In many engineering applications, including coating and lubrication operations, analyzing the temperature behavior of thin film flows on a vertically upward-moving tube is crucial to improving predictive models. This paper examines a steady third-grade fluid film flow with a surface tension gradient on a vertical tube. The mechanisms responsible for the fluid motion are upward tube motion, gravity, and surface tension gradient. This analysis focuses on heat transfer and stagnant ring dynamics. The formulated highly nonlinear ordinary differential equations are solved using the Adomian decomposition method. The conditions for stagnant rings and uniform film thickness are attained and discussed. The inverse capillary number C, Stokes number , Deborah number De, and Brinkman number Br emerged as flow control parameters. The temperature of the fluid film rises with an increase in the C, , De, and Br, whereas it decreases with an increase in thermal diffusion rate. The radius of stagnant rings tends to shrink by the increase in C, , and De. When the value of De is high, third-grade fluid behaves like solids; only free drainage happens with smaller radius stagnant rings and high temperatures. A comparison between Newtonian and third-grade fluids regarding surface tension, velocity, temperature, stationary rings, and fluid film thickness is also provided.
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October 2024
Research Article|
October 30 2024
Revealing the dynamics of stagnant rings of third-grade fluid film with heat transfer in the presence of surface tension
Amel Alaidrous (العيدروس أمل)
;
Amel Alaidrous (العيدروس أمل)
(Conceptualization, Formal analysis, Funding acquisition, Investigation, Project administration, Resources, Validation)
1
Mathematics Department, Faculty of Sciences, Umm Al-Qura University
, Makkah, Saudi Arabia
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Ayesha Siddiqa (صدیقہ عائشہ)
;
Ayesha Siddiqa (صدیقہ عائشہ)
(Conceptualization, Investigation, Software, Visualization, Writing – original draft)
2
Department of Mathematics, University of Okara
, Okara, Pakistan
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Hameed Ashraf (اشرف حمید)
Hameed Ashraf (اشرف حمید)
a)
(Conceptualization, Formal analysis, Investigation, Visualization, Writing – original draft)
2
Department of Mathematics, University of Okara
, Okara, Pakistan
a)Author to whom correspondence should be addressed: hameedashraf09@uo.edu.pk
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a)Author to whom correspondence should be addressed: hameedashraf09@uo.edu.pk
Physics of Fluids 36, 103130 (2024)
Article history
Received:
August 09 2024
Accepted:
October 08 2024
Citation
Amel Alaidrous, Ayesha Siddiqa, Hameed Ashraf; Revealing the dynamics of stagnant rings of third-grade fluid film with heat transfer in the presence of surface tension. Physics of Fluids 1 October 2024; 36 (10): 103130. https://doi.org/10.1063/5.0232610
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