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Applied Scientific Research

, Volume 23, Issue 1, pp 73–94 | Cite as

Laminar heat transfer in the entrance region of ducts

  • F. W. Schmidt
  • B. Zeldin
Article

Abstract

A finite difference technique is used for the evaluation of the rate of heat transfer in the thermal entrance region of ducts with axial conduction. The velocity profile is fully developed and flow in a tube and between parallel plates is studied. Local and average Nusselt numbers and mixing temperatures are presented as a function of the Péclet number. A criterion is also established which proves useful for predicting the conditions under which axial conduction may be ignored.

Keywords

Heat Transfer Velocity Profile Finite Difference Nusselt Number Parallel Plate 
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.

Nomenclature

C

transformation constant

cv

specific heat, constant volume

Dh

hydraulic diameter

h

local convective film coefficient, Eq. (15)

h*

local convective film coefficient, Eq. (16)

hm*

mean convective film coefficient, Eq. (17)

k

thermal conductivity

Nu

local Nusselt number, hDh/k

Nu*

local Nusselt number, h*Dh/k

Num*

mean Nusselt number, hQDh/k

Pe

Péclet number, Dhvm/α

q

rate of heat transfer

r

radial coordinate

ro

tube radius

R

nondimensional radial coordinate, r/ro

S

transformed axial coordinate, Eq. (10)

T

temperature

Te

entrance temperature

Tm

mixing temperature, Eq. (18)

Tw

wall temperature

vz

axial velocity

vm

mean axial velocity

V

nondimensional axial velocity, v z /vm

y

transverse coordinate in parallel plate flow

yo

half width of parallel plate duct

Y

nondimensional transverse coordinate, y/yo

z

axial coordinate

Z

nondimensional axial coordinate, z/ro or z/yo

Z+

nondimensional axial coordinate divided by Peclet number, Z/Pe

α

thermal diffusivity

Θ

nondimensional temperature, (T−Tw)/(TeTw)

\(\bar \Theta\)

mean nondimensional temperature, \(\bar \Theta = 2\smallint _0^1 R\Theta dR\)

Θm

nondimensional mixing temperature, Eq. (22)

ρ

density

i

axial position index

j

radial or transverse position index

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References

  1. [1]
    Sellars, J. R., M. Tribus and J. S. Klein, Trans. ASME 78 (1956) 441.Google Scholar
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    Millsaps, K. and K. Pohlhausen, Math. Rev. 18 (1957) 538.Google Scholar
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    Mercer, A. McD., Appl. Sci. Res. Part A 8 (1959) 357.Google Scholar
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    Mercer, A. McD., Appl. Sci. Res. Part A 9 (1960) 450.Google Scholar
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    Singh, S. N., Appl. Sci. Res. Part A 7 (1958) 325.Google Scholar
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    Agrawal, H. C., Appl. Sci. Res. Part A 9 (1960) 177.Google Scholar
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    Labuntsov, D. A., Sov. Phy. Docklady 3 (1958) 33.Google Scholar
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    Allen, D. N. de G and R. V. Southwell, Quart. Jr. Mech. and Appl. Math. Part 2 8 (1955) 129.Google Scholar

Copyright information

© Martinus Nijhoff Publishers 1970

Authors and Affiliations

  • F. W. Schmidt
    • 1
  • B. Zeldin
    • 1
  1. 1.Mech. Eng. Dept.The Pennsylvania State UniversityUniversity ParkU.S.A.

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