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Numerical modeling of entropy production in Al2O3/H2O nanofluid flowing through a novel Bessel-like converging pipe

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Abstract

Optimization of thermal systems requires higher heat transfer rate and lower entropy production rate. The review of literature shows that there are limited works on entropy production rate of nanofluids flowing through a converging pipe as the available ones only considered entropy production rate in a linear converging pipe. In this study, a 2D-computational fluid dynamic model is set up to investigate entropy production rate of Al2O3 nanofluid flowing through novel Bessel-like convergent pipes in laminar flow regime. The effect of Reynolds number \(\left( {300 \le {\text{Re}} \le 1200} \right)\), nanoparticle concentration \(\left( {0 \le \varphi \le 0.1} \right)\), and convergent index \(\left( {n = 0 - 3} \right)\) on the entropy production rate, heat transfer effectiveness number, and irreversibility distribution ratio were considered. The results obtained revealed that increase in convergent index enhances viscous entropy production rate, but diminishes thermal entropy production rate. For instance, the reduction in thermal entropy production rate at \({\text{Re}} = 900\) between pipe corresponds to \(n = 0\) and \(n = 3\) was 51.98% while the increase in viscous entropy production rate was 753.65%. Furthermore, a new correlation was developed using response surface methodology to estimate the entropy production rate as a function of the Reynolds number, nanoparticle concentration, and convergence index. The overall result shows that the usage of converging pipe in place of straight pipe is more advantageous.

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Abbreviations

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

Surface area (m2)

Be:

Bejan number

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

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

Dh :

Diameter of the pipe (m)

\(f\) :

Friction factor

\(h\) :

Coefficient of heat transfer (W/m2 K)

\(I_{{\text{a}}}\) :

Thermal effectiveness number

\(\dot{m}\) :

Mass flow rate

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

Dimensionless entropy production rate

\({\text{Nu}}\) :

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

\(R\) :

Radius

\(\alpha\) :

Thermal diffusivity (m2/s)

\(\lambda\) :

Thermal conductivity (W/m K)

\(\mu\) :

Dynamic viscosity (kg/ms)

\(\varphi\) :

Nanoparticle volume fraction (%)

\(\rho\) :

Density of base fluid (kg/m3)

\(\emptyset\) :

Irreversibility distribution function

\(\delta_{{{\text{th}}}}\) :

Thickness of thermal boundary layer

\(\Delta P\) :

Pressure drop

bulk:

Bulk

f:

Base fluid

gen:

Total

in:

Inlet

out:

Outlet

nf:

Nanofluid

p:

Nanoparticle

con:

Convergent

str:

Straight

ther:

Thermal

vis:

Viscous

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Authors and Affiliations

  1. Centre for Energy Research and Development, Obafemi Awolowo University, Ife, Nigeria

    Olatomide Gbenga Fadodun & Adebimpe Amos Amosun

  2. Department of Physics, Obafemi Awolowo University, Ife, Nigeria

    David Oluwatosin Olaloye

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  1. Olatomide Gbenga Fadodun
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  2. Adebimpe Amos Amosun
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  3. David Oluwatosin Olaloye
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Correspondence to Olatomide Gbenga Fadodun.

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Fadodun, O.G., Amosun, A.A. & Olaloye, D.O. Numerical modeling of entropy production in Al2O3/H2O nanofluid flowing through a novel Bessel-like converging pipe. Int Nano Lett 11, 159–178 (2021). https://doi.org/10.1007/s40089-021-00333-1

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