A general analytical solution for fluid flow and heat convection through arbitrary-shaped triangular ducts: A variational analysis

This paper presents an analytical solution for fluid flow and heat transfer inside arbitrarily-shaped triangular ducts for the first time. The former analytical solutions are limited to the special case of isosceles triangular ducts. The literature has no report about the analytical solution for the...
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Autor*in:	Amirhossein Hajiaghaei Tabalvandani [verfasserIn] Mahmood Norouzi [verfasserIn] Mohammad Hassan Kayhani [verfasserIn] Amir Komeili Birjandi [verfasserIn] Amin Emamian [verfasserIn] Mirae Kim [verfasserIn] Kyung Chun Kim [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2024

Schlagwörter:	Arbitrary-shaped triangular ducts Ritz method Analytical solution Heat transfer Viscous dissipation

Übergeordnetes Werk:	In: Heliyon - Elsevier, 2016, 10(2024), 4, Seite e25293-
Übergeordnetes Werk:	volume:10 ; year:2024 ; number:4 ; pages:e25293-

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1016/j.heliyon.2024.e25293

Katalog-ID:	DOAJ09561818X

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245	1	2	\|a A general analytical solution for fluid flow and heat convection through arbitrary-shaped triangular ducts: A variational analysis
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520			\|a This paper presents an analytical solution for fluid flow and heat transfer inside arbitrarily-shaped triangular ducts for the first time. The former analytical solutions are limited to the special case of isosceles triangular ducts. The literature has no report about the analytical solution for the general case of arbitrarily-shaped triangular ducts. Due to the significant role of fluid flow through non-circular channels in industry and the large number of triangular shapes, a method for solving the heat transfer problem for all triangular shapes is needed. The heat transfer of a fluid flow through a channel with an arbitrary triangular cross-section for the case of constant heat flux at the walls is solved in this work for the first time, considering viscous dissipation. Here, the functionals of flow and heat transfer equations are derived, and the resulting Euler–Lagrange equations are solved using the Ritz method. The effect of the duct geometry on the velocity profile and friction coefficient is studied in detail. The effect of the Brinkman number on the temperature distribution and Nusselt number is investigated for both cooling and heating cases. The results reveal that the critical Brinkman Number distinguishes between the cooling and heating cases and represents the critical point at which the Nusselt number approaches infinity. The value of the Nusselt number decreases with the increase of the Brinkman number in both the wall cooling and heating modes. It is also found that the equilateral triangle exhibits the minimum friction coefficient and the maximum value of the Poiseuille number.
650		4	\|a Arbitrary-shaped triangular ducts
650		4	\|a Ritz method
650		4	\|a Analytical solution
650		4	\|a Heat transfer
650		4	\|a Viscous dissipation
653		0	\|a Science (General)
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700	0		\|a Mahmood Norouzi \|e verfasserin \|4 aut
700	0		\|a Mohammad Hassan Kayhani \|e verfasserin \|4 aut
700	0		\|a Amir Komeili Birjandi \|e verfasserin \|4 aut
700	0		\|a Amin Emamian \|e verfasserin \|4 aut
700	0		\|a Mirae Kim \|e verfasserin \|4 aut
700	0		\|a Kyung Chun Kim \|e verfasserin \|4 aut
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allfields	10.1016/j.heliyon.2024.e25293 doi (DE-627)DOAJ09561818X (DE-599)DOAJ8ba6ec6f743b4463a6701e3751defe1f DE-627 ger DE-627 rakwb eng Q1-390 H1-99 Amirhossein Hajiaghaei Tabalvandani verfasserin aut A general analytical solution for fluid flow and heat convection through arbitrary-shaped triangular ducts: A variational analysis 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper presents an analytical solution for fluid flow and heat transfer inside arbitrarily-shaped triangular ducts for the first time. The former analytical solutions are limited to the special case of isosceles triangular ducts. The literature has no report about the analytical solution for the general case of arbitrarily-shaped triangular ducts. Due to the significant role of fluid flow through non-circular channels in industry and the large number of triangular shapes, a method for solving the heat transfer problem for all triangular shapes is