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Unsteady entrance heat transfer in laminar pipe flows with convection from the ambient

Instationäre konvektive Wärmeübertragung bei laminarer Rohreinlaufströmung

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Abstract

The characteristics of unsteady entrance heat transfer in the combined entrance heat transfer region of laminar pipe flows resulting from time-varying inlet temperature are numerically investigated. Three non-dimensional parameters,Nu 0, a*, andf are identified in the study. Also, their effects on the non-dimensional duct wall temperature, fluid bulk temperature, and duct wall heat flux are discussed in great detail. Comparisons are made with the zero thermal capacity wall solution.

Zusammenfassung

Die Eigenschaften der instationären Wärmeübertragung bei laminarer Rohreinlaufströmung, welche aus der zeitvariierten Einlaßtemperatur resultieren, werden numerisch untersucht. Drei dimensionslose ParameterNu 0, a*, undf werden in der Studie benutzt. Ebenso werden ihr Einfluß auf die dimensionslose Rohrwandtemperatur, die Flüssigkeitskerntemperatur und den Rohrwandwärmestrom im Detail diskutiert. Vergleiche mit Lösungen von wärmekapazitätslosen Wänden werden gemacht.

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Abbreviations

a * :

heat capacity ratio

A f ,A w :

cross-section areas of the fluid flow and the pipe, respec tively

b :

thickness of the pipe wall

C p :

specific heat of fluid

C pw :

specific heat of the pipe wall material

D :

inner pipe diameter,D=2R

h :

heat transfer coefficient inside the pipe

h 0 :

heat transfer coefficient in the ambient side

k :

thermal conductivity of the fluid in the pipe

Nu 0 :

local Nusselt number,h2R)/k

Nu 0 :

outside Nusselt number,h 0 R 0/k

P :

pressure

P :

dimensionless pressure

Pr :

Prandtl number

q″w :

duct wall heat flux

Q″w :

non-dimensional duct wall heat flux

r :

radius coordinate

R,R 0 :

pipe inner and outer radii, respectively

t :

time

T :

temperature

ΔT :

amplitude of inlet temperature variation

u :

axial velocity

U :

dimensionless axial velocity

v :

radial velocity

V :

dimensionless radial velocity

x :

axial coordinate

α :

thermal diffusivity of the fluid in the pipe

η :

dimensionless radial coordinate

θ :

dimensionless temperature

Δθ:

dimensionless amplitude of inlet temperature variation

ν :

kinematic viscosity

ξ :

dimensionless axial coordinate

τ:

dimensionless time

ϱ :

density of the fluid in the pipe

ϱ w :

density of the pipe wall material

ω:

circular frequency of inlet temperature variation

b :

bulk

e :

entrance

0:

ambient

w :

wall

References

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan, Republic of China

    W. -M. Yan & T. -F. Lin

Authors
  1. W. -M. Yan
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  2. T. -F. Lin
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Yan, W.M., Lin, T.F. Unsteady entrance heat transfer in laminar pipe flows with convection from the ambient. Wärme- und Stoffübertragung 23, 103–109 (1988). https://doi.org/10.1007/BF01637132

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  • DOI: https://doi.org/10.1007/BF01637132

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