Newtonian Heating Effects of Oldroyd-B Liquid Flow with Cross-Diffusion and Second Order Slip

The current study highlights the Newtonian heating and second-order slip velocity with cross-diffusion effects on Oldroyd-B liquid flow. The modified Fourier heat flux is included in the energy equation system. The present problem is modeled with the physical governing system. The complexity of the...

Full description

Autores:
Loganathan, K.
Tamilvanan, K.
Viloria, Amelec
Varela, Noel
Pineda Lezama, Omar Bonerge
Tipo de recurso:
Article of journal
Fecha de publicación:
2020
Institución:
Corporación Universidad de la Costa
Repositorio:
REDICUC - Repositorio CUC
Idioma:
eng
OAI Identifier:
oai:repositorio.cuc.edu.co:11323/8110
Acceso en línea:
https://hdl.handle.net/11323/8110
https://doi.org/10.1007/978-3-030-53956-6_61
https://repositorio.cuc.edu.co/
Palabra clave:
Oldroyd-B liquid
Second order slip
Cross diffusion effects
Convective heating
Cattaneo-Christov heat flux
Rights
openAccess
License
CC0 1.0 Universal
id RCUC2_34ec167d9ccaeed36e3979e1cedbcda5
oai_identifier_str oai:repositorio.cuc.edu.co:11323/8110
network_acronym_str RCUC2
network_name_str REDICUC - Repositorio CUC
repository_id_str
dc.title.spa.fl_str_mv Newtonian Heating Effects of Oldroyd-B Liquid Flow with Cross-Diffusion and Second Order Slip
title Newtonian Heating Effects of Oldroyd-B Liquid Flow with Cross-Diffusion and Second Order Slip
spellingShingle Newtonian Heating Effects of Oldroyd-B Liquid Flow with Cross-Diffusion and Second Order Slip
Oldroyd-B liquid
Second order slip
Cross diffusion effects
Convective heating
Cattaneo-Christov heat flux
title_short Newtonian Heating Effects of Oldroyd-B Liquid Flow with Cross-Diffusion and Second Order Slip
title_full Newtonian Heating Effects of Oldroyd-B Liquid Flow with Cross-Diffusion and Second Order Slip
title_fullStr Newtonian Heating Effects of Oldroyd-B Liquid Flow with Cross-Diffusion and Second Order Slip
title_full_unstemmed Newtonian Heating Effects of Oldroyd-B Liquid Flow with Cross-Diffusion and Second Order Slip
title_sort Newtonian Heating Effects of Oldroyd-B Liquid Flow with Cross-Diffusion and Second Order Slip
dc.creator.fl_str_mv Loganathan, K.
Tamilvanan, K.
Viloria, Amelec
Varela, Noel
Pineda Lezama, Omar Bonerge
dc.contributor.author.spa.fl_str_mv Loganathan, K.
Tamilvanan, K.
Viloria, Amelec
Varela, Noel
Pineda Lezama, Omar Bonerge
dc.subject.spa.fl_str_mv Oldroyd-B liquid
Second order slip
Cross diffusion effects
Convective heating
Cattaneo-Christov heat flux
topic Oldroyd-B liquid
Second order slip
Cross diffusion effects
Convective heating
Cattaneo-Christov heat flux
description The current study highlights the Newtonian heating and second-order slip velocity with cross-diffusion effects on Oldroyd-B liquid flow. The modified Fourier heat flux is included in the energy equation system. The present problem is modeled with the physical governing system. The complexity of the governing system was reduced to a nonlinear ordinary system with the help of suitable transformations. A homotopy algorithm was used to validate the nonlinear system. This algorithm was solved via MATHEMATICA software. Their substantial aspects are further studied and reported in detail. We noticed that the influence of slip velocity order two is lower than the slip velocity order one.
