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Numerical study on mixed convection of a non-Newtonian nanofluid with porous media in a two lid-driven square cavity

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Abstract

In the present numerical study, mixed flow of the non-Newtonian water/Al2O3 nanofluid with 0–4% nanoparticles volume fractions (φ) inside a two-dimensional square cavity with hot and cold lid-driven motion and porous media is simulated at Richardson numbers (Ri) of 0.01, 10 and 100 and Darcy numbers (Da) of 10−4 ≤ Da ≤ 10−2 using Fortran computer code. The obtained results for temperature domain, velocity, Nusselt number and streamlines indicate that by increasing Richardson number and decreasing axial velocity parameter of walls and similarity of flow behavior to natural flow mechanism, variations of velocity are reduced, which is due to the reduction in fluid momentum. By increasing Darcy number, penetrability of fluid motion enhances and fluid lightly moves along the cavity. Figuration of streamlines at lower Richardson numbers highly depends on the Darcy number changes. In case (2), due to the counterflow motion and buoyancy force, distinction of flow domain profiles is more obvious. On the other hand, this issue causes more velocity gradients and vortexes in special sections of cavity (central regions of cavity). In case (2), the behavior of streamlines is affected by some parameters such as variations of Darcy number, nanoparticles volume fraction and Richardson number more than case (1). By increasing Darcy number, flow lightly passes among hot and cold sources and leads to improve the heat transfer. Moreover, reduction in flow penetrability in cavity results in the reduction in fluid flow in its direction, sectional distribution and regions with higher temperature. Consequently, in these regions the growth of thermal boundary layer is more significant. In case (2), at lower Richardson numbers compared to higher ones, the affectability of lid-driven motion contrary to buoyancy force caused by density variations is less because of higher fluid momentum. At Ri = 0.01, because of the strength of lid-driven motion, flow direction is compatible with lid-driven motion. Also, temperature distribution is not uniform, and in these regions, fluid has the minimum velocity which leads to the enhancement of dimensionless temperature. In both studied cases, the increment of nanoparticles volume fraction as well as Darcy number and reduction in Richardson number result in the improvement of temperature distribution and decrease in dimensionless temperature.

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Abbreviations

C p :

Specific heat (J kg−1 K−1)

Da :

Darcy number

g :

Gravitational acceleration (m s−2)

Gr :

Grashof number

h :

Heat transfer coefficient (W m−2 K−1)

H :

Enclosure length (m)

k :

Thermal conductivity (W m−1 K−1)

K :

Permeability

Nu :

Nusselt number

P :

Dimensionless pressure

p :

Pressure (N m−2)

Pr :

Prandtl number

Re :

Reynolds number

Ri :

Richardson number

T :

Temperature (K)

u, v :

Velocity components (m s−1)

U, V :

Dimensionless velocity components

V b :

Wall velocity (m s−1)

x, y :

Cartesian coordinates (m)

X, Y :

Dimensionless Cartesian coordinates

ρ :

Density (kg m−3)

θ :

Dimensionless temperature

μ :

Dynamic viscosity (kg m s−1)

α :

Thermal diffusivity (m−2 s)

β :

Thermal expansion coefficient (1 K−1)

ν :

Kinematic viscosity (m2 s−1)

φ :

Volume fraction of nanoparticles

app:

Apparent

avg:

Average

C:

Cold

eff:

Effective

f:

Fluid

H:

Hot

nf:

Nanofluid

s:

Nanoparticle

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Authors and Affiliations

  1. Department of Mechanical Engineering, Razi University, Kermanshah, Iran

    Saeed Nazari

  2. Department of Mathematics & Statistics, FBAS, IIUI, Islamabad, Pakistan

    R. Ellahi

  3. Center for Modeling & Computer Simulation, Research Institute, King Fahd University of Petroleum & Minerals, Dhahran, 31261, Saudi Arabia

    R. Ellahi

  4. School of Mechanical Engineering, The University of Adelaide, Adelaide, South Australia, Australia

    M. M. Sarafraz

  5. Division of Computational Physics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Mohammad Reza Safaei

  6. Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Mohammad Reza Safaei

  7. Department of Mechanical Engineering, Faculty of Engineering, Bu Ali Sina University, Hamedan, Hamedan, Iran

    Ali Asgari

  8. Young Researchers and Elite Club, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran

    Omid Ali Akbari

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  1. Saeed Nazari
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  2. R. Ellahi
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  3. M. M. Sarafraz
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  4. Mohammad Reza Safaei
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Correspondence to Mohammad Reza Safaei.

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Nazari, S., Ellahi, R., Sarafraz, M.M. et al. Numerical study on mixed convection of a non-Newtonian nanofluid with porous media in a two lid-driven square cavity. J Therm Anal Calorim 140, 1121–1145 (2020). https://doi.org/10.1007/s10973-019-08841-1

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