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Laminar flow heat transfer in the entrance region of circular tubes

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Summary

The asymptotic solution of laminar convective heat transfer in the entrance region of a circular conduit where velocity and temperature profiles are developing simultaneously, is obtained for fluids with high Prandtl numbers. Numerical values of local and average Nusselt numbers as functions of Pr and dimensionless longitudinal distances have been evaluated and presented in graphical forms.

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Abbreviations

A 0, A 1 ... A k :

coefficients defined by (40)

B 0, B 1 ... B k :

coefficients defined by (39)

C p :

heat capacity of fluid

I n (x) = i −n J n (ix):

where J n is the n th order Bessel function

k :

thermal conductivity of fluid

Nu z :

local Nusselt number defined by (41)

Nu av :

average Nusselt number defined by (44)

P :

pressure

Pr :

Prandtl number of fluid defined as C p μ/k

q :

heat flux

Re :

Reynold number, defined as ŪPR/μ

R :

radius of pipe

r :

radial distance

r + :

dimensionless radial distance defined by (8)

T :

temperature of fluid

T 0 :

initial temperature of fluid

T w :

wall temperature

T + :

dimensionless temperature defined by (11)

T +0 , T +1 , ... T /+ k ...:

functions related to T + by (22).

u :

dimensionless variables defined by (20)

v r :

radial component of velocity

v z :

z-component of velocity

v + :

dimensionless velocity defined by (10)

y + :

dimensionless distance defined by (8)

X :

dimensionless parameter defined by (38)

z :

longitudinal distance

z + :

dimensionless longitudinal distance defined by (9)

α :

thermal diffusivity

β :

dimensionless parameter defined by (12)

γ :

a parameter appearing in (46)

Γ(x):

gamma function

ρ :

density

η :

dimensionless variable defined by (28)

θ :

parameter defined by (19)

ζ :

dimensionless variable defined by (32)

μ :

viscosity of fluid

ν :

kinematic viscosity of fluid

References

  1. Kays, W. M., Trans. A.S.M.E. 77 (1955) 1265.

    Google Scholar 

  2. Langhaar, H. L., J. Appl. Mech. 64 (1942) A-55.

    Google Scholar 

  3. Goldberg, P., M.S. Thesis, Mech. Eng. Dept., M.I.T., 1958. Also see Rosenhow, W. M. and H. Y. Choi, Heat Mass and Momentum Transfer, P. 165, Prentice-Hall Inc., 1961.

  4. Sparrow, E. M., N.A.C.A., TN 3331, 1955.

  5. Yau, J. and C. Tien, Can. J. Chem. Eng. 41 (1963) 139.

    Google Scholar 

  6. Acrivos, A., Phys. Fluids 3 (1960) 657.

    Google Scholar 

  7. Acrivos, A., Chem. Eng. Sci. 17 (1962) 457.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Chemical Engineering, Essex College, Assumption University of Windsor, Windsor, Ontario, Canada

    Chi Tien & Richard A. Pawelek

  2. Department of Chemical Engineering and Metallurgy, Syracuse University Syracuse, New York, USA

    Chi Tien

  3. Dominion Rubber Compagny, Montreal, Quebec, Canada

    Richard A. Pawelek

Authors
  1. Chi Tien
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  2. Richard A. Pawelek
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Tien, C., Pawelek, R.A. Laminar flow heat transfer in the entrance region of circular tubes. Appl. sci. Res. 13, 317–331 (1964). https://doi.org/10.1007/BF00382058

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  • DOI: https://doi.org/10.1007/BF00382058

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