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Thermodynamic Analysis of \({\hbox {Al}}_{2}\hbox {O}_{3}\)–Water Nanofluid Flow in an Open Cavity Under Pulsating Inlet Condition

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Abstract

This paper is meant to investigate the entropy generation for mixed convective pulsating nanofluid flow in a channel with an open cavity, heated from left side (assisting flow) with uniform temperature distribution. The Navier–Stokes and energy equations are numerically solved by the Finite Volume Method. The effects of parameters such as Reynolds number (Re), volume fraction of solid nanoparticles (\(\varphi \)) and frequency (St) and amplitude (A) of the pulsation on the flow and temperature fields as well as heat transfer and entropy generation rates are examined. Results show that the fluid flow, the temperature distribution, the heat transfer characteristics and the entropy generation are considerably affected by variations of these parameters. The pulsation enhances the heat transfer rates. The maximum enhancement is obtained with an optimum pulsation frequency which depends on the studied case. An enhancement of heat transfer rate with minimum entropy generation is obtained in the range of Strouhal number [0.6,1] for \(Re = 100\); [0.4,1] for \(Re = 200\) and [0.3,1] for \(Re = 300\).

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Abbreviations

A :

Amplitude of pulsation

Be :

Bejan number, \({S}_{gen\, C, m,}/S_{gen,m}\)

\({c}_{p}\) :

Specific heat at constant pressure (J/KgK)

f :

Frequency of pulsation (Hz)

g :

Gravitational acceleration \((\hbox {m/s}^{\mathrm{2}})\)

Gr :

Grashof number, \(g\beta _f \left( {T_H -T_C } \right) H^{3}/\nu _f^2 \)

h :

Heat transfer coefficient \((\hbox {W/m}^{\mathrm{2}}K)\)

H :

Cavity height (m)

k :

Thermal conductivity (W/mK)

l :

Channel length (m)

L :

Cavity length (m)

\(Nu_{s}\) :

Space averaged Nusselt number

\(Nu_{m}\) :

Time-space averaged Nusselt number

p :

Pressure (Pa)

P :

Dimensionless pressure, \(p/\rho _{f}u_0^2\)

Pr :

Prandtl number, \(\nu _f /\alpha _f \)

Re :

Reynolds number, \(\rho _{f\,} u_0 H/\mu _f\)

Ri :

Richardson number, \(g\beta \left( {T_H -T_C } \right) H/u_0^2 \)

\(S_{gen,s}\) :

Space averaged entropy generation

\(S_{gen,m}\) :

Time-spatial averaged entropy generation

St :

Strouhal number, \(fH/u_{0}\)

t :

Time (s)

\(t^{*}\) :

Dimensionless time, \(tu_{0}/H\)

T :

Temperature (K)

\(T_{0}\) :

Temperature of reference (K)

u, v :

Velocity components in x,y direction (m/s)

\(u_{0}\) :

Uniform velocity of the flow at the inlet (m/s)

U, V :

Dimensionless velocity, \(u/u_{0},v/u_{0}\)

w :

Channel height (m)

x, y :

Cartesian coordinates (m)

X, Y :

Dimensionless Cartesian coordinates, x / H, y / H

\(\alpha \) :

Thermal diffusivity \((\hbox {m}^{2}/\hbox {s})\)

\(\beta \) :

Thermal expansion coefficient (K\(^{-1}\))

\(\mu \) :

Dynamic viscosity (Kg/ms)

\(\nu \) :

Kinematic viscosity \((\hbox {m}^{2}/\hbox {s})\)

\(\rho \) :

Density \((\hbox {Kg/m}^{\mathrm{3}})\)

\(\theta \) :

Dimensionless temperature, \((T-T_{C})/(T_{H}-T_{C})\)

\(\varphi \) :

Solid volume fraction

\(\varPsi \) :

Dimensionless stream function

\(\tau \) :

Period of pulsation (s)

\(\chi \) :

Irreversibility factor

C :

Cold

H :

Hot

f :

Pure fluid

m :

Average

min :

Minimum

max :

Maximum

nf :

Nanofluid

s:

Solid, Spatial

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Authors and Affiliations

  1. Laboratoire d’Energétique et des Transferts Thermique et Massique (LETTM), Département de Physique, Faculté des Sciences de Tunis, Université d’el Manar, El Manar, 2092, Tunis, Tunisia

    Zouhaier Mehrez & Afif El Cafsi

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Mehrez, Z., El Cafsi, A. Thermodynamic Analysis of \({\hbox {Al}}_{2}\hbox {O}_{3}\)–Water Nanofluid Flow in an Open Cavity Under Pulsating Inlet Condition. Int. J. Appl. Comput. Math 3 (Suppl 1), 489–510 (2017). https://doi.org/10.1007/s40819-017-0366-9

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