Abstract
Laminar flow heat transfer is computed for a situation in which a fluid moves along a parallel plate channel with unequal wall heat fluxes (one wall is insulated). The fluid enters the heating section through an upstream region which is perfectly insulated. This situation serves to describe an upper bound for the commonly encountered case of double pipe heat exchangers with identical thermal conditions. A control volume approach has been employed for the numerical work enabling a fast calculation for the thermally developing regime in the parallel plate channel. The merits of the adopted procedure are assessed by comparison with other results available in the literature for the one-region and for the two-region problem.
Zusammenfassung
Es wird der Wärmetransport bei laminarer Strömung in einem von zwei parallelen Platten gebildeten Kanal berechnet, die ungleiche Wärmeflußdichte abgeben (eine Wand ist isoliert). Das Fluid gelangt in den beheizten Abschnitt über einen stromaufwärts gelegenen Bereich, der vollkommen isoliert ist. Diese Konfiguration dient als obere einhüllende, für den häufig vorkommenden Fall eines Doppelrohr-Wärmeaustauschers mit identischen thermischen Bedingungen.
Es wurde ein Kontrollvolumen für die numerische Bearbeitung eingeführt, das eine schnelle Berechnung der Entwicklung der thermischen Zustandsgrößen in dem Kanal zwischen den parallelen Platten erlaubt. Die Vorteile der hier angewandten Prozedur zeigen sich bei einem Vergleich mit anderen, in der Literatur vorhandenen Ergebnissen für Einbereichs- und Zweibereichs-Probleme.
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Abbreviations
- c p :
-
specific heat
- D h :
-
hydraulic diameter, 4L
- h :
-
local convective coefficient
- k :
-
thermal conductivity
- 2L :
-
channel width
- N u :
-
local Nusselt number,h D h/k
- P e :
-
Peclet number,U m Dh/α
- q w :
-
wall heat flux
- r :
-
radius
- T :
-
temperature
- U :
-
velocity
- U m :
-
mean velocity
- x, y :
-
coordinates
- Y :
-
dimensionless transversal coordinate,y/D h
- Z :
-
dimensionless axial coordinate,x/D h Pe
- α :
-
thermal diffusivity
- ϕ :
-
dimensionless temperature (T-T e) k/qw Dh
- ϱ :
-
density
- b :
-
bulk
- e :
-
entrance
- w :
-
wall
- 1:
-
inner
- 2:
-
outer
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Campo, A., Salazar, A. Forced convection — axial conduction between parallel walls with unequal heat fluxes. Wärme- und Stoffübertragung 20, 177–181 (1986). https://doi.org/10.1007/BF01303448
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DOI: https://doi.org/10.1007/BF01303448