Non-linear thermal radiative Williamson nanofluid flow with viscous dissipation and Joule heating

In this work, we analyzed unsteady viscous incompressible two-dimensional magnetohydrodynamics (MHD) Williamson nanofluid flow with effects of non-linear thermal radiation, viscous dissipation, Joule heating, thermo-solutal buoyancy forces, suction/injection, heat source/sink, and convective boundar...

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Main Authors: Subhan Ali, Salman Zeb, Muhammad Yousaf, Sultan Alshehery, Ilyas Khan
Format: Article
Language:English
Published: Elsevier 2025-06-01
Series:Results in Physics
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Online Access:http://www.sciencedirect.com/science/article/pii/S2211379725001330
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author Subhan Ali
Salman Zeb
Muhammad Yousaf
Sultan Alshehery
Ilyas Khan
author_facet Subhan Ali
Salman Zeb
Muhammad Yousaf
Sultan Alshehery
Ilyas Khan
author_sort Subhan Ali
collection DOAJ
description In this work, we analyzed unsteady viscous incompressible two-dimensional magnetohydrodynamics (MHD) Williamson nanofluid flow with effects of non-linear thermal radiation, viscous dissipation, Joule heating, thermo-solutal buoyancy forces, suction/injection, heat source/sink, and convective boundary conditions. The dimensionless variables are used to non-dimensionalize the governing equations of the Williamson nanofluid flow model into dimensionless non-linear partial differential equations (PDEs). Numerical solutions are obtained and the results are presented and examined for the effects of different governing parameters on the velocity, temperature, and concentration fields, and also on physical quantities Nusselt number, Sherwood number, and skin friction coefficient. The velocity profile observed increasing trend against the Reynolds number, thermal Grashof number, and solutal Grashof number while it is decreasing against the higher magnetic parameter. The temperature of the fluid increases for higher radiation parameter, temperature ratio parameter, Eckert number, thermal Biot number, and thermal Grashof number. The fluid concentration profile increases against the Schmidt number, thermophoresis parameter, and solutal Biot number while it declines for the thermal Biot number and Brownian motion parameter. The accuracy of our results are confirmed by comparing the Nusselt number against the radiation parameter with previous results in the literature.
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spelling doaj-art-07efb7ee44044cf0b4e0a1bdae26e4982025-08-20T03:19:17ZengElsevierResults in Physics2211-37972025-06-017310823910.1016/j.rinp.2025.108239Non-linear thermal radiative Williamson nanofluid flow with viscous dissipation and Joule heatingSubhan Ali0Salman Zeb1Muhammad Yousaf2Sultan Alshehery3Ilyas Khan4Department of Mathematics, University of Malakand, Chakdara, Dir Lower, 18800, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, University of Malakand, Chakdara, Dir Lower, 18800, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, University of Malakand, Chakdara, Dir Lower, 18800, Khyber Pakhtunkhwa, PakistanCollege of Engineering, Mechanical Engineering Department, King Khalid University, Abha, Saudi ArabiaDepartment of Mathematical Sciences, Saveetha School of Engineering, SIMATS, Chennai, Tamil Nadu, India; Hourani Center for Applied scientific Research, Al-Ahliyya Amman University, Amman, Jordan; Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia; Corresponding author at: Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia.In this work, we analyzed unsteady viscous incompressible two-dimensional magnetohydrodynamics (MHD) Williamson nanofluid flow with effects of non-linear thermal radiation, viscous dissipation, Joule heating, thermo-solutal buoyancy forces, suction/injection, heat source/sink, and convective boundary conditions. The dimensionless variables are used to non-dimensionalize the governing equations of the Williamson nanofluid flow model into dimensionless non-linear partial differential equations (PDEs). Numerical solutions are obtained and the results are presented and examined for the effects of different governing parameters on the velocity, temperature, and concentration fields, and also on physical quantities Nusselt number, Sherwood number, and skin friction coefficient. The velocity profile observed increasing trend against the Reynolds number, thermal Grashof number, and solutal Grashof number while it is decreasing against the higher magnetic parameter. The temperature of the fluid increases for higher radiation parameter, temperature ratio parameter, Eckert number, thermal Biot number, and thermal Grashof number. The fluid concentration profile increases against the Schmidt number, thermophoresis parameter, and solutal Biot number while it declines for the thermal Biot number and Brownian motion parameter. The accuracy of our results are confirmed by comparing the Nusselt number against the radiation parameter with previous results in the literature.http://www.sciencedirect.com/science/article/pii/S2211379725001330Williamson nanofluidNon-linear thermal radiationViscous dissipationJoule heatingConvection boundary conditions
spellingShingle Subhan Ali
Salman Zeb
Muhammad Yousaf
Sultan Alshehery
Ilyas Khan
Non-linear thermal radiative Williamson nanofluid flow with viscous dissipation and Joule heating
Results in Physics
Williamson nanofluid
Non-linear thermal radiation
Viscous dissipation
Joule heating
Convection boundary conditions
title Non-linear thermal radiative Williamson nanofluid flow with viscous dissipation and Joule heating
title_full Non-linear thermal radiative Williamson nanofluid flow with viscous dissipation and Joule heating
title_fullStr Non-linear thermal radiative Williamson nanofluid flow with viscous dissipation and Joule heating
title_full_unstemmed Non-linear thermal radiative Williamson nanofluid flow with viscous dissipation and Joule heating
title_short Non-linear thermal radiative Williamson nanofluid flow with viscous dissipation and Joule heating
title_sort non linear thermal radiative williamson nanofluid flow with viscous dissipation and joule heating
topic Williamson nanofluid
Non-linear thermal radiation
Viscous dissipation
Joule heating
Convection boundary conditions
url http://www.sciencedirect.com/science/article/pii/S2211379725001330
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AT muhammadyousaf nonlinearthermalradiativewilliamsonnanofluidflowwithviscousdissipationandjouleheating
AT sultanalshehery nonlinearthermalradiativewilliamsonnanofluidflowwithviscousdissipationandjouleheating
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