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MHD natural convection and thermal radiation of diamond–water nanofluid around rotating elliptical baffle inside inclined trapezoidal cavity

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Abstract

In this work, we study the natural convection and thermal radiation heat transfer of diamond–water nanofluid around rotating elliptical baffle inside inclined trapezoidal cavity under Lorentz forces effect in the presence of uniform heat generation/absorption. The trapezoidal cavity lateral walls are uniformly cooled, and the top and bottom walls are kept adiabatic. The interior rotating elliptical baffle is uniformly heated. Our numerical study is realized by the software Comsol Multiphysics based on the on the finite element method. The results extracted show that an increment on the convection heat transfer is reached by increasing Rayleigh number, the radiation parameter and the elliptical baffle horizontal radius; however, the increment of Hartmann number reduces it. The effect of cavity inclination on the convection heat transfer depends on the baffle position. The presence of uniform heat generation increases the temperature field inside cavity and improves the convection flow, but the presence of uniform heat absorption reduces it. Using nanoparticles with higher shape factor improves more the convection heat transfer.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: Data available on request from the authors.]

Change history

Abbreviations

\( B_{0} \) :

Magnetic field strength (T)

Cp:

Specific heat (J kg K−1)

g :

Gravitational acceleration (\( {\text{m}}\,{\text{s}}^{ - 2} \))

Ha:

Hartmann number, \( B_{0} L\sqrt {\sigma_{\rm f} {/}\rho_{\rm f} \nu_{\rm f} } \)

L :

Length of cavity (m)

m :

Particle shape factor

\( {\text{Nu}}_{\rm l} \) :

Local Nusselt number

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

Average Nusselt number

p :

Fluid pressure (N m−2)

p* :

Dimensionless pressure, \( p H^{2} \)/\( \rho_{\rm f} \alpha_{\rm f}^{2} \)

Pr:

Prandtl number, \( \vartheta_{\rm f} \)/\( \alpha_{\rm f} \)

\( Q_{0} \) :

Heat generation or absorption

q*:

Dimensionless heat generation or absorption

R :

Horizontal elliptical baffle radius

r :

Vertical elliptical baffle radius

Ra:

Rayleigh number, g \( \beta_{\rm f} H^{3} \left( {T_{\rm h} - T_{\rm c} } \right) \)/\( \vartheta_{\rm f} \alpha_{\rm f} \)

\( R_{d} \) :

Radiation parameter

T :

Temperature (\( {\text{K}} \))

T* :

Dimensionless temperature, (T − \( T_{\rm c} \))/(\( T_{\rm h} - T_{\rm c} \))

u, v :

Velocity components in x and y directions, (m \( {\text{s}}^{ - 1} \))

u*, v*:

Dimensionless velocity components

x, y :

Cartesian coordinates (m)

x*, y*:

Dimensionless coordinates

\( \alpha \) :

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

σ:

Electrical conductivity (\( {\text{Am}}\,{\text{V}}^{ - 1} \))

\( \varphi \) :

Solid volume fraction of nanoparticles

ρ :

Local density (kg m−3)

ν :

Cinematic viscosity (m2 s1)

\( \Delta T \) :

Temperature difference, \( T_{\rm h} - T_{c } , \left( {\text{K}} \right) \)

μ :

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

β :

Thermal expansion coefficient \( \left( {{\text{k}}^{ - 1} } \right) \)

\( \omega \) :

Elliptical baffle position (°)

\( \gamma \) :

Angle of inclination of cavity (°)

c:

Cold wall

nf:

Nanofluid

f:

Fluid

h:

Hot wall

p:

Nanoparticle

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Authors and Affiliations

  1. Chemical Engineering Department, College of Engineering, Ha’il University, Ha’il City, Saudi Arabia

    Mohamed Bechir Ben Hamida

  2. Research Unit of Ionized Backgrounds and Reagents Studies (UEMIR), Preparatory Institute for Engineering Studies of Monastir (IPEIM), University of Monastir, Monastir, Tunisia

    Mohamed Dhia Massoudi & Mohamed Bechir Ben Hamida

  3. Department of Mechanical Engineering, College of Engineering, Al Imam Mohammad Ibn Saud Islamic University, Riyadh, 11432, Saudi Arabia

    Mohamed Dhia Massoudi

  4. Higher School of Sciences and Technology of Hammam Sousse (ESSTHS), Physics Department, University of Sousse, 4011 Lamine Abassi Street, Sousse, Tunisia

    Mohamed Bechir Ben Hamida

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  1. Mohamed Dhia Massoudi
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Correspondence to Mohamed Bechir Ben Hamida.

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The original online version of this article was revised: In the original publication of the article, unfortunately the author Mohamed Bechir Ben Hamida has been linked to affiliation 3 by mistake.

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Massoudi, M.D., Ben Hamida, M.B. MHD natural convection and thermal radiation of diamond–water nanofluid around rotating elliptical baffle inside inclined trapezoidal cavity. Eur. Phys. J. Plus 135, 902 (2020). https://doi.org/10.1140/epjp/s13360-020-00921-8

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