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Coupled heat and mass transfer in the entrance region of a circular tube with fully-developed parabolic flow and external convective heating

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Abstract

Coupled heat and mass transfer in the entrance region of a circular tube with fully-developed parabolic flow and external heating is analyzed. The closed form solutions of temperature and concentration distributions, local Nusselt numbers based on the total external heat transfer and convective heat transfer inside the tube, as well as the Sherwood number were obtained. The effects of Biot and Lewis number on heat and mass transfer were investigated.

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Abbreviations

a :

Constant in Eq. 7

b :

Constant in Eq. 7

Bi :

Biot number

c p :

Specific heat at constant pressure (J/kg K)

D :

Mass diffusivity (m2/s)

h :

Heat transfer coefficient (W/m2 K)

h sg :

Latent heat of sublimation (J/kg)

k :

Thermal conductivity (W/m K)

L :

Dimensionless latent heat, Eq. 8

Le :

Lewis number

Nu e :

Nusselt number based on the external heat transfer coefficient

Nu i :

Nusselt number based on the convective heat transfer inside the tube

Pe :

Peclet number

Re :

Reynolds number

Sh :

Sherwood number

r :

Radial coordinate (m)

R :

Radius of the tube (m)

T :

Temperature (K)

u :

Fluid velocity (m/s)

u m :

Mean velocity (m/s)

x :

Axial coordinate (m)

X :

Dimensionless axial coordinate

α :

Thermal diffusivity (m2/s)

β :

Eigenvalue

γ :

Eigenvalue

φ :

Dimensionless concentration

η :

Dimensionless radial coordinate

ξ :

Dimensionless axial coordinate

θ :

Dimensionless temperature

ρ :

Density (kg/m3)

ω :

Mass fraction (dimensionless)

0:

Entrance

e:

External

i:

Internal

m:

Mean value control variable

w:

Wall

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO, 65211, USA

    Jian Shi, Chang Li, Yuwen Zhang & Hao Li

Authors
  1. Jian Shi
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  2. Chang Li
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  3. Yuwen Zhang
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  4. Hao Li
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Correspondence to Yuwen Zhang.

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Shi, J., Li, C., Zhang, Y. et al. Coupled heat and mass transfer in the entrance region of a circular tube with fully-developed parabolic flow and external convective heating. Heat Mass Transfer 46, 563–570 (2010). https://doi.org/10.1007/s00231-010-0601-y

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  • DOI: https://doi.org/10.1007/s00231-010-0601-y

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