needed. The heat transfer of a fluid flow through a channel with an arbitrary triangular cross-section for the case of constant heat flux at the walls is solved in this work for the first time, considering viscous dissipation. Here, the functionals of flow and heat transfer equations are derived, and the resulting Euler–Lagrange equations are solved using the Ritz method. The effect of the duct geometry on the velocity profile and friction coefficient is studied in detail. The effect of the Brinkman number on the temperature distribution and Nusselt number is investigated for both cooling and heating cases. The results reveal that the critical Brinkman Number distinguishes between the cooling and heating cases and represents the critical point at which the Nusselt number approaches infinity. The value of the Nusselt number decreases with the increase of the Brinkman number in both the wall cooling and heating modes. It is also found that the equilateral triangle exhibits the minimum friction coefficient and the maximum value of the Poiseuille number. Arbitrary-shaped triangular ducts Ritz method Analytical solution Heat transfer Viscous dissipation Science (General) Social sciences (General) Mahmood Norouzi verfasserin aut Mohammad Hassan Kayhani verfasserin aut Amir Komeili Birjandi verfasserin aut Amin Emamian verfasserin aut Mirae Kim verfasserin aut Kyung Chun Kim verfasserin aut In Heliyon Elsevier, 2016 10(2024), 4, Seite e25293- (DE-627)835893197 (DE-600)2835763-2 24058440 nnns volume:10 year:2024 number:4 pages:e25293- https://doi.org/10.1016/j.heliyon.2024.e25293 kostenfrei https://doaj.org/article/8ba6ec6f743b4463a6701e3751defe1f kostenfrei http://www.sciencedirect.com/science/article/pii/S2405844024013240 kostenfrei https://doaj.org/toc/2405-8440 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_171 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 10 2024 4 e25293-
spelling	10.1016/j.heliyon.2024.e25293 doi (DE-627)DOAJ09561818X (DE-599)DOAJ8ba6ec6f743b4463a6701e3751defe1f DE-627 ger DE-627 rakwb eng Q1-390 H1-99 Amirhossein Hajiaghaei Tabalvandani verfasserin aut A general analytical solution for fluid flow and heat convection through arbitrary-shaped triangular ducts: A variational analysis 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper presents an analytical solution for fluid flow and heat transfer inside arbitrarily-shaped triangular ducts for the first time. The former analytical solutions are limited to the special case of isosceles triangular ducts. The literature has no report about the analytical solution for the general case of arbitrarily-shaped triangular ducts. Due to the significant role of fluid flow through non-circular channels in industry and the large number of triangular shapes, a method for solving the heat transfer problem for all triangular shapes is needed. The heat transfer of a fluid flow through a channel with an arbitrary triangular cross-section for the case of constant heat flux at the walls is solved in this work for the first time, considering viscous dissipation. Here, the functionals of flow and heat transfer equations are derived, and the resulting Euler–Lagrange equations are solved using the Ritz method. The effect of the duct geometry on the velocity profile and friction coefficient is studied in detail. The effect of the Brinkman number on the temperature distribution and Nusselt number is investigated for both cooling and heating cases. The results reveal that the critical Brinkman Number distinguishes between the cooling and heating cases and represents the critical point at which the Nusselt number approaches infinity. The value of the Nusselt number decreases with the increase of the Brinkman number in both the wall cooling and heating modes. It is also found that the equilateral triangle exhibits the minimum friction coefficient and the maximum value of the Poiseuille number. Arbitrary-shaped triangular ducts Ritz method Analytical solution Heat transfer Viscous dissipation Science (General) Social sciences (General) Mahmood Norouzi verfasserin aut Mohammad Hassan Kayhani verfasserin aut Amir Komeili Birjandi verfasserin aut Amin Emamian verfasserin aut Mirae Kim verfasserin aut Kyung Chun Kim verfasserin aut In Heliyon Elsevier, 2016 10(2024), 4, Seite e25293- (DE-627)835893197 (DE-600)2835763-2 24058440 nnns volume:10 year:2024 number:4 pages:e25293- https://doi.org/10.1016/j.heliyon.2024.e25293 kostenfrei https://doaj.org/article/8ba6ec6f743b4463a6701e3751defe1f kostenfrei http://www.sciencedirect.com/science/article/pii/S2405844024013240 kostenfrei https://doaj.org/toc/2405-8440 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_171 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 10 2024 4 e25293-
