# First and second laws of thermodynamics analysis of nanofluid flow inside a heat exchanger duct with wavy walls and a porous insert

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## Abstract

This paper investigates the combined effects of using nanofluid, a porous insert and corrugated walls on heat transfer, pressure drop and entropy generation inside a heat exchanger duct. A series of numerical simulations are conducted for a number of pertinent parameters. It is shown that the waviness of the wall destructively affects the heat transfer process at low wave amplitudes and that it can improve heat convection only after exceeding a certain amplitude. Further, the pressure drop in the duct is found to be strongly influenced by the wave amplitude in a highly non-uniform way. The results, also, show that the second law and heat transfer performances of the system improve considerably by thickening the porous insert and decreasing its permeability. Yet, this is associated with higher pressure drops. It is argued that the hydraulic, thermal and entropic behaviours of the system are closely related to the interactions between a vortex formation near the wavy walls and nanofluid flow through the porous insert. Viscous irreversibilities are shown to be dominant in the core region of duct where the porous insert is placed. However, in the regions closer to the wavy walls, thermal entropy generation is the main source of irreversibility. A number of design recommendations are made on the basis of the findings of this study.

## Keywords

Nanofluid Porous insert Corrugated walls Heat exchanger duct Heat transfer Irreversibilities## List of symbols

*α*Amplitude of wave (m)

*C*_{F}Forchheimer coefficient (–)

*C*_{p}Specific heat at constant pressure (J kg

^{−1}K^{−1})*Da*Darcy number (–) \( \left( {Da = \frac{K}{{H^{2} }}} \right) \)

*f*Friction factor (–)

*h*Heat transfer coefficient (W m

^{−2}K^{−1})*H*Average distance between corrugated walls (m)

*H*_{P}Porous layer thickness (m)

*k*Thermal conductivity (W m

^{−1}K^{−1})*K*Permeability of porous material (m

^{2})*L*Heater length (m)

*L*_{w}Wavelength of the corrugated walls (m)

*N*Dimensionless average entropy generation rate (–)

*N*_{g}Dimensionless local volumetric entropy generation rate (–)

*Nu*Nusselt number (–)

*p*Pressure (

*Pa*)*P*Non-dimensional pressure

*R*_{k}Thermal conductivity ratio (–)

*Re*Reynolds number (–)

*S*Dimensionless porous layer thickness (–)\( \left( {S = \frac{{H_{P} }}{H}} \right) \)

*S*_{gen}Local volumetric entropy generation rate (W m

^{−3}K^{−1})*T*Temperature (

*K*)*u*,*v**V*elocity component in*x*and*y*directions, respectively (ms^{−1})*U*,*V*Non-dimensional velocity components (–)

*U*_{in}Inlet velocity (ms

^{−1})*x*,*y*Rectangular coordinates components (m)

*X*,*Y*Non-dimensional rectangular coordinates components (–)

## Greek symbols

*α*Non-dimensional wave amplitude (

*–*) \( \left( {\alpha = \frac{a}{H}} \right) \)- \( \varepsilon \)
Porosity (–)

- \( \Delta P^{*} \)
Dimensionless pressure drop (–) \( \left( {\Delta P^{*} = \frac{\Delta P}{{\rho U_{\text{in}}^{2} }}} \right) \)

- \( \mu \)
Dynamic viscosity (kg m

^{−1}s^{−1})- \( \nu \)
Kinematic viscosity (m

^{2}s^{−1})- \( \theta \)
Dimensionless temperature (–)

- \( \rho \)
Density of the fluid (kg m

^{−3})- \( \varphi \)
Volume fraction of nanoparticles

## Subscripts/superscripts

*ave*Average value

*eff*Effective

*nf*Nanofluid

*in*Inlet

*w*Wall

- x
Local value

## Notes

### Acknowledgements

N. Karimi acknowledges the financial support by EPSRC through Grant No. EP/N020472/1 (Therma-pump).

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