Convective Heat Transfer in Uniformly Accelerated and Decelerated Turbulent Pipe Flows
This study presents a detailed investigation of the temporal evolution of the Nusselt number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mi>u</mi></mrow></s...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-11-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/22/3560 |
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| Summary: | This study presents a detailed investigation of the temporal evolution of the Nusselt number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mi>u</mi></mrow></semantics></math></inline-formula>) in uniformly accelerated and decelerated turbulent pipe flows under a constant heat flux using direct numerical simulations. The influence of different acceleration and deceleration rates on heat transfer is systematically studied, addressing a gap in the previous research. The simulations confirm several key experimental findings, including the presence of three distinct phases in the Nusselt number temporal response—delay, recovery, and quasi-steady phases—as well as the characteristics of thermal structures in unsteady pipe flow. In accelerated flows, the delay in the turbulence response to changes in velocity results in reduced heat transfer, with average <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mi>u</mi></mrow></semantics></math></inline-formula> values up to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>48</mn><mo>%</mo></mrow></semantics></math></inline-formula> lower than those for steady-flow conditions at the same mean Reynolds number. Conversely, decelerated flows exhibit enhanced heat transfer, with average <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mi>u</mi></mrow></semantics></math></inline-formula> exceeding steady values by up to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>42</mn><mo>%</mo></mrow></semantics></math></inline-formula> due to the onset of secondary instabilities that amplify turbulence. To characterize the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mi>u</mi></mrow></semantics></math></inline-formula> response across the full range of acceleration and deceleration rates, a new model based on a hyperbolic tangent function is proposed, which provides a more accurate description of the heat transfer response than previous models. The results suggest the potential to design unsteady periodic cycles, combining slow acceleration and rapid deceleration, to enhance heat transfer compared to steady flows. |
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| ISSN: | 2227-7390 |