Wärme - und Stoffübertragung

, Volume 28, Issue 4, pp 169–176 | Cite as

An analysis of the effect of the solid layer for the modified chemical vapor deposition process

  • Y. T. Lin
  • M. Choi
  • R. Greif
Article

Abstract

The heat transfer problem relative to the modified chemical vapor deposition process has been analyzed and the effects of solid layer thickness, torch speed and tube rotation are studied. The quasi-steady three-dimensional energy equations have been solved for the temperature fields in the gas and the solid layer with a Gaussian heat flux boundary condition on the outer surface. Of particular interest is the effect of the solid layer thickness and the torch speed on inner surface temperature, gas temperature and thermophoretic velocity. The large change of the axial temperature distribution of the surface occurs for different solid layer thicknesses or torch speeds. The presence of the solid layer and tube rotation reduce the effects of nonuniform torch heating in the circumferential direction and the resulting surface temperatures are very uniform in this direction.

Nomenclature

A (\(\tilde r\))

polynomial in Eq. (7)

Aj

coefficients ofA(\(\tilde r\)) in Eq. (7)

C1,2

coefficients in Eq. (11)

h

heat transfer coefficient

H

dimensionless temperature =\(\frac{{T - T_\infty }}{{T_\infty }}\)

Hj

coefficients in Eq. (8)

i

√−1

Jn

Bessel functions of first kind of ordern

k

thermal conductivity

K

thermophoretic coefficient

n

Fourier Mode

Pe

Peclet number,VavR0 /α

qwall

applied heat flux on the outer surface

qmax

maximum value of the applied heat flux,qwall

Q

gas flow rate

r

radial coordinate

Ri

inner tube radius

R0

outer tube radius

\(\hat r\)

dimensionless variable defined in Eq. (10)

t

time

T

temperature

Trxn

reaction temperature

Vtorch

torch speed

Vav

average velocity of gas in the axial direction

(VT)r

thermophoretic velocity in the radial direction

x

axial coordinate

Yn

Bessel functions of second kind of ordern

z

complex transformed coordinate

Greek letter

α

thermal diffusivity

β

exponent in Eq. (8) (=n)

Γ

rotation parameter,R0Ω /Vav

θ

angle

ϱ

density

λ1

parameter in torch heating distribution (axial)

λ2

parameter in torch heating distribution (circumferential)

ν

kinematic viscosity

ζ

moving coordinate,xVtorcht

Ω

angular velocity of tube

Subscripts

g

gas

imag

imaginary part

ambient

real

real part

s

solid layer

Superscripts

dimensionless

=

double transformation

-

transformed, after Fourier inversion

Untersuchung des Einflusses der Feststoffschicht auf den modifizierten chemischen Aufdampfprozeß

Zusammenfassung

Es wurde das Wärmeübergangsproblem beim modifizierten chemischen Aufdampfprozeß untersucht, und zwar im Hinblick auf die Einflüsse bezüglich Feststoffdichtdicke, Brennergeschwindigkeit und Rohrrotation. Die Lösung der quasistationären dreidimensionalen Energiegleichungen für die Temperaturfelder im Gas und in der Feststoffschicht erfolgte unter Ausprägung einer Gaußschen Wärmefluß-Randbedingung am Außenumfang. Von besonderem Interesse ist der Einfluß der Feststoffschichtdicke und der Brennergeschwindigkeit auf die Temperaturverteilung am Innenumfang, die Gastemperatur und die Thermophoresegeschwindigkeit. Starke Änderungen der achsialen Temperaturverteilung am Innenumfang resultieren sowohl aus verschiedenen Feststoffschichtdicken wie Brennergeschwindigkeiten. Zunehmende Schichtdicke und Rohrrotation reduzieren den Einfluß ungleichförmiger Aufheizung durch den Brenner in Umfangrichtung und bewirken dort eine sehr gleichförmige Oberflächentemperatur.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Y. T. Lin
    • 1
  • M. Choi
    • 2
  • R. Greif
    • 3
  1. 1.Yvan-Ze Institute of TechnologyChung-LiTaiwan
  2. 2.Seoul National UniversitySeoulSouth Korea
  3. 3.Department of Mechanical EngineeringUniversity of California at BerkeleyBerkeleyUSA

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