Spectral method solutions of a variable aspect ratio duct flow in a uniform transverse magnetic field with two different thermal boundary conditions
<p dir="ltr">A laminar electrically-conducting flow inside an electrically-insulated rectangular duct in a uniform transverse magnetic field with both uniform surface temperature and uniform heat flux boundary conditions are considered numerically. The problem with aspect ratios of t...
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2020
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| _version_ | 1864513557726494720 |
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| author | Mohammed Al-Khawaja (17093017) |
| author2 | Mohamed Selmi (17093020) |
| author2_role | author |
| author_facet | Mohammed Al-Khawaja (17093017) Mohamed Selmi (17093020) |
| author_role | author |
| dc.creator.none.fl_str_mv | Mohammed Al-Khawaja (17093017) Mohamed Selmi (17093020) |
| dc.date.none.fl_str_mv | 2020-11-01T00:00:00Z |
| dc.identifier.none.fl_str_mv | 10.1016/j.ijft.2020.100046 |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/journal_contribution/Spectral_method_solutions_of_a_variable_aspect_ratio_duct_flow_in_a_uniform_transverse_magnetic_field_with_two_different_thermal_boundary_conditions/24242590 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Engineering Fluid mechanics and thermal engineering Physical sciences Condensed matter physics Rectangular duct flow MHD flow MFM flow Liquid metal Electrically conducted fluid Spectral method Aspect ratio Chebyshev polynomials |
| dc.title.none.fl_str_mv | Spectral method solutions of a variable aspect ratio duct flow in a uniform transverse magnetic field with two different thermal boundary conditions |
| dc.type.none.fl_str_mv | Text Journal contribution info:eu-repo/semantics/publishedVersion text contribution to journal |
| description | <p dir="ltr">A laminar electrically-conducting flow inside an electrically-insulated rectangular duct in a uniform transverse magnetic field with both uniform surface temperature and uniform heat flux boundary conditions are considered numerically. The problem with aspect ratios of the range from 1:10 to 10:1 and Hartmann number M up to 1000 is solved using a highly accurate technique which is spectral method. The flow variables are expanded in terms of linear combinations of Chebyshev polynomials chosen to satisfy the boundary conditions implicitly. The resulting equations are collocated using the Gauss points to produce a system of nonlinear algebraic equations which is solved iteratively using Gauss elimination. Convergence properties of the numerical method reveals that for aspect ratio of less than 4 to 1, the flow is well resolved with as small as 29 by 29 Chebyshev polynomials; however, as the aspect ratio increases to more than 4 to 1, the number of polynomials required for an adequate resolution can be as high as 49 by 49 polynomials. It is found when the magnetic field is turned on, the pressure drop, in general, increases with the field for different aspect ratios. However, the pressure drop increase will be slower near the aspect ratio of 10. Also, the heat transfer increases with the field for most of the cases, but for some cases the field will have adverse effect on the heat transfer, particularly, for constant surface temperature boundary condition at aspect ratio > 4 and M < 100. On the other hand, this effect will be noticed at aspect ratio > 4 and M < 10 for uniform wall heat flux boundary condition.</p><h2>Other Information</h2><p dir="ltr">Published in: International Journal of Thermofluids<br>License: <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank">http://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1016/j.ijft.2020.100046" target="_blank">https://dx.doi.org/10.1016/j.ijft.2020.100046</a></p> |
| eu_rights_str_mv | openAccess |
| id | Manara2_38f2f1107531bb5e7e4b6261d712dd48 |
| identifier_str_mv | 10.1016/j.ijft.2020.100046 |
| network_acronym_str | Manara2 |
| network_name_str | Manara2 |
| oai_identifier_str | oai:figshare.com:article/24242590 |
| publishDate | 2020 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | Spectral method solutions of a variable aspect ratio duct flow in a uniform transverse magnetic field with two different thermal boundary conditionsMohammed Al-Khawaja (17093017)Mohamed Selmi (17093020)EngineeringFluid mechanics and thermal engineeringPhysical sciencesCondensed matter physicsRectangular duct flowMHD flowMFM flowLiquid metalElectrically conducted fluidSpectral methodAspect ratioChebyshev polynomials<p dir="ltr">A laminar electrically-conducting flow inside an electrically-insulated rectangular duct in a uniform transverse magnetic field with both uniform surface temperature and uniform heat flux boundary conditions are considered numerically. The problem with aspect ratios of the range from 1:10 to 10:1 and Hartmann number M up to 1000 is solved using a highly accurate technique which is spectral method. The flow variables are expanded in terms of linear combinations of Chebyshev polynomials chosen to satisfy the boundary conditions implicitly. The resulting equations are collocated using the Gauss points to produce a system of nonlinear algebraic equations which is solved iteratively using Gauss elimination. Convergence properties of the numerical method reveals that for aspect ratio of less than 4 to 1, the flow is well resolved with as small as 29 by 29 Chebyshev polynomials; however, as the aspect ratio increases to more than 4 to 1, the number of polynomials required for an adequate resolution can be as high as 49 by 49 polynomials. It is found when the magnetic field is turned on, the pressure drop, in general, increases with the field for different aspect ratios. However, the pressure drop increase will be slower near the aspect ratio of 10. Also, the heat transfer increases with the field for most of the cases, but for some cases the field will have adverse effect on the heat transfer, particularly, for constant surface temperature boundary condition at aspect ratio > 4 and M < 100. On the other hand, this effect will be noticed at aspect ratio > 4 and M < 10 for uniform wall heat flux boundary condition.</p><h2>Other Information</h2><p dir="ltr">Published in: International Journal of Thermofluids<br>License: <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank">http://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1016/j.ijft.2020.100046" target="_blank">https://dx.doi.org/10.1016/j.ijft.2020.100046</a></p>2020-11-01T00:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.1016/j.ijft.2020.100046https://figshare.com/articles/journal_contribution/Spectral_method_solutions_of_a_variable_aspect_ratio_duct_flow_in_a_uniform_transverse_magnetic_field_with_two_different_thermal_boundary_conditions/24242590CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/242425902020-11-01T00:00:00Z |
| spellingShingle | Spectral method solutions of a variable aspect ratio duct flow in a uniform transverse magnetic field with two different thermal boundary conditions Mohammed Al-Khawaja (17093017) Engineering Fluid mechanics and thermal engineering Physical sciences Condensed matter physics Rectangular duct flow MHD flow MFM flow Liquid metal Electrically conducted fluid Spectral method Aspect ratio Chebyshev polynomials |
| status_str | publishedVersion |
| title | Spectral method solutions of a variable aspect ratio duct flow in a uniform transverse magnetic field with two different thermal boundary conditions |
| title_full | Spectral method solutions of a variable aspect ratio duct flow in a uniform transverse magnetic field with two different thermal boundary conditions |
| title_fullStr | Spectral method solutions of a variable aspect ratio duct flow in a uniform transverse magnetic field with two different thermal boundary conditions |
| title_full_unstemmed | Spectral method solutions of a variable aspect ratio duct flow in a uniform transverse magnetic field with two different thermal boundary conditions |
| title_short | Spectral method solutions of a variable aspect ratio duct flow in a uniform transverse magnetic field with two different thermal boundary conditions |
| title_sort | Spectral method solutions of a variable aspect ratio duct flow in a uniform transverse magnetic field with two different thermal boundary conditions |
| topic | Engineering Fluid mechanics and thermal engineering Physical sciences Condensed matter physics Rectangular duct flow MHD flow MFM flow Liquid metal Electrically conducted fluid Spectral method Aspect ratio Chebyshev polynomials |