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Effect of the second outlet location and the applied magnetic field within a ventilated cubic cavity crossed by a nanofluid on mixed convection mode: best configurations

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Abstract

The present numerical study consists of a mixed convection heat transfer, taking place within a ventilated cubic cavity crossed by an alumina–water nanofluid. The ventilation is assured by three openings, practiced on the walls of the cavity. So, the cold nanofluid enters by an opening placed at the top of the left vertical wall and exits by two opening: one is placed at the bottom of the right vertical wall, and the second opening occupied several possibility of location along the four walls of the cavity. All the enclosure’s walls are maintained at a same temperature, higher than that of the entering fluid, except of the side walls which are adiabatic. The governing equations are discretized using the finite volume method and the SIMPLER algorithm to treat the coupling velocity–pressure. The method line by line is used to solve iteratively the algebraic equations. The simulations were carried for different values of the Richardson number (0 ≼ Ri ≼ 10), the Hartmann number (0 ≼ Ha ≼ 100) and a solid volume fractions φ = 4% using Koo–Kleinstreuer–Lee model for the evaluation of effective thermal conductivity and dynamic viscosity of nanofluid. The results are presented in the form of streamlines, isotherms, velocity vectors and average Nusselt number.

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Abbreviations

B 0 :

External magnetic field (T)

Cp:

Constant pressure specific heat (\( {\text{J}}\,{\text{kg}}^{ - 1} \,{\text{K}}^{ - 1} \))

F :

Lorentz force (\( {\text{N}}\,{\text{m}}^{ - 3} \))

G :

Gravitational acceleration (\( {\text{ms}}^{ - 2} \))

H :

Height of cavity (m)

Ha:

Hartman number

K :

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

L :

Length of the cavity (m)

Nu:

Nusselt number

P :

Pressure (Pa)

P :

Dimensionless pressure

Pr:

Prandtl number

Re:

Reynolds number

Ri:

Richardson number

S :

Coordinate adopted for distance along the walls (m)

S :

Dimensionless coordinate, \( S\, = \,s\,H^{ - 1} \)

T :

Temperature (K)

x, y, z :

Cartesian coordinates (m)

X, Y, Z :

Dimensionless Cartesian coordinates

u, v, w :

Velocity components in the x-direction, y-direction and z-direction (ms−1)

U, V, W :

Dimensionless velocity components

Α :

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

β :

Thermal expansion coefficient (\( {\text{K}}^{ - 1} \))

Ρ :

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

Ν :

Kinematic viscosity (\( {\text{m}}^{2} {\text{s}}^{ - 1} \))

µ :

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

θ :

Dimensionless temperature

φ :

Particle volume fraction

σ :

Electrical conductivity (\( \Omega ^{ - 1} \,{\text{m}}^{ - 1} \))

Avg:

Average

Bf:

Base fluid

Nf:

Nanofluid

S:

Solid particles

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Authors and Affiliations

  1. Laboratory of Transport Phenomena, USTHB, BP. 32 El Alia, 16111, Bab Ezzouar, Algiers, Algeria

    Seddik Kherroubi, Karim Ragui, Abdelghani Bensaci, Nabila Labsi, Abdelkader Boutra & Youb Khaled Benkahla

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  1. Seddik Kherroubi
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  2. Karim Ragui
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  6. Youb Khaled Benkahla
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Correspondence to Seddik Kherroubi.

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Kherroubi, S., Ragui, K., Bensaci, A. et al. Effect of the second outlet location and the applied magnetic field within a ventilated cubic cavity crossed by a nanofluid on mixed convection mode: best configurations. J Therm Anal Calorim 139, 2243–2264 (2020). https://doi.org/10.1007/s10973-019-08638-2

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