publishDate 2020
dc.date.issued.none.fl_str_mv 2020-07-13
dc.date.accessioned.none.fl_str_mv 2021-04-08T21:23:03Z
dc.date.available.none.fl_str_mv 2021-04-08T21:23:03Z
dc.type.spa.fl_str_mv Artículo de revista
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_6501
dc.type.content.spa.fl_str_mv Text
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/article
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/ART
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
format http://purl.org/coar/resource_type/c_6501
status_str acceptedVersion
dc.identifier.uri.spa.fl_str_mv https://hdl.handle.net/11323/8110
dc.identifier.doi.spa.fl_str_mv https://doi.org/10.1007/978-3-030-53956-6_61
dc.identifier.instname.spa.fl_str_mv Corporación Universidad de la Costa
dc.identifier.reponame.spa.fl_str_mv REDICUC - Repositorio CUC
dc.identifier.repourl.spa.fl_str_mv https://repositorio.cuc.edu.co/
url https://hdl.handle.net/11323/8110
https://doi.org/10.1007/978-3-030-53956-6_61
https://repositorio.cuc.edu.co/
identifier_str_mv Corporación Universidad de la Costa
REDICUC - Repositorio CUC
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.references.spa.fl_str_mv Loganathan, K., Sivasankaran, S., Bhuvaneshwari, M., Rajan, S.: Second-order slip, cross- diffusion and chemical reaction effects on magneto-convection of Oldroyd-B liquid using Cattaneo-Christov heat flux with convective heating. J. Therm. Anal. Calorim. 136, 401–409 (2019). https://doi.org/10.1007/s10973-018-7912-5
Hayat, T., Imtiaz, M., Alsaedi, A., Almezal, S.: On Cattaneo-Christov heat flux in MHD flow of Oldroyd-B fluid with homogeneous-heterogeneous reactions. J. Magn. Mater. 401(1), 296–303 (2016)
Eswaramoorthi, S., Sivasankaran, S., Bhuvaneswari, M., Rajan, S.: Soret and Dufour effects on viscoelastic boundary layer flow over a stretchy surface with convective boundary condition with radiation and chemical reaction. Sci. Iran B. 23(6), 2575–2586 (2016)
Elanchezhian, E., Nirmalkumar, R., Balamurugan, M., Mohana, K., Prabu, K.M.: Amelec Viloria: heat and mass transmission of an Oldroyd-B nanofluid flow through a stratified medium with swimming of motile gyrotactic microorganisms and nanoparticles. J. Therm. Anal. Calorim. (2020). https://doi.org/10.1007/s10973- 020-09847-w
Loganathan, K., Rajan, S.: An entropy approach of Williamson nanofluid flow with Joule heating and zero nanoparticle mass flux. J. Therm. Anal. Calorim. (2020). https://doi.org/10.1007/s10973-020-09414-3
Bhuvaneswari, M., Eswaramoorthi, S., Sivasankaran, S., Hussein, A.K.: Cross- diffusion effects on MHD mixed convection over a stretching surface in a porous medium with chemical reaction and convective condition. Eng. Trans. 67(1), 3–19 (2019)
Loganathan, K., Sivasankaran, S., Bhuvaneswari, M., Rajan, S.: Dufour and Soret effects on MHD convection of Oldroyd-B liquid over stretching surface with chem- ical reaction and radiation using Cattaneo-Christov heat flux. IOP: Mater. Sci. Eng. 390, 012077 (2018)
Bhuvaneswari, M., Eswaramoorthi, S., Sivasankaran, S., Rajan, S., Saleh Alshom- rani, A.: Effects of viscous dissipation and convective heating on convection flow of a second-grade liquid over a stretching surface: an analytical and numerical study. Sci. Iran. B 26(3), 1350–1357 (2019)
Muhammad, T., Alamri, S.Z., Waqas, H., et al.: Bioconvection flow of magnetized Carreau nanofluid under the influence of slip over a wedge with motile microor- ganisms. J. Therm. Anal. Calorim. (2020). https://doi.org/10.1007/s10973-020- 09580-4
Abbasbandy, S., Hayat, T., Alsaedi, A., Rashidi, M.M.: Numerical and analytical solutions for Falkner-Skan flow of MHD Oldroyd-B fluid. Int. J. Numer. Methods Heat Fluid Flow 24, 390–401 (2014)
Liao, S., Tan, Y.A.: General approach to obtain series solutions of nonlinear dif- ferential. Stud. Appl. Math. 119(4), 297–354 (2007)
Liao, S.J.: An explicit, totally analytic approximation of Blasius viscous flow prob- lems. Int. J. Non-Linear Mech. 34, 759–778 (1999)
Loganathan, K., Mohana, K., Mohanraj, M., Sakthivel, P., Rajan, S., Impact of 3rd-grade nanofluid flow across a convective surface in the presence of inclined Lorentz force: an approach to entropy optimization. J. Therm. Anal. Calorim. (2020). https://doi.org/10.1007/s10973-020-09751-3
