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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2024-11-01
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| author | Ismael Essarroukh José M. López |
| author_facet | Ismael Essarroukh José M. López |
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| description | 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. |
| format | Article |
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| language | English |
| publishDate | 2024-11-01 |
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| spelling | doaj-art-1850d19f76d84c19bad54e2ac662633c2025-08-20T01:53:57ZengMDPI AGMathematics2227-73902024-11-011222356010.3390/math12223560Convective Heat Transfer in Uniformly Accelerated and Decelerated Turbulent Pipe FlowsIsmael Essarroukh0José M. López1Department of Mechanical, Thermal, and Fluid Engineering, Edificio de Ingenierías UMA, University of Malaga, Arquitecto Francisco Peñalosa, 6, Campanillas, 29071 Málaga, SpainDepartment of Mechanical, Thermal, and Fluid Engineering, Edificio de Ingenierías UMA, University of Malaga, Arquitecto Francisco Peñalosa, 6, Campanillas, 29071 Málaga, SpainThis 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.https://www.mdpi.com/2227-7390/12/22/3560unsteady flowNusselt numberturbulent pipe flowheat transferdirect numerical simulationflow acceleration |
| spellingShingle | Ismael Essarroukh José M. López Convective Heat Transfer in Uniformly Accelerated and Decelerated Turbulent Pipe Flows Mathematics unsteady flow Nusselt number turbulent pipe flow heat transfer direct numerical simulation flow acceleration |
| title | Convective Heat Transfer in Uniformly Accelerated and Decelerated Turbulent Pipe Flows |
| title_full | Convective Heat Transfer in Uniformly Accelerated and Decelerated Turbulent Pipe Flows |
| title_fullStr | Convective Heat Transfer in Uniformly Accelerated and Decelerated Turbulent Pipe Flows |
| title_full_unstemmed | Convective Heat Transfer in Uniformly Accelerated and Decelerated Turbulent Pipe Flows |
| title_short | Convective Heat Transfer in Uniformly Accelerated and Decelerated Turbulent Pipe Flows |
| title_sort | convective heat transfer in uniformly accelerated and decelerated turbulent pipe flows |
| topic | unsteady flow Nusselt number turbulent pipe flow heat transfer direct numerical simulation flow acceleration |
| url | https://www.mdpi.com/2227-7390/12/22/3560 |
| work_keys_str_mv | AT ismaelessarroukh convectiveheattransferinuniformlyacceleratedanddeceleratedturbulentpipeflows AT josemlopez convectiveheattransferinuniformlyacceleratedanddeceleratedturbulentpipeflows |