Time-dependent analysis of heat transfer enhancement and entropy generation of hybrid nanofluids in a tube with a solid and elliptical‑cut twisted tape insert with non-uniform heat flux

ABSTRACT

This numerical study investigates the improvement of transient heat transfer in a plain tube using hybrid nanofluids consisting of solid particles and twisted tapes with elliptical cuts, under non-uniform heat flux conditions. The analysis includes the calculation of the Bejan number and entropy production. Different working fluids, including water, CuO/water nanofluid, and a hybrid nanofluid with a 2% volume concentration of Al₂O₃-Cu/water, are used with varying concentrations of the hybrid nanofluid ranging from 1% to 4%. Effects of heat flux distribution and local concentration ratio (LCR) are investigated. The computational results indicate that conventional and elliptical cut twisted tapes enhance transient heat transmission. A slight rise in the heat transfer coefficient is observed when the fluid has higher thermal conductivity. The flow velocity gradually stabilizes over time. The hybrid nanofluid of (Al₂O₃-Cu/water) significantly affects transient heat transmission, reducing the maximum temperature difference by approximately 4.1% compared to water and 6.2% compared to the nanofluid. Transient heat transmission is further intensified by TECT. Moreover, frictional entropy production dominates the system’s irreversibility. This study contributes to the understanding of transient heat transfer enhancement and its dependence on hybrid nanofluids, providing insights for engineering applications.

KEYWORDS:

• Bejan number
• elliptical‑cut twisted tape
• hybrid nanofluids
• total and local entropy production
• transient heat transfer

Nomenclature

a	=	Diameter-cut width (m)
b	=	Diameter-cut long (m)
Be	=	Bejan number (-)
$C_1,$$C_2,C_{\mu }$	=	Model constants (-)
$C_p$	=	Specific heat (J Kg−1 C−1)
D	=	Pipe diameter (m)
$f$	=	Friction Factor (-)
$G_k$	=	Production of turbulent kinetic energy (J Kg−1)
h	=	Heat transfer coefficient (W m−2 C−1)
k	=	Turbulent kinetic energy (J Kg−1)
$k_c$	=	Thermal conductivity (W m−1 C−1)
L	=	Length of duct (m)
Nu	=	Nusselt number (-)
P	=	Pressure (Pa)
Re	=	Reynolds number (-)
Sij	=	Linear distortion rate (-)
$S_{F,F}$	=	Fractional entropy creation (W m−3 C−1)
t	=	Time (s)
T	=	Fluid temperature (C)
u	=	Velocity (m s−1)
w	=	Width of twisted tape (m)
y	=	Twisted tape pitch (m)
Greek Symbols	=
$\rho$	=	Density (Kg m−3)
$\mathrm{\varnothing }$	=	Solid volume fraction (-)
$\mu$	=	Dynamic viscosity (Pa-S)
${\tau }_w$	=	Wall shear stress (Pa)
$\eta$	=	Thermal efficiency factor (-)
$\delta$	=	Thickness (m)
${\sigma }_{\epsilon }$	=	Model constant (-)
$\mathrm{\Delta }p$	=	Drop of pressure (Pa)
Acronyms	=
PT	=	Plain pipe
TECT	=	Twisted pipe with elliptical cut
TPT	=	Classical twisted tape

Acknowledgements

The first author gratefully acknowledges the Government of Libya for funding his doctoral studies at Glasgow University.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Ministry of Higher Education and Scientific Research in Libya.

Notes on contributors

Amir Mohamad Khfagi

Dr Amir Khfagi I completed my first degree in mechanical engineering in 2003 at Ajdabya faculty of engineering in Libya. This was followed by a master's degree in advanced mechanical engineering at Sheffield Hallam University 2015. I was accepted to the University of Glasgow to study for a PhD in Mechanical Engineering in June 2019. I completed my PhD in June 2023 in the investigation of entropy generation and thermohydraulics of forced and mixed convection of Al2O3-Cu/water in a parabolic trough receiver tube.

Graeme Hunt

Dr Graeme Hunt I completed my first degree in Chemistry at the University of St Andrews in 1994. Following many years working outside of academia, I completed a further degree in Mathematics at the Open University. I was accepted to the University of Glasgow to study for a PhD in Mechanical Engineering in 2015 and won a scholarship to fund it. I completed my PhD on non-equilibrium thermodynamics in porous media in early 2020 and have worked as a PDRA on multiple projects at the University of Glasgow since then.

Manosh C Paul

Prof. Manosh C Paul Professor of Thermofluids at Mechanical Engineering and member of the Energy and Sustainability Group within the Systems, Power & Energy Research Division of the James Watt School of Engineering, University of Glasgow, UK. Recently, he held a prestigious RAEng/Leverhulme Trust Senior Research Fellowship. He joined the University of Glasgow in August 2003 as a Lecturer, and was promoted to Senior Lecturer in 2013, Reader in 2017, and Professor in 2020. Prior to Glasgow, he was a PDRA at the Department of Mechanical Engineering of Imperial College London. He received his PhD in Thermofluids in 2002 from the Department of Mechanical Engineering, University of Bath. He has first class degrees, with distinctions and gold medals, in both MSc (Applied Mathematics) and BSc honours (Mathematics) obtained from the University of Dhaka in 1999 and 1997 respectively. He is a Chartered Engineer (CEng), Fellow of the Higher Education Academy (FHEA), and member of the Engineering Professors' Council, Institution of Mechanical Engineers (IMechE), UK Combustion Institute, and International Association of Engineers (IAENG).

Nader Karimi

Dr Nader Karimi completed his first degree in mechanical engineering in 2000 at AmirKabir University of Technology in Tehran/Iran. This was followed by a master's degree in energy conversion at Sharif University of Technology, Tehran in 2003. He was awarded a PhD in 2009 for his experimental and theoretical work on unsteady combusting flows at University of Melbourne in Australia. In between 2009 and 2011, he was a Marie Currie post-doctoral researcher at Darmstadt University of Technology in Germany. He then moved to the Department of Engineering at University of Cambridge in the UK and worked there as a research associate for almost two years. In late 2013, he was appointed as a lecturer in mechanical engineering at James Watt School of Engineering, University of Glasgow where he served till early 2020. Nader is currently a Reader in Mechanical Engineering at the School of Engineering and Materials Science, Queen Mary University of London.