Fuzzy TOPSIS optimization of heat transfer rate of magnetized radiative Casson nanofluid over a stretching sheet

Shanmugapriya Marayanagaraj; Sundareswaran Raman; Augustine Wisely Bezalel; Abirami Thirupathy

doi:10.1515/cppm-2025-0060

Article

Fuzzy TOPSIS optimization of heat transfer rate of magnetized radiative Casson nanofluid over a stretching sheet

Shanmugapriya Marayanagaraj , Sundareswaran Raman , Augustine Wisely Bezalel and Abirami Thirupathy

Published/Copyright: July 17, 2025

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From the journal Chemical Product and Process Modeling

Abstract

Nanofluids provide an innovative solution for heat transfer and energy efficiency, making them highly beneficial across various industries. Their superior thermal conductivity, improved heat dissipation, and optimized energy efficiency makes them well-suited for applications in automotive cooling, industrial heat exchangers, electronics, renewable energy systems, hyperthermia cancer treatment, and targeted drug delivery. This study aims to determine a numerical solution for the flow of a magnetized radiative Casson nanofluid (CNF) composed of Aluminium Oxide (Al₂O₃)/Ethylene Glycol (C₂H₆O₂) and Copper oxide (CuO)/Ethylene Glycol (C₂H₆O₂) over an unsteady stretching, considering its wide range of applications. The objective of this work is to formulate a mathematical model of the physical flow problem and numerically solve the governing equations using shooting method via MATLAB. Furthermore, the most influential parameter for optimizing the rate of heat transfer is identified using Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). The outcome of the influencing dimensionless parameters like unsteadiness parameter (S), stretching parameter (C), magnetic parameter (M), radiation parameter (Rd), Prandtl number (Pr), Eckert number (Ec) and heat generation parameter (He) are discussed via contour plots and tables. According to the study, an increase in radiation parameter (Rd), and heat generation parameter (He) result in increased temperatures. Additionally, the increase in the heat transfer coefficient is greater in CuO/C₂H₆O₂ nanofluid compared to Al₂O₃/C₂H₆O₂ nanofluid. Furthermore, Fuzzy TOPSIS analysis indicates that alternative A20 represents the optimal best combination of physical parameters for enhancing the heat transfer rate for both Al₂O₃/C₂H₆O₂ and CuO/C₂H₆O₂ nanofluids.

Keywords: magnetohydrodynamics; Casson nanofluid; thermal radiation; heat generation; fuzzy TOPSIS

Corresponding author: Shanmugapriya Marayanagaraj, Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Chennai 603 110, India, E-mail: shanmugapriyam@ssn.edu.in

Acknowledgements

The authors would like to thank the Management, Principal, Sri Sivasubramaniya Nadar College of Engineering, Chennai, India.

Research ethics: Not applicable.
Informed consent: Not applicable.
Author contributions: Conceptualization, M.S.P. Methodology, M.S.P., A.W.B., T.B., and R.S.W. Software, M.S.P., A.W.B., and T.B. Validation, M.S.P., A.W.B., and T.B. Formal analysis, M.S.P., and R.S.W. Investigation, M.S.P., and R.S.W. Data curation, M.S.P., and R.S.W. Writing- original draft preparation, M.S.P., and R.S.W. Writing – review and editing, M.S.P., and R.S.W. Visualization, M.S.P., A.W.B., and T.B Supervision, M.S.P., and R.S.W. All four authors have read and agreed to the published version of the manuscript.
Use of Large Language Models, AI and Machine Learning Tools: None declared.
Conflict of interest: The authors declare that there are no conflicts of interest for this article. No copyediting or translation services were used for the preparation of this manuscript.
Research funding: This research did not receive any external funding.
Data availability: The datasets analysed during the current study are available from the corresponding author on reasonable request.

Nomenclature

u ˜ w , u ˜ e: Stretching and free stream velocity [m/s]
B ˜ 0: Magnetic induction parameter, [T]
q _r: radiative heat flux
T ˜ w , T ˜ ∞: Temperature near and far away from the stretching sheet surface, [K]
Q ˜ 0 π: Product component of the distortion rate
P ˜ y: Yield stress
π c: Product of critical based on non-Newtonian model
T ˜: Temperature of the nanofluid, [K]
u ˜ , v ˜: Velocity components of x ˜ and y ˜ directions [m/s]
x ˜: Distance along the surface, [m]
y ˜: Distance normal to the surface, [m]
M: magnetic parameter
S: Unsteadiness parameter
C: Stretching sheet parameter
Pr: Prandtl number
R _d: Radiation parameter
Ec: Eckert number
He: Heat generation parameter
C f x ˜: Coefficient of skin friction, [pascal]
N u x ˜: Local Nusselt number
R e x ˜: Reynolds number

Greek symbols

η ˜: Similarity variable
τ: Ratio of heat capacity of the nanoparticle
ψ ˜: Stream function
σ ^*: Stefan–Boltzmann constant, [W/m² K⁴]
k ^*: Mean absorption coefficient, [1/m]
μ ˜ b: Plastic dynamic viscosity
φ _CuO: Solid volume fraction of CuO
φ A l 2 O 3: Solid volume fraction of Al₂O₃
β: Casson nanofluid parameter
τ _w: Surface shear stress
q _w: Radiative heat flux
ϑ C 2 H 6 O 2: Kinematic viscosity of EG, [m²/s]
μ C 2 H 6 O 2: Dynamic viscosity of EG, [kg/m s]
ρ C 2 H 6 O 2: Density of EG, [kg/m³]
k C 2 H 6 O 2: Thermal conductivity of EG, [W/m K]
ρ c p C 2 H 6 O 2: Effective heat capacity of EG, [kg/m³K]
ρ c p nf: Heat capacity of the nanofluid, [kg/m³K]
k _nf: Thermal conductivity of the nanofluid, [W/m K]
ϑ _nf: Kinematic viscosity of the nanofluid, [m²/s]
μ _nf: Dynamic viscosity of the nanofluid, [kg/m s]

Subscripts

bf: Base fluid
nf: Nanofluid
w: Quantities at wall
∞: Quantities at free stream

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Received: 2025-03-25

Accepted: 2025-06-28

Published Online: 2025-07-17

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https://doi.org/10.1515/cppm-2025-0060

Keywords for this article

magnetohydrodynamics; Casson nanofluid; thermal radiation; heat generation; fuzzy TOPSIS