Sadeghy, K., Hajibeygi, H., Taghavi, S.M.: Stagnation-point flow of upper- convected Maxwell fluids. Int. J. Non-linear Mech. 41, 1242 (2006)
Mukhopadhyay, S.: Heat transfer analysis of the unsteady flow of a Maxwell fluid over a stretching surface in the presence of a heat source/sink. Chin. Phys. Lett. 29, 054703 (2012)
Abbasi, F.M., Mustafa, M., Shehzad, S.A., Alhuthali, M.S., Hayat, T.: Analytical study of Cattaneo-Christov heat flux model for a boundary layer flow of Oldroyd-B fluid. Chin. Phys. B. 25(1), 014701 (2016)
dc.rights.spa.fl_str_mv CC0 1.0 Universal
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/publicdomain/zero/1.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.coar.spa.fl_str_mv http://purl.org/coar/access_right/c_abf2
rights_invalid_str_mv CC0 1.0 Universal
http://creativecommons.org/publicdomain/zero/1.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Corporación Universidad de la Costa
dc.source.spa.fl_str_mv Lecture Notes in Computer Science book series (LNCS, volume 12145)
institution Corporación Universidad de la Costa
dc.source.url.spa.fl_str_mv https://link.springer.com/chapter/10.1007/978-3-030-53956-6_61
bitstream.url.fl_str_mv https://repositorio.cuc.edu.co/bitstreams/bb349673-8be0-4052-94af-1c8c24b2147a/download
https://repositorio.cuc.edu.co/bitstreams/a435fc0d-cbe4-4c59-a556-7b81303316dd/download
https://repositorio.cuc.edu.co/bitstreams/df0cc160-4189-42c0-b031-f8efef681e8d/download
https://repositorio.cuc.edu.co/bitstreams/5c20df57-7fa5-43a9-a898-b628f081382f/download
https://repositorio.cuc.edu.co/bitstreams/769372d6-fb79-4f04-a4b7-81ffbcc3bdcc/download
bitstream.checksum.fl_str_mv 42fd4ad1e89814f5e4a476b409eb708c
e30e9215131d99561d40d6b0abbe9bad
93aef76e220c573aa7e0d15ee97a71a1
316957c2b49a82c4501223e4980c9935
4fb8051c0c0d24671c949154fe28f205
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositorio de la Universidad de la Costa CUC
repository.mail.fl_str_mv repdigital@cuc.edu.co
_version_ 1811760712918237184
spelling Loganathan, K.Tamilvanan, K.Viloria, AmelecVarela, NoelPineda Lezama, Omar Bonerge2021-04-08T21:23:03Z2021-04-08T21:23:03Z2020-07-13https://hdl.handle.net/11323/8110https://doi.org/10.1007/978-3-030-53956-6_61Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/The current study highlights the Newtonian heating and second-order slip velocity with cross-diffusion effects on Oldroyd-B liquid flow. The modified Fourier heat flux is included in the energy equation system. The present problem is modeled with the physical governing system. The complexity of the governing system was reduced to a nonlinear ordinary system with the help of suitable transformations. A homotopy algorithm was used to validate the nonlinear system. This algorithm was solved via MATHEMATICA software. Their substantial aspects are further studied and reported in detail. We noticed that the influence of slip velocity order two is lower than the slip velocity order one.Loganathan, K.Tamilvanan, K.Viloria, AmelecVarela, NoelPineda Lezama, Omar Bonergeapplication/pdfengCorporación Universidad de la CostaCC0 1.0 Universalhttp://creativecommons.org/publicdomain/zero/1.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Lecture Notes in Computer Science book series (LNCS, volume 12145)https://link.springer.com/chapter/10.1007/978-3-030-53956-6_61Oldroyd-B liquidSecond order slipCross diffusion effectsConvective heatingCattaneo-Christov heat fluxNewtonian Heating Effects of Oldroyd-B Liquid Flow with Cross-Diffusion and Second Order SlipArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/acceptedVersionLoganathan, K., Sivasankaran, S., Bhuvaneshwari, M., Rajan, S.: Second-order slip, cross- diffusion and chemical reaction effects on magneto-convection of Oldroyd-B liquid using Cattaneo-Christov heat flux with convective heating. J. Therm. Anal. Calorim. 136, 401–409 (2019). https://doi.org/10.1007/s10973-018-7912-5Hayat, T., Imtiaz, M., Alsaedi, A., Almezal, S.: On Cattaneo-Christov heat flux in MHD flow of Oldroyd-B fluid with homogeneous-heterogeneous reactions. J. Magn. Mater. 