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Laminar heat transfer in the entrance region of ducts

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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.

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Abbreviations

C :

transformation constant

c v :

specific heat, constant volume

D h :

hydraulic diameter

h :

local convective film coefficient, Eq. (15)

h*:

local convective film coefficient, Eq. (16)

h *m :

mean convective film coefficient, Eq. (17)

k :

thermal conductivity

Nu :

local Nusselt number, hD h/k

Nu*:

local Nusselt number, h*D h/k

Nu *m :

mean Nusselt number, hQD h/k

Pe :

Péclet number, D h v m/α

q :

rate of heat transfer

r :

radial coordinate

r o :

tube radius

R :

nondimensional radial coordinate, r/r o

S :

transformed axial coordinate, Eq. (10)

T :

temperature

T e :

entrance temperature

T m :

mixing temperature, Eq. (18)

T w :

wall temperature

v z :

axial velocity

v m :

mean axial velocity

V :

nondimensional axial velocity, v z /v m

y :

transverse coordinate in parallel plate flow

y o :

half width of parallel plate duct

Y :

nondimensional transverse coordinate, y/y o

z :

axial coordinate

Z :

nondimensional axial coordinate, z/r o or z/y o

Z + :

nondimensional axial coordinate divided by Peclet number, Z/Pe

α :

thermal diffusivity

Θ :

nondimensional temperature, (T−T w)/(T e−T w)

\(\bar \Theta\) :

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

Θ m :

nondimensional mixing temperature, Eq. (22)

ρ :

density

i :

axial position index

j :

radial or transverse position index

References

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Authors and Affiliations

  1. Mech. Eng. Dept., The Pennsylvania State University, University Park, Pennsylvania, U.S.A.

    F. W. Schmidt & B. Zeldin

Authors
  1. F. W. Schmidt
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  2. B. Zeldin
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Schmidt, F.W., Zeldin, B. Laminar heat transfer in the entrance region of ducts. Appl. Sci. Res. 23, 73–94 (1971). https://doi.org/10.1007/BF00413188

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  • DOI: https://doi.org/10.1007/BF00413188

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