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Heat transfer in two-phase laminar flow for timewise linear variation of inlet temperature in a circular pipe

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Acta Physica Academiae Scientiarum Hungaricae

Abstract

Exact solutions of the forced convection energy equations of dust particles and of liquid with fully developed flow in a circular pipe are obtained in the present problem when the inlet temperatures vary linearly with time and an interpretation of the case of laminar flows is given.

The meaning of any other symbols is given in the text as they occur.

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Abbreviations

\(\bar T\) :

temperature of dust particle

\(\bar T\) :

temperature of liquid

c p :

specific heat of dust particle

c :

specific heat of liquid

a :

pipe radius

K p :

thermal conductivity of dust particle

K :

thermal conductivity of liquid

\(\bar t\) :

time

u p :

velocity component of dust particle in\(\bar z - direction\)

u :

velocity component of liquid in\(\bar z - direction\)

ū:

average velocity

\(\bar r,\bar \Phi ,\bar z\) :

cylindrical polar coordinates (\(\bar z - flow\) direction)

ϱ:

liquid density

mN :

mass of dust particle per unit volume (=mN 0, constant)

μ:

coefficient of viscosity of liquid

ν:

kinematic coefficient of viscosity of liquid

P :

Prandtl number (=μc/K)

R :

Reynolds number (=aū/ν)

h p :

heat transfer coefficient for flow over dust particle

A p :

surface area of dust particle

V p :

volume of dust particle

T 0,T 1,T 2 :

known temperature constants

References

  1. L. Farbar andM. J. Morley, Ind. Eng. Chem.,49, 1143, 1957.

    Article  Google Scholar 

  2. D. C. Schluderberg, The Application of Gas-Ceramic Mixtures to Nuclear Power, Rept. No. CF 55-8-199 ORSORT, AEC, 1955.

  3. H. A. Johnson, Trans. ASME,77, 1257, 1955.

    Google Scholar 

  4. J. J. Salomone andM. Newmann, Ind. Eng. Chem.,47, 283, 1955.

    Article  Google Scholar 

  5. C. L. Tien, Transport Processes in Two-Phase Turbulent Flow, Ph. D. thesis, Princeton University, USA, 1959.

    Google Scholar 

  6. C. L. Tien, Trans. ASME,83 b, 183, 1961.

    Google Scholar 

  7. S. L. Soo, Fluid Dynamics of Multiphase Systems, Blaisdell Publishing Co., London, 1967.

    MATH  Google Scholar 

  8. S. N. Dube andC. L. Sharma, Acta Phys. Hung.,41, 95, 1976.

    Article  Google Scholar 

  9. P. J. Schneider, Trans. ASME,79, 765, 1957.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Himachal Pradesh University, 171005, Simla, India

    S. N. Dube

Authors
  1. S. N. Dube
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Dube, S.N. Heat transfer in two-phase laminar flow for timewise linear variation of inlet temperature in a circular pipe. Acta Physica 43, 163–171 (1977). https://doi.org/10.1007/BF03158286

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  • DOI: https://doi.org/10.1007/BF03158286

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