401(1), 296–303 (2016)Eswaramoorthi, S., Sivasankaran, S., Bhuvaneswari, M., Rajan, S.: Soret and Dufour effects on viscoelastic boundary layer flow over a stretchy surface with convective boundary condition with radiation and chemical reaction. Sci. Iran B. 23(6), 2575–2586 (2016)Elanchezhian, E., Nirmalkumar, R., Balamurugan, M., Mohana, K., Prabu, K.M.: Amelec Viloria: heat and mass transmission of an Oldroyd-B nanofluid flow through a stratified medium with swimming of motile gyrotactic microorganisms and nanoparticles. J. Therm. Anal. Calorim. (2020). https://doi.org/10.1007/s10973- 020-09847-wLoganathan, K., Rajan, S.: An entropy approach of Williamson nanofluid flow with Joule heating and zero nanoparticle mass flux. J. Therm. Anal. Calorim. (2020). https://doi.org/10.1007/s10973-020-09414-3Bhuvaneswari, M., Eswaramoorthi, S., Sivasankaran, S., Hussein, A.K.: Cross- diffusion effects on MHD mixed convection over a stretching surface in a porous medium with chemical reaction and convective condition. Eng. Trans. 67(1), 3–19 (2019)Loganathan, K., Sivasankaran, S., Bhuvaneswari, M., Rajan, S.: Dufour and Soret effects on MHD convection of Oldroyd-B liquid over stretching surface with chem- ical reaction and radiation using Cattaneo-Christov heat flux. IOP: Mater. Sci. Eng. 390, 012077 (2018)Bhuvaneswari, M., Eswaramoorthi, S., Sivasankaran, S., Rajan, S., Saleh Alshom- rani, A.: Effects of viscous dissipation and convective heating on convection flow of a second-grade liquid over a stretching surface: an analytical and numerical study. Sci. Iran. B 26(3), 1350–1357 (2019)Muhammad, T., Alamri, S.Z., Waqas, H., et al.: Bioconvection flow of magnetized Carreau nanofluid under the influence of slip over a wedge with motile microor- ganisms. J. Therm. Anal. Calorim. (2020). https://doi.org/10.1007/s10973-020- 09580-4Abbasbandy, S., Hayat, T., Alsaedi, A., Rashidi, M.M.: Numerical and analytical solutions for Falkner-Skan flow of MHD Oldroyd-B fluid. Int. J. Numer. Methods Heat Fluid Flow 24, 390–401 (2014)Liao, S., Tan, Y.A.: General approach to obtain series solutions of nonlinear dif- ferential. Stud. Appl. Math. 119(4), 297–354 (2007)Liao, S.J.: An explicit, totally analytic approximation of Blasius viscous flow prob- lems. Int. J. Non-Linear Mech. 34, 759–778 (1999)Loganathan, K., Mohana, K., Mohanraj, M., Sakthivel, P., Rajan, S., Impact of 3rd-grade nanofluid flow across a convective surface in the presence of inclined Lorentz force: an approach to entropy optimization. J. Therm. Anal. Calorim. (2020). https://doi.org/10.1007/s10973-020-09751-3Sadeghy, K., Hajibeygi, H., Taghavi, S.M.: Stagnation-point flow of upper- convected Maxwell fluids. Int. J. Non-linear Mech. 41, 1242 (2006)Mukhopadhyay, S.: Heat transfer analysis of the unsteady flow of a Maxwell fluid over a stretching surface in the presence of a heat source/sink. Chin. Phys. Lett. 29, 054703 (2012)Abbasi, F.M., Mustafa, M., Shehzad, S.A., Alhuthali, M.S., Hayat, T.: Analytical study of Cattaneo-Christov heat flux model for a boundary layer flow of Oldroyd-B fluid. Chin. Phys. B. 25(1), 014701 (2016)PublicationCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8701https://repositorio.cuc.edu.co/bitstreams/bb349673-8be0-4052-94af-1c8c24b2147a/download42fd4ad1e89814f5e4a476b409eb708cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-83196https://repositorio.cuc.edu.co/bitstreams/a435fc0d-cbe4-4c59-a556-7b81303316dd/downloade30e9215131d99561d40d6b0abbe9badMD53ORIGINALLoganathan2020_Chapter_NewtonianHeatingEffectsOfOldro.pdfLoganathan2020_Chapter_NewtonianHeatingEffectsOfOldro.pdfapplication/pdf806711https://repositorio.cuc.edu.co/bitstreams/df0cc160-4189-42c0-b031-f8efef681e8d/download93aef76e220c573aa7e0d15ee97a71a1MD51THUMBNAILLoganathan2020_Chapter_NewtonianHeatingEffectsOfOldro.pdf.jpgLoganathan2020_Chapter_NewtonianHeatingEffectsOfOldro.pdf.jpgimage/jpeg39946https://repositorio.cuc.edu.co/bitstreams/5c20df57-7fa5-43a9-a898-b628f081382f/download316957c2b49a82c4501223e4980c9935MD54TEXTLoganathan2020_Chapter_NewtonianHeatingEffectsOfOldro.pdf.txtLoganathan2020_Chapter_NewtonianHeatingEffectsOfOldro.pdf.txttext/plain13258https://repositorio.cuc.edu.co/bitstreams/769372d6-fb79-4f04-a4b7-81ffbcc3bdcc/download4fb8051c0c0d24671c949154fe28f205MD5511323/8110oai:repositorio.cuc.edu.co:11323/81102024-09-17 10:45:46.66http://creativecommons.org/publicdomain/zero/1.0/CC0 1.0 Universalopen.accesshttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa CUCrepdigital@cuc.edu.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