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Heat and Mass Transfer

, Volume 49, Issue 11, pp 1659–1679 | Cite as

Hydrodynamic and thermal interactions of a cluster of solid particles in a pool of liquid of different Prandtl numbers using two-fluid model

  • Pallab S. Mahapatra
  • Nirmal K. MannaEmail author
  • Koushik Ghosh
Original

Abstract

The knowledge of thermal interaction between hot particles and liquid is essential for many engineering applications. The main focus of the present study is to understand the underlying phenomena of transient interaction between the hot particles and the liquid of varying Prandtl number under different parametric conditions. Analysis is carried out numerically using in-house multiphase code based on Eulerian two-fluid laminar model. The code is validated against existing results. The dispersion and penetration characteristics of the particles are observed to be a strong function of Prandtl number as well as volume fraction and particle diameter, with a stronger mushrooming observed for lower particle size or high Prandtl number liquid. The thermal interaction is observed to be between the particles and the narrow thermal envelope surrounding the particles. The particles cooling rate are observed to be several orders faster in a liquid with lower Prandtl number.

Keywords

Prandtl Number Heat Transfer Rate Particle Temperature Liquid Sodium Thermal Interaction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

C>D

Drag coefficient

C>L

Lift coefficient

d

Particle diameter (m)

g

Gravitational acceleration (m/s2)

Pr

Prandtl Number

P

Pressure (Pa)

Re>D

Reynolds number

t

Time (s)

T

Temperature (K)

T*

Normalized temperature

u>r

Radial velocity (m/s)

u>z

Axial velocity (m/s)

\( \vec{v} \)

Velocity vector (m/s)

V>rel

Relative velocity (m/s)

ρ

Density (kg/m3)

\( \mathop {Q_{pl} }\limits^{.} \)

Heat transfer rate from particles to liquid (kg/s)

μ

Viscosity (kg/m s)

α

Volume fraction

Subscript

amb

Ambient

l

Liquid

li

Liquid initial

p

Particle

pi

Particle initial

Notes

Acknowledgments

Authors gratefully acknowledge several constructive suggestions made by Prof. Achintya Mukhopadhyay (Now on lien to Indian Institute of Technology, Madras) and Prof. Swarnendu Sen of Department of Mechanical Engineering, Jadavpur University. The financial support for this work from Bhabha Atomic Research Centre (BARC), India, and Council of Science and Industrial Research (CSIR), India is gratefully acknowledged. The authors also acknowledge the encouragement and suggestions of Deb Mukhopadhyay of BARC for carrying out the research.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Pallab S. Mahapatra
    • 1
  • Nirmal K. Manna
    • 1
    Email author
  • Koushik Ghosh
    • 1
  1. 1.Department of Mechanical EngineeringJadavpur UniversityKolkataIndia

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