allfields_unstemmed	10.1016/j.heliyon.2024.e25293 doi (DE-627)DOAJ09561818X (DE-599)DOAJ8ba6ec6f743b4463a6701e3751defe1f DE-627 ger DE-627 rakwb eng Q1-390 H1-99 Amirhossein Hajiaghaei Tabalvandani verfasserin aut A general analytical solution for fluid flow and heat convection through arbitrary-shaped triangular ducts: A variational analysis 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper presents an analytical solution for fluid flow and heat transfer inside arbitrarily-shaped triangular ducts for the first time. The former analytical solutions are limited to the special case of isosceles triangular ducts. The literature has no report about the analytical solution for the general case of arbitrarily-shaped triangular ducts. Due to the significant role of fluid flow through non-circular channels in industry and the large number of triangular shapes, a method for solving the heat transfer problem for all triangular shapes is needed. The heat transfer of a fluid flow through a channel with an arbitrary triangular cross-section for the case of constant heat flux at the walls is solved in this work for the first time, considering viscous dissipation. Here, the functionals of flow and heat transfer equations are derived, and the resulting Euler–Lagrange equations are solved using the Ritz method. The effect of the duct geometry on the velocity profile and friction coefficient is studied in detail. The effect of the Brinkman number on the temperature distribution and Nusselt number is investigated for both cooling and heating cases. The results reveal that the critical Brinkman Number distinguishes between the cooling and heating cases and represents the critical point at which the Nusselt number approaches infinity. The value of the Nusselt number decreases with the increase of the Brinkman number in both the wall cooling and heating modes. It is also found that the equilateral triangle exhibits the minimum friction coefficient and the maximum value of the Poiseuille number. Arbitrary-shaped triangular ducts Ritz method Analytical solution Heat transfer Viscous dissipation Science (General) Social sciences (General) Mahmood Norouzi verfasserin aut Mohammad Hassan Kayhani verfasserin aut Amir Komeili Birjandi verfasserin aut Amin Emamian verfasserin aut Mirae Kim verfasserin aut Kyung Chun Kim verfasserin aut In Heliyon Elsevier, 2016 10(2024), 4, Seite e25293- (DE-627)835893197 (DE-600)2835763-2 24058440 nnns volume:10 year:2024 number:4 pages:e25293- https://doi.org/10.1016/j.heliyon.2024.e25293 kostenfrei https://doaj.org/article/8ba6ec6f743b4463a6701e3751defe1f kostenfrei http://www.sciencedirect.com/science/article/pii/S2405844024013240 kostenfrei https://doaj.org/toc/2405-8440 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_171 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 10 2024 4 e25293-
allfieldsGer	10.1016/j.heliyon.2024.e25293 doi (DE-627)DOAJ09561818X (DE-599)DOAJ8ba6ec6f743b4463a6701e3751defe1f DE-627 ger DE-627 rakwb eng Q1-390 H1-99 Amirhossein Hajiaghaei Tabalvandani verfasserin aut A general analytical solution for fluid flow and heat convection through arbitrary-shaped triangular ducts: A variational analysis 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper presents an analytical solution for fluid flow and heat transfer inside arbitrarily-shaped triangular ducts for the first time. The former analytical solutions are limited to the special case of isosceles triangular ducts. The literature has no report about the analytical solution for the general case of arbitrarily-shaped triangular ducts. Due to the significant role of fluid flow through non-circular channels in industry and the large number of triangular shapes, a method for solving the heat transfer problem for all triangular shapes is needed. The heat transfer of a fluid flow through a channel with an arbitrary triangular cross-section for the case of constant heat flux at the walls is solved in this work for the first time, considering viscous dissipation. Here, the functionals of flow and heat transfer equations are derived, and the resulting Euler–Lagrange equations are solved using the Ritz method. The effect of the duct geometry on the velocity profile and friction coefficient is studied in detail. The effect of the Brinkman number on the temperature distribution and Nusselt number