Unsteady slip flow of special second-grade fluid induced by Fe3O4 particles past a movable sheet with magnetic and nonlinear heat source/sink
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 9 May 2024
Issue publication date: 16 July 2024
Abstract
Purpose
Ferrofluids are aqueous or non-aqueous solutions with colloidal particles of iron oxide nanoparticles with high magnetic characteristics. Their magnetic characteristics enable them to be controlled and manipulated when ferrofluids are exposed to magnetic fields. This study aims to inspect the features of unsteady stagnation point flow (SPF) and heat flux from the surface by incorporating ferromagnetic particles through a special kind of second-grade fluid (SGF) across a movable sheet with a nonlinear heat source/sink and magnetic field effect. The mass suction/injection and stretching/shrinking boundary conditions are also inspected to calculate the fine points of the features of multiple solutions.
Design/methodology/approach
The leading equations that govern the ferrofluid flow are reduced to a group of ordinary differential equations by applying similarity variables. The converted equations are numerically solved through the bvp4c solver. Afterward, study and discussion are carried out to examine the different physical parameters of the characteristics of nanofluid flow and thermal properties.
Findings
Multiple solutions are revealed to happen for situations of unsteadiness, shrinking as well as stretching sheets. Greater suction slows the separation of the boundary layers and causes the critical values to expand. The region where the multiple solutions appear is observed to expand with increasing values of the magnetic, non-Newtonian and suction parameters. Moreover, the fluid velocity significantly uplifts while the temperature declines due to the suction parameter.
Originality/value
The novelty of the work is to deliberate the impact of mass suction/injection on the unsteady SPF through the special second-grade ferrofluids across a movable sheet with an erratic heat source/sink. The confirmed results provide a very good consistency with the accepted papers. Previous studies have not yet fully explored the entire analysis of the proposed model.
Keywords
Acknowledgements
Expression of Concern: The publisher of International Journal of Numerical Methods for Heat & Fluid Flow is issuing an Expression of Concern for the article Khan, U., Zaib, A., Ishak, A., Sherif, E.S.M. and Wróblewski, P. (2024), “Unsteady slip flow of special second–grade fluid induced by Fe3O4 particles past a movable sheet with magnetic and nonlinear heat source/sink”, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 34 No. 6, pp. 2321-2344. https://doi.org/10.1108/HFF-01-2024-0030, to inform readers that concerns have been raised regarding its authorship. An investigation is ongoing and is currently unresolved. The authors of this article would like to note that they do not agree with the content of this notice. Further information will be provided by the International Journal of Numerical Methods for Heat & Fluid Flow as it becomes available.
This research has been funded by the Universiti Kebangsaan Malaysia project number “DIP-2023–005.” Also, the authors extend their appreciation to the Researchers Supporting Project Number (RSP2024R33), King Saud University, Riyadh, Saudi Arabia.
Data availability statement: The data sets used and/or analyzed during the current study are available from the corresponding author upon reasonable request.
Conflict of interest: There is no conflict of interest.
Author contributions: Umair Khan: Conceptualization, Methodology, Software, Formal analysis, Validation; Writing – original draft. Aurang Zaib: Writing – original draft, Data curation, Investigation, Visualization, Validation. Anuar Ishak: Conceptualization, Writing – original draft, Writing – review and editing, Supervision, Resources. El-Sayed M. Sherif and Piotr Wróblewski: Validation, Investigation, Writing – review and editing, Formal analysis; Project administration; Funding acquisition, Software.
Citation
Khan, U., Zaib, A., Ishak, A., Sherif, E.-S.M. and Wróblewski, P. (2024), "Unsteady slip flow of special second-grade fluid induced by Fe3O4 particles past a movable sheet with magnetic and nonlinear heat source/sink", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 34 No. 6, pp. 2321-2344. https://doi.org/10.1108/HFF-01-2024-0030
Publisher
:Emerald Publishing Limited
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