Entropy generation and thermohydraulics of mixed convection of hybrid-nanofluid in a vertical tube fitted with elliptical‑cut twisted tape inserts - a computational study

ABSTRACT

A numerical investigation is carried out to study the mixed convection of Al₂O₃-Cu/water hybrid-nanofluid in a vertical tube fitted with elliptical-cut twisted tape inserts (TECT). Thermodynamic irreversibilities are evaluated by calculating the Bejan number, as well as the system’s local and total entropy generation. Heat transfer, friction factor, thermal performance factor, and entropy generation analyses are conducted for a range of volumetric concentrations of nanoparticles and flow Reynolds numbers between 7000 and 15,000. The realizable k-$\mathit{\epsilon }$ model is employed to simulate the turbulent and heat transferring flow computationally. The results clearly demonstrate the influence of mixed convection on heat transfer and entropy generation. In particular, mixed convection simulations predict greater Nusselt number, friction factor, and thermal performance factor than the corresponding forced convection simulations. Further, it is shown that the Nusselt number and the thermal performance factor for mixed convection are 4.6% and 5.5% higher than those for forced convection, respectively. The results also reveal that at Reynolds numbers of 7000, 9000, and 11,000, the thermal entropy production dominates the total irreversibility of the system. Likewise, frictional entropy production is the dominant mode of total irreversibility in the system at high Reynolds numbers of 13,000 and 15,000.

KEYWORDS:

• Entropy generation
• Bejan number
• heat transfer augmentation
• turbulent mixed convection
• hybrid nanofluids

Nomenclature

a	=	Diameter-cut width (m)
b	=	Diameter-cut length (m)
Be	=	Bejan number (-)
C1ε, C1ε, C1ε, Cμ Model constant	=
$C_p$	=	Specific heat of fluid (J Kg−1 K−1)
D	=	Pipe diameter (m)
$\mathit{f}$	=	Friction Factor
g	=	Gravitational acceleration (m/s2)
$G_k$	=	Turbulent kinetic energy generation (J Kg−1)
$G_b$	=	Generation of turbulence Kinetic energy due to buoyancy
h	=	Coefficient of heat transfer (W m−2 K−1)
k	=	Turbulent kinetic energy (J Kg−1)
$k_c$	=	Fluid thermal conductivity (W m−1 K−1)
L	=	Tube length (m)
Nu	=	Nusselt number (-)
P	=	Pressure (Pa)
Re	=	Reynolds number (-)
S	=	Velocity strain rate tensor
Sij	=	Linear deformation rate for a fluid element (-)
$S_{\mathit{F},\mathit{F}}$	=	Frictional Entropy production (W m−3 K−1)
$S_{\mathit{H},\mathit{T}}$	=	Thermal entropy production (W m−3 K−1)
$S_{\mathit{g},\mathit{t}}$	=	Total entropy production (W m−3 K−1)
T	=	Temperature (K)
$T_0$	=	Reference Fluid temperature (K)
u	=	Velocity of Fluid (m s−1)
w	=	Twisted tape width (m)
y	=	Twisted tape pitch (m)
Greek symbols	=
$\mathit{\rho }$	=	Fluid density (Kg m−3)
${\rho }_0$	=	Reference fluid density (Kg m−3)
$\mathit{\mu }$	=	Dynamic viscosity (Pa-S)
$\mathrm{\Delta p}$	=	Drop of pressure (Pa)
$\mathrm{\varnothing }$	=	Solid volume fraction
$\mathit{\eta }$	=	Thermal efficiency factor (-)
${\sigma }_{\epsilon }$	=	Model constant (-)
$\mathit{\delta }$	=	Thickness (m)
$\mathit{\epsilon }$	=	Turbulent dissipation rate
Sub-scripts	=
A	=	Al2O3
C	=	Cu
f	=	Basic fluid
$\mathit{eff}$	=	Effective
hnf	=	Hybrid-nanofluid
$\mathit{\beta }$:	=	Thermal expansion coefficient
o	=	Reference
p	=	Plain tube

Acknowledgements

A. Khfagi would like to thank the Government of Libya for funding his doctoral studies.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

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

Notes on contributors

Amir Mohamad Khfagi

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. Amir currently doing his PhD degree in Investigation of entropy generation and thermohydraulics of forced and mixed convection 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.