<p>The heat source models of cylinder with constant and variable cross-sections under the condition of natural convection are established herein. According to constructal theory, constructal designs for the models are performed with the minimum dimensionless maximum thermal resistance as goal. Influences of heat source height, thermal conductivity ratio, and cylindrical shape on optimal constructs of cylinder heat sources are analyzed. The results show that under natural convection condition, with increase of the height of constant cross-section cylinder heat source, the optimal heat source position and radius ratio (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$b_{{{\text{opt}}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>b</mi> <mtext>opt</mtext> </msub> </math></EquationSource> </InlineEquation>) of cylinder heat source all decrease first, then increase, and eventually stabilize. Increasing the thermal conductivity can effectively enhance heat-transfer capability of heat source, but the increase is no longer obvious after it is increased to a certain extent. When the variable cross-section cylinder heat source model is used, the optimal radius ratio is <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$f_{{{\text{opt}}}} = 0.476$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>f</mi> <mtext>opt</mtext> </msub> <mo>=</mo> <mn>0.476</mn> </mrow> </math></EquationSource> </InlineEquation> for the cylinder heat source with any height, so that dimensionless maximum thermal resistance of variable cross-section cylinder heat source can be minimized. When the dimensionless heat source height is <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\tilde{H} = 0.7$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mover accent="true"> <mi>H</mi> <mo stretchy="false">~</mo> </mover> <mo>=</mo> <mn>0.7</mn> </mrow> </math></EquationSource> </InlineEquation>, minimum dimensionless maximum thermal resistance of variable cross-section cylinder heat source is 23.8% lower than that of constant cross-section cylinder heat source.</p>

Constructal design for cylinder heat source considering minimum hotspot temperature under natural convection

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发表日期：

2026年1月6日

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Lingen Chen,
Wenlong Zhang,
Shuwen Gong,
Huijun Feng,
Yanlin Ge

摘要

The heat source models of cylinder with constant and variable cross-sections under the condition of natural convection are established herein. According to constructal theory, constructal designs for the models are performed with the minimum dimensionless maximum thermal resistance as goal. Influences of heat source height, thermal conductivity ratio, and cylindrical shape on optimal constructs of cylinder heat sources are analyzed. The results show that under natural convection condition, with increase of the height of constant cross-section cylinder heat source, the optimal heat source position and radius ratio ( $b_{{{\text{opt}}}}$ $b_{opt}$ ) of cylinder heat source all decrease first, then increase, and eventually stabilize. Increasing the thermal conductivity can effectively enhance heat-transfer capability of heat source, but the increase is no longer obvious after it is increased to a certain extent. When the variable cross-section cylinder heat source model is used, the optimal radius ratio is $f_{{{\text{opt}}}} = 0.476$ $f_{opt} = 0.476$ for the cylinder heat source with any height, so that dimensionless maximum thermal resistance of variable cross-section cylinder heat source can be minimized. When the dimensionless heat source height is $\tilde{H} = 0.7$ $\tilde{H} = 0.7$ , minimum dimensionless maximum thermal resistance of variable cross-section cylinder heat source is 23.8% lower than that of constant cross-section cylinder heat source.