is investigated for both cooling and heating cases. The results reveal that the critical Brinkman Number distinguishes between the cooling and heating cases and represents the critical point at which the Nusselt number approaches infinity. The value of the Nusselt number decreases with the increase of the Brinkman number in both the wall cooling and heating modes. It is also found that the equilateral triangle exhibits the minimum friction coefficient and the maximum value of the Poiseuille number. Arbitrary-shaped triangular ducts Ritz method Analytical solution Heat transfer Viscous dissipation Science (General) Social sciences (General) Mahmood Norouzi verfasserin aut Mohammad Hassan Kayhani verfasserin aut Amir Komeili Birjandi verfasserin aut Amin Emamian verfasserin aut Mirae Kim verfasserin aut Kyung Chun Kim verfasserin aut In Heliyon Elsevier, 2016 10(2024), 4, Seite e25293- (DE-627)835893197 (DE-600)2835763-2 24058440 nnns volume:10 year:2024 number:4 pages:e25293- https://doi.org/10.1016/j.heliyon.2024.e25293 kostenfrei https://doaj.org/article/8ba6ec6f743b4463a6701e3751defe1f kostenfrei http://www.sciencedirect.com/science/article/pii/S2405844024013240 kostenfrei https://doaj.org/toc/2405-8440 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_171 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 10 2024 4 e25293-
allfieldsSound	10.1016/j.heliyon.2024.e25293 doi (DE-627)DOAJ09561818X (DE-599)DOAJ8ba6ec6f743b4463a6701e3751defe1f DE-627 ger DE-627 rakwb eng Q1-390 H1-99 Amirhossein Hajiaghaei Tabalvandani verfasserin aut A general analytical solution for fluid flow and heat convection through arbitrary-shaped triangular ducts: A variational analysis 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper presents an analytical solution for fluid flow and heat transfer inside arbitrarily-shaped triangular ducts for the first time. The former analytical solutions are limited to the special case of isosceles triangular ducts. The literature has no report about the analytical solution for the general case of arbitrarily-shaped triangular ducts. Due to the significant role of fluid flow through non-circular channels in industry and the large number of triangular shapes, a method for solving the heat transfer problem for all triangular shapes is needed. The heat transfer of a fluid flow through a channel with an arbitrary triangular cross-section for the case of constant heat flux at the walls is solved in this work for the first time, considering viscous dissipation. Here, the functionals of flow and heat transfer equations are derived, and the resulting Euler–Lagrange equations are solved using the Ritz method. The effect of the duct geometry on the velocity profile and friction coefficient is studied in detail. The effect of the Brinkman number on the temperature distribution and Nusselt number is investigated for both cooling and heating cases. The results reveal that the critical Brinkman Number distinguishes between the cooling and heating cases and represents the critical point at which the Nusselt number approaches infinity. The value of the Nusselt number decreases with the increase of the Brinkman number in both the wall cooling and heating modes. It is also found that the equilateral triangle exhibits the minimum friction coefficient and the maximum value of the Poiseuille number. Arbitrary-shaped triangular ducts Ritz method Analytical solution Heat transfer Viscous dissipation Science (General) Social sciences (General) Mahmood Norouzi verfasserin aut Mohammad Hassan Kayhani verfasserin aut Amir Komeili Birjandi verfasserin aut Amin Emamian verfasserin aut Mirae Kim verfasserin aut Kyung Chun Kim verfasserin aut In Heliyon Elsevier, 2016 10(2024), 4, Seite e25293- (DE-627)835893197 (DE-600)2835763-2 24058440 nnns volume:10 year:2024 number:4 pages:e25293- https://doi.org/10.1016/j.heliyon.2024.e25293 kostenfrei https://doaj.org/article/8ba6ec6f743b4463a6701e3751defe1f kostenfrei http://www.sciencedirect.com/science/article/pii/S2405844024013240 kostenfrei https://doaj.org/toc/2405-8440 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_171 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 10 2024 4 e25293-
language	English
source	In Heliyon 10(2024), 4, Seite e25293- volume:10 year:2024 number:4 pages:e25293-
sourceStr	In Heliyon 10(2024), 4, Seite e25293- volume:10 year:2024 number:4 pages:e25293-
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Arbitrary-shaped triangular ducts Ritz method Analytical solution Heat transfer Viscous dissipation Science (General) Social sciences (General)
