Relative Influences of Inertia and Polymeric Viscoelastic Effects on Nusselt Numbers within Rotating Couette Flows
In past investigations of elastic instabilities and elastic turbulence, almost no attention has been devoted to the effects and influences of inertial phenomena. Within the present investigation, Nusselt number data are provided to illustrate the relative influences of inertia and polymeric viscoela...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/8/10/258 |
| _version_ | 1827720963487170560 |
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| author | Phil Ligrani Valerie Hietsch Mengying Su |
| author_facet | Phil Ligrani Valerie Hietsch Mengying Su |
| author_sort | Phil Ligrani |
| collection | DOAJ |
| description | In past investigations of elastic instabilities and elastic turbulence, almost no attention has been devoted to the effects and influences of inertial phenomena. Within the present investigation, Nusselt number data are provided to illustrate the relative influences of inertia and polymeric viscoelastic phenomena within a rotating Couette flow (RCF) environment. Data are provided from experimental measurements of local surface heat transfer characteristics for different flow passage heights, one radial position, and different values of disk rotational speed for polyacrylamide polymer concentrations <i>ρ</i> of 0 ppm, 100 ppm, 150 ppm, and 300 ppm. With this approach, data for a wide range of shear rate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mrow><mi>γ</mi></mrow><mo>˙</mo></mover></mrow></semantics></math></inline-formula> values, Weissenberg numbers, and first normal stress difference values are provided. Nusselt number data are provided as dependent upon a newly developed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mo>′</mo></mrow></semantics></math></inline-formula> parameter, equal to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>R</mi><mi>e</mi></mrow><mrow><mi>E</mi><mi>I</mi></mrow></msub><mo>/</mo><msup><mrow><mi>R</mi><mi>e</mi></mrow><mrow><mn>0.22</mn></mrow></msup></mrow></semantics></math></inline-formula>, which collapse into a single distribution over the range of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mo>′</mo></mrow></semantics></math></inline-formula> values considered which range from 0 to about 182. Such characteristics indicate that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mo>′</mo></mrow></semantics></math></inline-formula> parameter provides an appropriate means to simultaneously account for the relative influences of inertia and polymeric viscoelastic effects. The use of such a power law dependence for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula> additionally gives <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mo>′</mo></mrow></semantics></math></inline-formula> values which are dominated by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>R</mi><mi>e</mi></mrow><mrow><mi>E</mi><mi>I</mi></mrow></msub></mrow></semantics></math></inline-formula> values when the Weissenberg number <i>Wi</i> is greater than the elastic instability transition onset value. The experimental conditions associated with this value correspond to the change from inertia domination (with buoyance influences) to polymeric viscoelastic domination which occurs for shear rates in the vicinity of 11 to 12 s<sup>−1</sup>. For Weissenberg numbers greater than the onset value, Nusselt numbers associated with <i>H</i> = 5 mm are generally the highest values measured, with magnitudes that steadily increase with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mrow><mi>γ</mi></mrow><mo>˙</mo></mover></mrow></semantics></math></inline-formula>. Associated Nusselt numbers become as high as about 3.0, whereas zero-shear rate values (obtained with zero rotation) are in the vicinity of 1.0. At lower Weissenberg number magnitudes (below the transition onset value), Nusselt numbers cover a wide range of values as experimental conditions and configuration are varied, as a consequence of the complicated and simultaneous influences of inertia, buoyancy, and dilute polymer presence. |
| first_indexed | 2024-03-10T21:15:29Z |
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| id | doaj.art-37e7307d97664a09987a92d702e0f36a |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-10T21:15:29Z |
| publishDate | 2023-09-01 |
