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Transport Phenomena Study of Low-Prandtl-Number Fluid Flow Using Thermal Lattice Boltzmann Technique

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Abstract

The impetus of this paper is to examine the natural convection of low-Prandtl-number fluid flow driven by buoyancy force in a differentially heated enclosure using the single-relaxation-time thermal lattice Boltzmann method owing to the broad range of applications of convective-based problems in industry, such as melting processes as well as energy storage systems. In this study, a proper force term incorporated in the collision operator has been utilized for computer code convergence (especially for Prandtl numbers less than 0.71). The side walls of the geometry are maintained by constant temperatures, Th and Tc, and the upper and lower walls are thermally insulated. The effects of Prandtl (\(0.05\le {\text{Pr}}\le 0.71\)) and Rayleigh numbers (\({10}^{4}\le {\text{Ra}}\le {5\times 10}^{5}\)) on the temperature fields, streamline functions, and average Nusselt number have been studied and found that at a given Prandtl number, the magnitude of vortices at the corner of the enclosure rises while those could disappear by Prandtl number increase. In addition, in the vicinity of hot and cold walls, the isotherms concentration increases due to rising temperature gradient and Prandtl number. The heat transfer coefficient grows with an increase in Ra and Pr numbers, experiencing a dramatic rise of 66.67% at the hot wall for Pr = 0.1. Similarly, the maximum velocity values near the cold wall rose by 185.71%. The suggested scheme has been validated by results shown in the literature, and excellent agreement has been found.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Abbreviations

\(c\) :

Lattice speed (\( \frac{{\text{m}}}{{\text{s}}} \))

\(c\) :

Lattice speed (\( \frac{{\text{m}}}{{\text{s}}} \))

\({{\varvec{c}}}_{i}\) :

Discrete velocity vectors (\( \frac{{\text{m}}}{{\text{s}}} \))

\({c}_{\text{s}}\) :

Speed of sound (\( \frac{{\text{m}}}{{\text{s}}} \))

f :

Density distribution function (\( \frac{{{\text{kg}}}}{{{\text{m}}^{3} }}\))

g :

Thermal distribution function (\( \frac{{{\text{kg}}}}{{{\text{m}}^{3} }}\))

H :

Height of the enclosure (m)

\(L\) :

Length of the enclosure (m)

\({F}_{i}\) :

Discrete body force (\( \frac{{{\text{kg}}}}{{{\text{m}}^{3} {\text{s}}}} \))

g :

Acceleration owing to gravity (\( \frac{{{\text{kg}}}}{{{\text{m}}^{3} {\text{s}}}} \))

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

Nusselt number

\({\text{Pr}}\) :

Prandtl number

Ra:

Rayleigh number

T :

Temperature (K)

\({T}_{\text{h}}\) :

Hot wall temperature (K)

\({T}_{\text{c}}\) :

Cold wall temperature (K)

\({T}_{{\text{ref}}}\) :

Reference temperature (K)

t :

Time (s)

V :

Velocity vector (\( \frac{{\text{m}}}{{\text{s}}} \))

x :

Location (m)

\(\alpha \) :

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

\(\beta \) :

Volume expansion coefficient (1/K)

\(\upsilon \) :

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

\(\delta t\) :

Time step (s)

\(\Delta T\) :

Temperature difference between the hot and cold side walls (K)

\(\delta x\) :

Step by step (m)

\(\rho \) :

Density (\( \frac{{{\text{kg}}}}{{{\text{m}}^{3} }} \))

\({\tau }_{\alpha }\) :

Thermal Relaxation time

\({\tau }_{\nu }\) :

Relaxation time related to fluid viscosity

\({\omega }_{i}\) :

Weight factors

c:

Cold

eq:

Equilibrium

h:

Hot

i:

Direction in a discrete lattice

l:

Left

r:

Right

ref:

Reference

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  1. Department of Mechanical Engineering, Faculty of Engineering and Information Technology, University of Melbourne, Parkville, VIC, 3010, Australia

    Ehsan Kamali Ahangar

  2. Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    Ehsan Kamali Ahangar

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EKA contributed to conceptualization, methodology, software, validation, formal analysis, investigation, resources, data curation, writing—original draft, writing—review & editing, visualization, supervision, project administration.

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Correspondence to Ehsan Kamali Ahangar.

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Ahangar, E.K. Transport Phenomena Study of Low-Prandtl-Number Fluid Flow Using Thermal Lattice Boltzmann Technique. Arab J Sci Eng (2024). https://doi.org/10.1007/s13369-024-08786-0

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