isfreeaccess_bool	true
container_title	Heliyon
authorswithroles_txt_mv	Amirhossein Hajiaghaei Tabalvandani @@aut@@ Mahmood Norouzi @@aut@@ Mohammad Hassan Kayhani @@aut@@ Amir Komeili Birjandi @@aut@@ Amin Emamian @@aut@@ Mirae Kim @@aut@@ Kyung Chun Kim @@aut@@
publishDateDaySort_date	2024-01-01T00:00:00Z
hierarchy_top_id	835893197
id	DOAJ09561818X
language_de	englisch
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The effect of the Brinkman number on the temperature distribution and Nusselt number is investigated for both cooling and heating cases. The results reveal that the critical Brinkman Number distinguishes between the cooling and heating cases and represents the critical point at which the Nusselt number approaches infinity. The value of the Nusselt number decreases with the increase of the Brinkman number in both the wall cooling and heating modes. 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callnumber-first	Q - Science
author	Amirhossein Hajiaghaei Tabalvandani
spellingShingle	Amirhossein Hajiaghaei Tabalvandani misc Q1-390 misc H1-99 misc Arbitrary-shaped triangular ducts misc Ritz method misc Analytical solution misc Heat transfer misc Viscous dissipation misc Science (General) misc Social sciences (General) A general analytical solution for fluid flow and heat convection through arbitrary-shaped triangular ducts: A variational analysis
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topic_title	Q1-390 H1-99 A general analytical solution for fluid flow and heat convection through arbitrary-shaped triangular ducts: A variational analysis Arbitrary-shaped triangular ducts Ritz method Analytical solution Heat transfer Viscous dissipation
topic	misc Q1-390 misc H1-99 misc Arbitrary-shaped triangular ducts misc Ritz method misc Analytical solution misc Heat transfer misc Viscous dissipation misc Science (General) misc Social sciences (General)
topic_unstemmed	misc Q1-390 misc H1-99 misc Arbitrary-shaped triangular ducts misc Ritz method misc Analytical solution misc Heat transfer misc Viscous dissipation misc Science (General) misc Social sciences (General)
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title	A general analytical solution for fluid flow and heat convection through arbitrary-shaped triangular ducts: A variational analysis
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title_full	A general analytical solution for fluid flow and heat convection through arbitrary-shaped triangular ducts: A variational analysis
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title_sort	general analytical solution for fluid flow and heat convection through arbitrary-shaped triangular ducts: a variational analysis
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title_auth	A general analytical solution for fluid flow and heat convection through arbitrary-shaped triangular ducts: A variational analysis
abstract	This paper presents an analytical solution for fluid flow and heat transfer inside arbitrarily-shaped triangular ducts for the first time. The former analytical solutions are limited to the special case of isosceles triangular ducts. The literature has no report about the analytical solution for the general case of arbitrarily-shaped triangular ducts. Due to the significant role of fluid flow through non-circular channels in industry and the large number of triangular shapes, a method for solving the heat transfer problem for all triangular shapes is needed. The heat transfer of a fluid flow through a channel with an arbitrary triangular cross-section for the case of constant heat flux at the walls is solved in this work for the first time, considering viscous dissipation. Here, the functionals of flow and heat transfer equations are derived, and the resulting Euler–Lagrange equations are solved using the Ritz method. The effect of the duct geometry on the velocity profile and friction coefficient is studied in detail. The effect of the Brinkman number on the temperature distribution and Nusselt number is investigated for both cooling and heating cases. The results reveal that the critical Brinkman Number distinguishes between the cooling and heating cases and represents the critical point at which the Nusselt number approaches infinity. The value of the Nusselt number decreases with the increase of the Brinkman number in both the wall cooling and heating modes. It is also found that the equilateral triangle exhibits the minimum friction coefficient and the maximum value of the Poiseuille number.
