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Impacts of magnetic field and non-homogeneous nanofluid model on convective heat transfer and entropy generation in a cavity with heated trapezoidal body

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Abstract

A numerical study is made on the entropy generation and magnetohydrodynamics natural convection of \(\hbox {Al}_{2}\hbox {O}_3\)-water non-homogeneous nanofluid inside a square enclosure equipped with a heated trapezoidal body. The Galerkin weighted residual finite element method is applied to solve the dimensionless governing equations within the utilized computational domain along with the algorithm of Newton–Raphson iteration that is used for simplifying the nonlinear terms in the equations. The characteristics of fluid flow fields, temperature distributions and entropy generation are studied for an enormous range of the Rayleigh number \((10^{3}\le Ra \le 10^{6})\), volume fraction of nanoparticles (\(0\le \phi \le 0.04\)), Hartmann number \((0\le Ha \le 50)\), thermal conductivity of the trapezoidal solid body (\(k_{\mathrm{w}}=0.5\), 0.76, 1.95, 7 and 16) and the height of the trapezoidal solid body (\(0.15 \le D \le 0.45\)). It is shown that the streamlines pattern is more sensitive to the increase in the Hartmann number in comparison with the augmentation of the volume fraction of nanoparticles. Also, for a more thermodynamically optimized system, the higher Hartmann number at a higher solid volume fraction of nanofluid is recommended as they show less entropy generation.

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Abbreviations

\(\mathbf{B}\) :

Applied magnetic field

\(\mathbf B\) :

Magnitude of magnetic field

Be :

Bejan number

\(C_{\mathrm{p}}\) :

Specific heat capacity

\(d_{\mathrm{f}}\) :

Diameter of the base fluid molecule

\(d_{\mathrm{p}}\) :

Diameter of the nanoparticle

D :

Dimensionless length of the trapezoidal solid body, \(D=d/L\)

\(D_{\mathrm{B}}\) :

Brownian diffusion coefficient

\(D_{\mathrm{B}0}\) :

Reference Brownian diffusion coefficient

\(D_{\mathrm{T}}\) :

Thermophoretic diffusivity coefficient

\(D_{\mathrm{T}0}\) :

Reference thermophoretic diffusion coefficient

g :

Acceleration of the gravity

GEG:

Dimensionless global entropy generation

H :

Dimensionless width of the trapezoidal solid body, \(H=h/L\)

Ha :

Hartmann number

k :

Thermal conductivity

\(K_{\mathrm{r}}\) :

Square wall to nanofluid thermal conductivity ratio, \(K_{\mathrm{r}}=k_{\mathrm{w}}/k_{\mathrm{nf}}\)

L :

Width and height of enclosure

Le :

Lewis number

\(N_{\mathrm{BT}}\) :

Ratio of Brownian to thermophoretic diffusivity

\(N_{\mu }\) :

Irreversibility distribution ratio

\(\overline{Nu}\) :

Average Nusselt number

Pr :

Prandtl number

\(Re_{\mathrm{B}}\) :

Brownian motion Reynolds number

Sc :

Schmidt number

\(S_{\mathrm{gen}}\) :

Entropy generation rate

\(S_{\mathrm{GEN}}\) :

Dimensionless entropy generation rate

\(S_{\theta }\) :

Dimensionless entropy generation due to heat transfer irreversibility

\(S_{\varPsi }\) :

Dimensionless entropy generation nanofluid friction irreversibility

T :

Temperature

\(T_0\) :

Reference temperature (310 K)

\(T_{\mathrm{fr}}\) :

Freezing point of the base fluid (273.15 K)

\(\mathbf v\), \(\mathbf V\) :

Velocity and dimensionless velocity vector

\(u_{\mathrm{B}}\) :

Brownian velocity of the nanoparticle

x, y and X, Y :

Space coordinates and dimensionless space coordinates

\(\alpha\) :

Thermal diffusivity

\(\gamma\) :

Inclination angle of magnetic field

\(\beta\) :

Thermal expansion coefficient

\(\delta\) :

Normalized temperature parameter

\(\theta\) :

Dimensionless temperature

\(\mu\) :

Dynamic viscosity

\(\nu\) :

Kinematic viscosity

\(\rho\) :

Density

\(\sigma\) :

Electrical conductivity

\(\varphi\) :

Solid volume fraction

\(\varphi ^{*}\) :

Normalized solid volume fraction

\(\phi\) :

Average solid volume fraction

b:

Bottom wall

c:

Cold

f:

Base fluid

h:

Hot

nf:

Nanofluid

p:

Solid nanoparticles

t:

Top wall

w:

Trapezoidal solid wall

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Acknowledgements

The work was supported by the Universiti Kebangsaan Malaysia (UKM) research grant DIP-2017-010.

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Authors and Affiliations

  1. Refrigeration and Air-conditioning Technical Engineering Department, College of Technical Engineering, The Islamic University, Najaf, Iraq

    A. I. Alsabery

  2. School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Bangi, Selangor, Malaysia

    A. I. Alsabery & I. Hashim

  3. School of Engineering, Damghan University, P.O. Box: 3671641167, Damghan, Iran

    R. Mohebbi

  4. Department of Mechanical Engineering, Prince Sultan Endowment for Energy and the Environment, Prince Mohammad Bin Fahd University, Al-Khobar, 31952, Saudi Arabia

    A. J. Chamkha

  5. RAK Research and Innovation Center, American University of Ras Al Khaimah, P.O. Box 10021, Ras Al Khaimah, United Arab Emirates

    A. J. Chamkha

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  1. A. I. Alsabery
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Correspondence to A. I. Alsabery.

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Alsabery, A.I., Mohebbi, R., Chamkha, A.J. et al. Impacts of magnetic field and non-homogeneous nanofluid model on convective heat transfer and entropy generation in a cavity with heated trapezoidal body. J Therm Anal Calorim 138, 1371–1394 (2019). https://doi.org/10.1007/s10973-019-08249-x

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