Numerical investigation of second law analysis of PGGNP/H2O nanofluid in various converging pipes


This paper studies entropy production rate of propylene glycol-treated graphene nanoplatelet-based water (PGGNP-water) nanofluid flowing through three converging pipes (linear, Bessel and exponential) in laminar flow regime using computational fluid dynamics. The simulation is performed for range of Reynolds number \(\left( {400 \le Re \le 1600} \right)\) and nanoparticle concentration \(\left( {0\% \le \varphi \le 0.1\% } \right)\). The effect of Reynolds number and nanoparticle concentration were investigated on entropy production rates and Bejan number. The result showed that thermal entropy production rate of nanofluid in converging pipes was lower compared with straight pipes. In addition, increase in Reynolds number enhances viscous entropy production rate but decreases thermal entropy production rate. Furthermore, increase in nanoparticle concentration by 0.1% enhanced the viscous entropy production rate by a factor of 48.93 and reduced the thermal entropy production rate by 18.69%.

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\(A_{{\text{s}}}\) :

Surface area (m2)

Be :

Bejan number

\(c_{{\text{p}}}\) :

Specific heat capacity at constant pressure (J/kg K)

D h :

Diameter of the pipe (m)

\(f\) :

Friction factor

\(h\) :

Coefficient of heat transfer (W/m2 K)

\(\dot{m}\) :

Mass flow rate

\(Nu\) :

Nusselt number

\(Pr\) :

Prandtl number of base fluid

Re :

Reynolds number

\(S\) :

Entropy production

\(T_{{}}\) :

Temperature of base fluid (K)

u r, u x :

Component velocity (m/s)

\(u_{{{\text{in}}}}\) :

Inlet velocity

\(r\left( x \right)\) :

Axial radius

\(R\) :


\(\alpha\) :

Thermal diffusivity (m2/s)

\(\lambda\) :

Thermal conductivity (W/m K)

μ :

Dynamic viscosity (kg/ms)

\(\varphi\) :

Nanoparticle volume fraction (%)

ρ :

Density of base fluid (kg/m3)

\(\Delta P\) :

Pressure drop




Base fluid



















\(^{\prime \prime \prime}\) :



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Correspondence to Adefope Adeyanju Owojori.

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Owojori, A.A., Olokuntoye, B.A. & Fadodun, O.G. Numerical investigation of second law analysis of PGGNP/H2O nanofluid in various converging pipes. Int Nano Lett (2021).

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  • Thermal entropy
  • Viscous entropy
  • Nanofluid
  • Reynolds number
  • Converging pipe
  • Bejan number
  • Heat transfer