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Heat transfer in laminar flow in circular and flat conduits with (constant) surface resistance

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Summary

Graetz's solution is extended to include surface resistance to heat transfer in laminar flow in circular tubes and flat conduits. The computed eigenvalues, eigenfunctions, coefficients and average mean temperatures for various surface resistances are presented. The solution presented is general and contains Graetz's solution as a particular case of zero boundary resistance.

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Abbreviations

A n :

constant, (6), (24)

a n :

constant, (10)

B n :

constant, (17), (30)

C n :

constant, (18), (31)

C p :

specific heat capacity, volumetric

D :

diameter

D n :

constant, (19), (32)

D H :

hydraulic diameter [4R for duct]

E n :

constant, (21), (35)

F :

function, (12)

Gz :

Graetz number [RePrD H /x]

k :

thermal conductivity

Pr :

Prandtl number

r :

distance from centre (tube or duct)

R :

radius of tube or half-height of duct

Re :

Reynolds number [= D H V m /η]

T :

temperature

V :

velocity

U :

overall heat-transfer coefficient

x :

longitudinal distance from inlet

Y :

eigenfunction, (6), (24)

α :

thermal diffusivity

θ :

dimensionless temperature [(T−T s )/(T in −T s )]

λ :

eigenvalue

ρ :

dimensionless distance from centre

φ :

cylindrical co-ordinate

ξ :

dimensionless parameter

i :

running index [i=0, 1, 2, ...]

in :

inlet

m :

mean (velocity, temperature)

n :

running index (of eigenvalues) [n=1, 2, 3, ...]

s :

external environment

References

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  3. Brown, G. M., Am. Inst. Chem. Eng. J., 6 (1960) 179.

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  4. Graetz, L., Ann. Phys. U. Chem. 18 (1883) 79; 25 (1885) 337.

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  5. Schenk, J. and J. M. Dumore, Appl. sci. Res. A 4 (1953) 39.

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  8. Sideman, S. and R. Peck, “Graphical solutions for heat transfer in one- and two-phase laminar flow”, presented at the 53rd AIChE Meeting, Pittsburgh, May, 1964.

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Author notes

  1. D. Luss

    Present address: Department of Chemical Engineering, University of Minnesota, Minneapolis, Min., USA

Authors and Affiliations

  1. Department of Chemical Engineering, Technion-Israel Institute of Technology, Haifa, Israel

    S. Sideman, D. Luss & R. E. Peck

  2. Department of Chemical Engineering, Illinois Institute of Technology, Chicago, Ill., USA

    R. E. Peck

Authors
  1. S. Sideman
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  2. D. Luss
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  3. R. E. Peck
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Sideman, S., Luss, D. & Peck, R.E. Heat transfer in laminar flow in circular and flat conduits with (constant) surface resistance. Appl. Sci. Res. 14, 157–171 (1965). https://doi.org/10.1007/BF00382240

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  • DOI: https://doi.org/10.1007/BF00382240

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