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Second law analysis of MHD mixed convection heat transfer in a vented irregular cavity filled with Ag–MgO/water hybrid nanofluid

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Abstract

The present paper investigates numerically the effect of an external magnetic field on heat transfer and entropy generation of Ag–MgO (50:50 vol%)/water hybrid nanofluid flow in a partially heated irregular ventilated cavity. A finite-volume FORTRAN code has been written to solve the governing partial differential equations. New empirical correlations specifically dedicated to predict the dynamic viscosity and the thermal conductivity of the considered hybrid nanofluid were employed. After validation of model, the analysis has been done for a wide range of Reynolds number (10 ≼ Re ≼ 600), Hartmann number (0 ≼ Ha ≼ 80) and total nanoparticle volume fraction (0 ≼ φ ≼ 0.02). The results are presented in terms of streamlines, isotherms and isentropic lines as well as the average Nusselt number (Num), the average entropy generation (Sgen,m) and the Bejan number (Beavg). The criterion ξ = Sgen,m/Num is adopted to discuss the thermal performances of the system. The results reveal that the intensification of the magnetic field tends to attenuate the heat transfer convection and to reduce the thickness of the thermal boundary layer, close to the active walls. Globally, adding nanoparticles to the base fluid improves the heat transfer but increases the total entropy generation.

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Abbreviations

B 0 :

Magnetic induction (T)

Be avg :

Average Bejan number

c p :

Specific heat capacity (J kg−1 K−1)

d :

Dimensional length of the heat source (m)

D :

Dimensionless distance of heat source from the entrance e1/W

e 1 :

Distance of heat source from the entrance (m)

e 2 :

Distance of heat source from the right vertical wall (m)

Ec :

Eckert number

g :

Gravitational acceleration (m s−2)

Gr :

Grashof number

h :

Opening width (m)

H :

Height of the cavity (m)

Ha :

Hartmann number

k :

Thermal conductivity (W m−1 K−1)

Nu l :

Local Nusselt number

Nu m :

Average Nusselt number

Nu * :

Normalized Nusselt number

p :

Pressure (Pa)

P :

Dimensionless pressure

Pr :

Prandtl number

Re :

Reynolds number

Ri :

Richardson number

S ′gen :

Dimensional local entropy generation (W K−1 m−3)

S gen :

Dimensionless local entropy generation

S avg,θ :

Dimensionless average entropy generation due to heat transfer

S avg,ψ :

Dimensionless average entropy generation due to fluid friction

S avg, Mag :

Dimensionless average entropy generation due to magnetic field

S * :

Normalized entropy generation

T :

Temperature (K)

u, v :

Velocity components (m s−1)

U 0 :

Velocity of the flow at the inlet (m s−1)

U, V :

Dimensionless velocity components

x, y :

Dimensional Cartesian coordinates (m)

X, Y :

Dimensionless Cartesian coordinates

W :

Width of the cavity (m)

α :

Thermal diffusivity (m2 s−1)

β :

Thermal expansion coefficient (K−1)

ε :

Dimensionless length of the heat source d/W

ξ :

Thermal performance criterion (Sgen,m/Num)

φ :

Nanoparticle volume fraction

μ :

Dynamic viscosity (kg m−1 s−1)

υ :

Kinematic viscosity (m2 s−1)

θ :

Dimensionless temperature

ρ :

Density (kg m−3)

σ :

Fluid electrical conductivity (Ω−1 m−1)

χ :

Irreversibility factor

C:

Cold

H:

Hot

f:

Base fluid

l:

Local

m:

Average

hyb,nf:

Hybrid nanofluid

0:

Reference state

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Authors and Affiliations

  1. Laboratory of Transport Phenomena, Faculty of Mechanical and Process Engineering, USTHB, BP 32, El-Alia Bab-Ezzouar, 16111, Algiers, Algeria

    Mahdi Benzema, Youb Khaled Benkahla, Nabila Labsi & Seif-Eddine Ouyahia

  2. LERMAB, IUT Longwy, Université de Lorraine, 54400, Cosnes et Romain, France

    Mohammed El Ganaoui

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  1. Mahdi Benzema
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  2. Youb Khaled Benkahla
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  3. Nabila Labsi
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  4. Seif-Eddine Ouyahia
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Benzema, M., Benkahla, Y.K., Labsi, N. et al. Second law analysis of MHD mixed convection heat transfer in a vented irregular cavity filled with Ag–MgO/water hybrid nanofluid. J Therm Anal Calorim 137, 1113–1132 (2019). https://doi.org/10.1007/s10973-019-08017-x

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