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Free convection/radiation and entropy generation analyses for nanofluid of inclined square enclosure with uniform magnetic field

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Abstract

This paper studies the generation of entropy and free convective heat transfer of Al2O3/water nanofluid in an inclined enclosure affected by a magnetic field considering radiation effects. There is a circular quadrant at temperature \(T_{\text{h}}\) in the bottom section of the left wall of the enclosure. The right wall of enclosure is kept at a fixed temperature \(T_{\text{c}}\). The other walls are insulated. The governing equations for fluid flow are resolved using the algorithm of SIMPLE. The effect of variations of Rayleigh number (Ra), Hartmann number (Ha), the enclosure angle and concentration of nanoparticles (\(\varphi\)) on the flow field, isothermal field, entropy field, Nusselt number (Nu), Bejan number (Be) and total generation of entropy is investigated. The results indicate that the Nu enhances by 160% and 40% by augmenting the Ra and decreasing the Ha, respectively. Be diminishes by enhancing the Ra and reducing the Ha. The maximum generation of entropy intensifies by 288% and 39% by augmenting the Ra and reducing the Ha, respectively. The highest average Nusselt umber (\({\text{Nu}}_{\text{M}}\)) and an overall generation of entropy occur at the inclination angle of 30°.

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Abbreviations

AR:

Aspect ratio

\(B_{0}\) :

MF strength

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

Specific heat \(({\text{J}}\;{\text{kg}}^{ - 1} \;{\text{K}}^{ - 1} )\)

G :

Gravity \(({\text{m}}\;{\text{s}}^{ - 2} )\)

H :

Height of enclosure (m)

\({\text{Ha}}\) :

Hartmann number (dimensionless)

K :

Thermal conductivity \(({\text{W}}\;{\text{m}}^{ - 1} \;{\text{K}}^{ - 1} )\)

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

Nusselt number (dimensionless)

\(P\) :

Pressure \(({\text{kg}}\;{\text{s}}^{ - 2} \;{\text{m}}^{ - 1} )\)

\({ \Pr }\) :

Prandtl number (dimensionless)

R :

Fin width (m)

\({\text{Ra}}\) :

Rayleigh number (dimensionless)

S :

Entropy (W K−1)

\(T\) :

Temperature (K)

\(u\) :

X-component of velocity \(({\text{m}}\;{\text{s}}^{ - 1} )\)

\(v\) :

Y-component of velocity \(({\text{m}}\;{\text{s}}^{ - 1} )\)

\(x,y\) :

Cartesian coordinates \(({\text{m}})\)

Γ :

Angle of cavity (°)

\(\sigma\) :

The electrical conductivity \((\Omega \;{\text{m}})\)

\(\varphi\) :

Solid volume fraction (dimensionless)

\(\alpha\) :

Thermal diffusivity \(({\text{m}}^{2} \;{\text{s}}^{ - 1} )\)

\(\rho\) :

Density \(({\text{kg}}\;{\text{m}}^{ - 3} )\)

\(\mu\) :

Dynamic viscosity \(({\text{kg}}\;{\text{m}}^{ - 1} \;{\text{s}}^{ - 1} )\)

\(\varPsi\) :

Stream function value \(({\text{m}}^{2} \;{\text{s}}^{ - 1} )\)

Λ :

Convection heat transfer coefficient \(({\text{W}}\;{\text{m}}^{ - 2} \;{\text{K}}^{ - 1} )\)

c:

Cold

f:

Fluid (water)

h:

Hot

m:

Average

nf:

NF

p:

Nanoparticle

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Number 51979215).

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Authors and Affiliations

  1. Hubei Key Laboratory of Inland Shipping Technology, Wuhan University of Technology, 588 Youyi Avenue, Wuhan, China

    Yuanzhou Zheng

  2. School of Navigation, Wuhan University of Technology, 588 Youyi Avenue, Wuhan, China

    Yuanzhou Zheng

  3. Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

    Somaye Yaghoubi, Saeed Aghakhani & Arash Karimipour

  4. Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran

    Amin Dezfulizadeh

  5. Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Iskander Tlili

  6. Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Iskander Tlili

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  1. Yuanzhou Zheng
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  2. Somaye Yaghoubi
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Zheng, Y., Yaghoubi, S., Dezfulizadeh, A. et al. Free convection/radiation and entropy generation analyses for nanofluid of inclined square enclosure with uniform magnetic field. J Therm Anal Calorim 141, 635–648 (2020). https://doi.org/10.1007/s10973-020-09497-y

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