Free convection heat transfer has many applications in thermal systems. The novel transient inverse computational fluid dynamics technique along with the experimental data is applied to investigate three-dimensional free convection heat transfer in a cubic cavity with a conductive horizontal fin on a hot vertical wall. The aim is to predict unknown heat transfer rate, the range of Rayleigh number Ra(t) and suitable correlations for the early, transition and quasi-steady stages. In addition, the selection criteria for a suitable flow model are also investigated in this study. The boundary conditions on the hot wall in this study are non-isothermal and non-constant heat flux during the entire heating time. The steady velocity and temperature fields are in good agreement with the existing shadowgraph images. The estimates of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">${Nu}_{\text{h}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mi mathvariant="italic">Nu</mi> </mrow> <mtext>h</mtext> </msub> </math></EquationSource> </InlineEquation>(t) and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">${V}_{\text{max}}(t)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>V</mi> <mtext>max</mtext> </msub> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> are in good agreement with the proposed correlations, so the proposed method can be used to present a reasonable and smooth intermittent correlation in the transition region. The predictions of critical Ra at the beginning and end of the transition stage are consistent with previous results. Thus, the present estimates are accurate. The velocity and temperature fields become complex with time due to the increase in Ra and the buoyancy and blocking effects caused by the fin. Ra increases with the increase of t and gradually approaches the steady-state value of 1.05 <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\times {10}^{7}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>×</mo> <msup> <mrow> <mn>10</mn> </mrow> <mn>7</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> from t = 6000 s. The flow field in the early stage with Ra < 1.54 <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\times {10}^{6}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>×</mo> <msup> <mrow> <mn>10</mn> </mrow> <mn>6</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> and t < 240 s is laminar. The flow field in the quasi-steady stage with Ra <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\ge$</EquationSource> <EquationSource Format="MATHML"><math> <mo>≥</mo> </math></EquationSource> </InlineEquation> 9.90 <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\times {10}^{6}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>×</mo> <msup> <mrow> <mn>10</mn> </mrow> <mn>6</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> and t <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\ge$</EquationSource> <EquationSource Format="MATHML"><math> <mo>≥</mo> </math></EquationSource> </InlineEquation> 6000 s is turbulent. The method used in this study is novel and has not appeared in the available literature.

A novel study of 3D transient inverse natural convection heat in a cubic cavity with a horizontal fin on the hot wall

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2026年1月13日

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Han-Taw Chen,
Ming-Yan Zeng,
Hao-Chi Chang,
Saman Rashidi,
Wei-Mon Yan

摘要

Free convection heat transfer has many applications in thermal systems. The novel transient inverse computational fluid dynamics technique along with the experimental data is applied to investigate three-dimensional free convection heat transfer in a cubic cavity with a conductive horizontal fin on a hot vertical wall. The aim is to predict unknown heat transfer rate, the range of Rayleigh number Ra(t) and suitable correlations for the early, transition and quasi-steady stages. In addition, the selection criteria for a suitable flow model are also investigated in this study. The boundary conditions on the hot wall in this study are non-isothermal and non-constant heat flux during the entire heating time. The steady velocity and temperature fields are in good agreement with the existing shadowgraph images. The estimates of ${Nu}_{\text{h}}$ ${Nu}_{h}$ (t) and ${V}_{\text{max}}(t)$ $V_{max} (t)$ are in good agreement with the proposed correlations, so the proposed method can be used to present a reasonable and smooth intermittent correlation in the transition region. The predictions of critical Ra at the beginning and end of the transition stage are consistent with previous results. Thus, the present estimates are accurate. The velocity and temperature fields become complex with time due to the increase in Ra and the buoyancy and blocking effects caused by the fin. Ra increases with the increase of t and gradually approaches the steady-state value of 1.05 $\times {10}^{7}$ $\times 10^{7}$ from t = 6000 s. The flow field in the early stage with Ra < 1.54 $\times {10}^{6}$ $\times 10^{6}$ and t < 240 s is laminar. The flow field in the quasi-steady stage with Ra $\ge$ $\geq$ 9.90 $\times {10}^{6}$ $\times 10^{6}$ and t $\ge$ $\geq$ 6000 s is turbulent. The method used in this study is novel and has not appeared in the available literature.