the common assumption of constant thermophysical properties. This study addresses this limitation by incorporating temperature-dependent properties into a numerical analysis of natural convection in water-based nanofluids inside a rectangular enclosure. A single-phase model evaluates the effects of nanoparticle material, volume fraction, and enclosure aspect ratio on heat transfer. Three nanoparticle materials (TiO2, CDiamond, Ag) are considered over Rayleigh numbers \(\left(\text{Ra}\right)\) Ra from \({10}^{3}\) 10 3 to \({10}^{6}\) 10 6 . The findings reveal that incorporating variable properties improves Nusselt number predictions, particularly at lower \(\text{Ra}\) Ra and nanoparticle concentrations. The variable properties model corrects Nu underprediction by up to \(39\%\) 39 % at low \(\text{Ra}\) Ra and reduces overpredictions at high \(\text{Ra}\) Ra by up to \(7\%\) 7 % compared to constant property models. The effect of nanoparticle concentration varies with \(\text{Ra}\) Ra , influencing heat transfer trends. Silver nanoparticles achieve the highest heat transfer performance, with enhancements up to \(43\%\) 43 % , while TiO2 shows the lowest. Aspect ratio \((\text{AR}\) ( AR ) also significantly impacts heat transfer, with \(\text{AR}=1\) AR = 1 yielding the greatest enhancement with TiO2 compared to \(\text{AR}=1.5\) AR = 1.5 or \(4\) 4 . These results highlight the limitations of assuming constant properties and demonstrate the interplay of nanoparticle concentration, \(\text{Ra}\) Ra , material, and \(\text{AR}\) AR in nanofluid convection. Thus, incorporating temperature-dependent models is essential for accurately predicting nanofluid heat transfer rates, particularly in applications such as electronics cooling and advanced heat exchangers.