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| spelling | doaj.art-37e7307d97664a09987a92d702e0f36a2023-11-19T16:28:19ZengMDPI AGFluids2311-55212023-09-0181025810.3390/fluids8100258Relative Influences of Inertia and Polymeric Viscoelastic Effects on Nusselt Numbers within Rotating Couette FlowsPhil Ligrani0Valerie Hietsch1Mengying Su2Department of Mechanical and Aerospace Engineering, University of Alabama in Huntsville, Huntsville, AL 35899, USADepartment of Mechanical and Aerospace Engineering, University of Alabama in Huntsville, Huntsville, AL 35899, USADepartment of Mechanical and Aerospace Engineering, University of Alabama in Huntsville, Huntsville, AL 35899, USAIn past investigations of elastic instabilities and elastic turbulence, almost no attention has been devoted to the effects and influences of inertial phenomena. Within the present investigation, Nusselt number data are provided to illustrate the relative influences of inertia and polymeric viscoelastic phenomena within a rotating Couette flow (RCF) environment. Data are provided from experimental measurements of local surface heat transfer characteristics for different flow passage heights, one radial position, and different values of disk rotational speed for polyacrylamide polymer concentrations <i>ρ</i> of 0 ppm, 100 ppm, 150 ppm, and 300 ppm. With this approach, data for a wide range of shear rate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mrow><mi>γ</mi></mrow><mo>˙</mo></mover></mrow></semantics></math></inline-formula> values, Weissenberg numbers, and first normal stress difference values are provided. Nusselt number data are provided as dependent upon a newly developed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mo>′</mo></mrow></semantics></math></inline-formula> parameter, equal to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>R</mi><mi>e</mi></mrow><mrow><mi>E</mi><mi>I</mi></mrow></msub><mo>/</mo><msup><mrow><mi>R</mi><mi>e</mi></mrow><mrow><mn>0.22</mn></mrow></msup></mrow></semantics></math></inline-formula>, which collapse into a single distribution over the range of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mo>′</mo></mrow></semantics></math></inline-formula> values considered which range from 0 to about 182. Such characteristics indicate that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mo>′</mo></mrow></semantics></math></inline-formula> parameter provides an appropriate means to simultaneously account for the relative influences of inertia and polymeric viscoelastic effects. The use of such a power law dependence for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula> additionally gives <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mo>′</mo></mrow></semantics></math></inline-formula> values which are dominated by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>R</mi><mi>e</mi></mrow><mrow><mi>E</mi><mi>I</mi></mrow></msub></mrow></semantics></math></inline-formula> values when the Weissenberg number <i>Wi</i> is greater than the elastic instability transition onset value. The experimental conditions associated with this value correspond to the change from inertia domination (with buoyance influences) to polymeric viscoelastic domination which occurs for shear rates in the vicinity of 11 to 12 s<sup>−1</sup>. For Weissenberg numbers greater than the onset value, Nusselt numbers associated with <i>H</i> = 5 mm are generally the highest values measured, with magnitudes that steadily increase with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mrow><mi>γ</mi></mrow><mo>˙</mo></mover></mrow></semantics></math></inline-formula>. Associated Nusselt numbers become as high as about 3.0, whereas zero-shear rate values (obtained with zero rotation) are in the vicinity of 1.0. At lower Weissenberg number magnitudes (below the transition onset value), Nusselt numbers cover a wide range of values as experimental conditions and configuration are varied, as a consequence of the complicated and simultaneous influences of inertia, buoyancy, and dilute polymer presence.https://www.mdpi.com/2311-5521/8/10/258elastic instabilityinertia phenomenapolymeric viscoelastic phenomenaWeissenberg numberrotating Couette flowconvective heat transfer |
| spellingShingle | Phil Ligrani Valerie Hietsch Mengying Su Relative Influences of Inertia and Polymeric Viscoelastic Effects on Nusselt Numbers within Rotating Couette Flows Fluids elastic instability inertia phenomena polymeric viscoelastic phenomena Weissenberg number rotating Couette flow convective heat transfer |
| title | Relative Influences of Inertia and Polymeric Viscoelastic Effects on Nusselt Numbers within Rotating Couette Flows |
| title_full | Relative Influences of Inertia and Polymeric Viscoelastic Effects on Nusselt Numbers within Rotating Couette Flows |
| title_fullStr | Relative Influences of Inertia and Polymeric Viscoelastic Effects on Nusselt Numbers within Rotating Couette Flows |
| title_full_unstemmed | Relative Influences of Inertia and Polymeric Viscoelastic Effects on Nusselt Numbers within Rotating Couette Flows |
| title_short | Relative Influences of Inertia and Polymeric Viscoelastic Effects on Nusselt Numbers within Rotating Couette Flows |
| title_sort | relative influences of inertia and polymeric viscoelastic effects on nusselt numbers within rotating couette flows |
| topic | elastic instability inertia phenomena polymeric viscoelastic phenomena Weissenberg number rotating Couette flow convective heat transfer |
| url | https://www.mdpi.com/2311-5521/8/10/258 |
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