abstractGer	This paper presents an analytical solution for fluid flow and heat transfer inside arbitrarily-shaped triangular ducts for the first time. The former analytical solutions are limited to the special case of isosceles triangular ducts. The literature has no report about the analytical solution for the general case of arbitrarily-shaped triangular ducts. Due to the significant role of fluid flow through non-circular channels in industry and the large number of triangular shapes, a method for solving the heat transfer problem for all triangular shapes is needed. The heat transfer of a fluid flow through a channel with an arbitrary triangular cross-section for the case of constant heat flux at the walls is solved in this work for the first time, considering viscous dissipation. Here, the functionals of flow and heat transfer equations are derived, and the resulting Euler–Lagrange equations are solved using the Ritz method. The effect of the duct geometry on the velocity profile and friction coefficient is studied in detail. The effect of the Brinkman number on the temperature distribution and Nusselt number is investigated for both cooling and heating cases. The results reveal that the critical Brinkman Number distinguishes between the cooling and heating cases and represents the critical point at which the Nusselt number approaches infinity. The value of the Nusselt number decreases with the increase of the Brinkman number in both the wall cooling and heating modes. It is also found that the equilateral triangle exhibits the minimum friction coefficient and the maximum value of the Poiseuille number.
abstract_unstemmed	This paper presents an analytical solution for fluid flow and heat transfer inside arbitrarily-shaped triangular ducts for the first time. The former analytical solutions are limited to the special case of isosceles triangular ducts. The literature has no report about the analytical solution for the general case of arbitrarily-shaped triangular ducts. Due to the significant role of fluid flow through non-circular channels in industry and the large number of triangular shapes, a method for solving the heat transfer problem for all triangular shapes is needed. The heat transfer of a fluid flow through a channel with an arbitrary triangular cross-section for the case of constant heat flux at the walls is solved in this work for the first time, considering viscous dissipation. Here, the functionals of flow and heat transfer equations are derived, and the resulting Euler–Lagrange equations are solved using the Ritz method. The effect of the duct geometry on the velocity profile and friction coefficient is studied in detail. The effect of the Brinkman number on the temperature distribution and Nusselt number is investigated for both cooling and heating cases. The results reveal that the critical Brinkman Number distinguishes between the cooling and heating cases and represents the critical point at which the Nusselt number approaches infinity. The value of the Nusselt number decreases with the increase of the Brinkman number in both the wall cooling and heating modes. It is also found that the equilateral triangle exhibits the minimum friction coefficient and the maximum value of the Poiseuille number.
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title_short	A general analytical solution for fluid flow and heat convection through arbitrary-shaped triangular ducts: A variational analysis
url	https://doi.org/10.1016/j.heliyon.2024.e25293 https://doaj.org/article/8ba6ec6f743b4463a6701e3751defe1f http://www.sciencedirect.com/science/article/pii/S2405844024013240 https://doaj.org/toc/2405-8440
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up_date	2024-07-03T15:37:07.100Z
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The former analytical solutions are limited to the special case of isosceles triangular ducts. The literature has no report about the analytical solution for the general case of arbitrarily-shaped triangular ducts. Due to the significant role of fluid flow through non-circular channels in industry and the large number of triangular shapes, a method for solving the heat transfer problem for all triangular shapes is needed. The heat transfer of a fluid flow through a channel with an arbitrary triangular cross-section for the case of constant heat flux at the walls is solved in this work for the first time, considering viscous dissipation. Here, the functionals of flow and heat transfer equations are derived, and the resulting Euler–Lagrange equations are solved using the Ritz method. The effect of the duct geometry on the velocity profile and friction coefficient is studied in detail. The effect of the Brinkman number on the temperature distribution and Nusselt number is investigated for both cooling and heating cases. The results reveal that the critical Brinkman Number distinguishes between the cooling and heating cases and represents the critical point at which the Nusselt number approaches infinity. The value of the Nusselt number decreases with the increase of the Brinkman number in both the wall cooling and heating modes. 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A general analytical solution for fluid flow and heat convection through arbitrary-shaped triangular ducts: A variational analysis

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