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Wärme - und Stoffübertragung

, Volume 22, Issue 3–4, pp 179–183 | Cite as

Transient temperatures from periodic surface heat flux for slabs, cylinders, and spheres

  • D. E. Glass
  • M. N. Özişik
Article

Abstract

The transient temperatures resulting from a periodically varying surface heat flux boundary condition have numerous applications. In this work, explicit, analytic solutions are presented for the transient surface and medium temperatures due to periodically varying step changes in surface heat flux for geometries such as a slab, cylinder, and sphere. The nonlinear case allowing for the added effects of radiation from the surface into an external ambient are studied numerically.

Keywords

Radiation Boundary Condition Heat Flux Apply Physic Surface Heat 
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

f0

reference heat flux

f(ξ)

dimensionless applied surface heat flux=q(t)/f0

ΔFi

dimensionless stepchange in surface heat flux for linear problem

Ji(z)

Bessel function

k

thermal conductivity

L

half thickness of slab, half radius of cylinder and sphere

N

conduction-to-radiation parameter=\(\frac{{{{kT_r } \mathord{\left/ {\vphantom {{kT_r } L}} \right. \kern-\nulldelimiterspace} L}}}{{\sigma T_r^4 }}\)

P

period of on-off surface heat flux

q (t)

applied surface heat flux

t

time

T(x, t)

temperature

Tr

reference temperature=(f0/σ)1/4

U(z)

unit step function

x

physical distance

Greek symbols

α

thermal diffusivity

βm

eigenvalues

ɛ0

surface emissivity

η

dimensionless spacial distance=x/2L

θ (η, ξ)

dimensionless temperature=T/Tr

00

dimensionless initial temperature

λi

dimensionless times at which step changes in surface heat flux occur

ξ

dimensionless time=αt/2 L2

σ

Stefan-Boltzmann constant

φ

fraction of periodP during which the surface heat flux is non-zero

ς (η, ξ)

dimensionless temperature

Temperaturschwankungen aus periodischen Änderungen des Wärmeflusses an der Oberfläche von Platten, Zylindern und Kugeln

Zusammenfassung

Temperaturschwankungen herrührend von periodischen Änderungen des Wärmeflusses an der Oberfläche und der Grenzschichtbedingungen haben zahlreiche Anwendungen. In dieser Arbeit wird eine explizite analytische Lösung für die transienten Temperaturen an der Oberfläche und in der Mitte von Platten, Zylindern und Kugeln angegeben, die durch periodische stufenweise Änderungen des Wärmeflusses an der Oberfläche entstehen. Der nichtlineare Fall mit zusätzlichem Einfluß der Wärmestrahlung in die Umgebung wurde numerisch studiert.

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References

  1. 1.
    Hein, J. C.: Heat conduction in a plane wall subject to periodic temperature changes. Wärme-und Stoffübertrag. 18 (1984) 61–67Google Scholar
  2. 2.
    Putterman, S. J.; Guibert, R.: Enhancement of diffusive transfer by periodic pulsation between dirichlet and Newmann type boundary conditions. Appl. Sci. Res. 40 (1983) 271–277Google Scholar
  3. 3.
    Özişik, N. M.: Heat conduction. New York: Wiley 1980Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • D. E. Glass
    • 1
  • M. N. Özişik
    • 1
  1. 1.Department of Mechanical and Aerospace EngineeringNorth Carolina State UniversityRaleighUSA

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