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Numerical Analysis of Mixed Convection Coupled with Thermal Radiation in a Ventilated Channel Containing Various Heat-Generating Blocks

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Advances in Applied Mechanics (JET 2022)

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

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Abstract

In this study, thermal radiation and mixed convection in a ventilated horizontal channel are analyzed. The channel contains five cylindrical blocks that produce different volumetric heat rates. The channel is ventilated by two openings; the inlet is located on the left wall, and the outflow is on the top one. All the channel walls are adiabatic, except for the upper wall, which is held at a constant low temperature of TC = 20 ℃. To numerically solve the differential equations governing the current problem, a numerical code based on the finite volume approach and the SIMPLE algorithm is utilized. The discrete ordinate method is used to discretize the radiative transfer equation. The impacts of the Reynolds number and the emissivity of the surfaces on the heat transfer and fluid flow are analyzed. The numerical simulations indicate that increasing the Reynolds number or the emissivity considerably decreases the maximum temperature in the cavity and improves the performance of the considered system.

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Abbreviations

\(d\):

cylinders diameter, \(\mathrm{m}\)

\(D\):

cylinders diameter \(D= d/H\)

\(g\):

gravitational acceleration, \({\mathrm{ms}}^{-2}\)

\({h}^{*}\):

openings size \({h}^{*}= h/H\)

\(h\):

openings size, \(\mathrm{m}\)

\(H\):

cavity’s height, \(\mathrm{m}\)

\(i\):

radiation intensity, \({\mathrm{Wm}}^{-2}\)

\(I\):

dimensionless intensity

\(k\):

thermal conductivity, \({\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}\)

\(K\):

conductivity ratio \(K = {k}_{S}/{k}_{f}\)

\(L\):

cavity’s length, \(\mathrm{m}\)

\(\mathrm{Nu}\):

Nusselt number

\(\mathrm{Pr}\):

Prandtl number

Pl:

Planck number

\(P\):

dimensionless pressure

\(Q\):

internal heat generation, \({\mathrm{Wm}}^{-3}\)

\(\mathrm{Ri}\):

Richardson number

\(\mathrm{Re}\):

Reynolds number

\(\mathrm{Ra}\):

Rayleigh number

\({T}_{R}\):

temperature ratio

\(T\):

dimensional temperature, \(^\circ \mathrm{C}\)

\(t\):

time, \(\mathrm{s}\)

\(U\), \(V\):

velocity components

\(X\), \(Y\):

Cartesian coordinates

\(\sigma \):

Stefan-Boltzmann constant, \({\mathrm{Wm}}^{-2}{\mathrm{K}}^{-4}\)

\(\alpha \):

thermal diffusivity, \({\mathrm{m}}^{2}{\mathrm{s}}^{-1}\)

\(\beta \):

thermal expansion coefficient, \({\mathrm{K}}^{-1}\)

\(\varepsilon \):

emissivity of radiative surface

\(\omega \):

scattering albedo

\(\phi \):

phase function

\(\theta \):

dimensionless temperature

\(\upsilon \):

kinematic viscosity, \({\mathrm{m}}^{2}{\mathrm{s}}^{-1}\)

\(\Omega \):

solid angle, \(\mathrm{sr}\)

\(\lambda \):

heat generation parameter

\(\rho \):

density, \({\mathrm{kgm}}^{-3}\)

\(\tau \):

dimensionless time

\(\mu \), \(\eta \):

direction cosines

\({\tau }^{*}\):

optical thickness

\(\psi \):

dimensionless stream function

\(\mathrm{C}\):

convective term, cell, or cold wall

\(\mathrm{f}\):

fluid

\(\mathrm{i}\):

block index

in:

inlet

\(\mathrm{LR}\):

local radiative

\(\mathrm{LC}\):

local convective

\(\mathrm{max}\):

maximum

\(\mathrm{R}\):

radiative

\(\mathrm{s}\):

solid (blocks)

\(\mathrm{T}\):

total

B:

block

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Author information

Authors and Affiliations

  1. LMFE, Department of Physics, Faculty of Sciences Semlalia, Cadi Ayyad University, B.P. 2390, Marrakesh, Morocco

    Rachid Hidki, Lahcen El Moutaouakil, Mohammed Boukendil, Zouhair Charqui, Zaki Zrikem & Abdelhalim Abdelbaki

Authors
  1. Rachid Hidki
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  2. Lahcen El Moutaouakil
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  3. Mohammed Boukendil
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  4. Zouhair Charqui
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  5. Zaki Zrikem
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  6. Abdelhalim Abdelbaki
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Corresponding author

Correspondence to Mohammed Boukendil .

Editor information

Editors and Affiliations

  1. Ecole Nationale d’Ingénieurs de Metz, LEM3, University of Lorraine, Metz, France

    Zitouni Azari

  2. Higher Institute for Maritime Studies, Casablanca, Morocco

    Khalid El Had

  3. Mohammadia School of Engineers, Mohammed V University in Rabat, Rabat, Morocco

    Mohamed ElAmine Ait Ali

  4. Acoustics Laboratory (LAUM), Université du Maine, Le Mans, France

    Aberrahim El Mahi

  5. Sfax, Tunisia

    Fakher Chaari

  6. Sfax, Tunisia

    Mohamed Haddar

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Hidki, R., El Moutaouakil, L., Boukendil, M., Charqui, Z., Zrikem, Z., Abdelbaki, A. (2024). Numerical Analysis of Mixed Convection Coupled with Thermal Radiation in a Ventilated Channel Containing Various Heat-Generating Blocks. In: Azari, Z., El Had, K., Ait Ali, M.E., El Mahi, A., Chaari, F., Haddar, M. (eds) Advances in Applied Mechanics. JET 2022. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-49727-8_8

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  • DOI: https://doi.org/10.1007/978-3-031-49727-8_8

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