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Effects of viscous dissipation on heat transfer parameters for flow between parallel plates

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Zusammenfassung

Für die Strömung zwischen zwei ebenen Platten wird der Einfluss der viskosen Energiedissipation auf Temperaturprofil und Wärmeübertragung in der thermischen Anlaufstrecke untersucht. Die Strömung wird als voll entwickelte Laminarströmung betrachtet. Ein Wärmeentwicklungsparameter wird eingeführt. Die Relation zwischen dem Wärmeentwicklungsparameter und der Eckertschen und der Brinkmanschen Zahl wird diskutiert. Die Entwicklung des Temperaturprofils und der lokalen Nusseltzahl wird graphisch dargestellt für Werte des Wärmeentwicklungsparameters von 0; 0,5; 0,75; 1,0.

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Abbreviations

A :

surface area through which heat is transferred,

a :

one-half of the duct height,

Br :

μ u 2/k (tb−t0), Brinkman number,

C p :

specific heat,

D e :

equivalent diameter of the duct, 4a,

Ec :

u 2/Cp (tb−t0), Eckert number,

h :

heat transfer coefficient,

k :

thermal conductivity,

L :

duct length,

Nu x :

h xDe/k, local Nusselt number,

Pr :

μC p/k, Prandtl number,

q :

rate of heat transfer,

q n :

-q/A, negative rate of heat transfer per unit area,

Re a :

ϱ u 0 a/μ, Reynolds number,

t :

temperature,

u :

velocity inx-direction,

U :

u/u 0, dimensioneless velocity inx-direction,

x :

variable distance along length of duct,

X :

μ x/ϱ a u 0 Pr, dimensionless variable distance along length of duct,

Y :

y/a, dimensionless variable distance across height of duct,

z :

variable distance along width of duct,

y :

variable distance across height of duct,

η:

u 20 μ/a q′′, heat generation parameter,

ϱ:

density,

μ:

viscosity,

θ:

(t−t 0)/(a q′′/k), dimensionless temperature,

Ψ:

−4/GDθ, pseudo-local Nusselt number

b :

bulk,

j :

atjth position alongx axis,

k :

atkth position acrossy axis,

w :

at the walls or plates,

x :

local,

0:

at initial position alongx axis

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Authors and Affiliations

  1. Kansas State University, Manhattan, Kansas, USA

    Ching-Lai Hwang, Philip J. Knieper & Liang-Tseng Fan

Authors
  1. Ching-Lai Hwang
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  2. Philip J. Knieper
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  3. Liang-Tseng Fan
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Additional information

This study was supported by the Air Force Office of Scientific Research Grant AF-AFOSR-463-64.

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Hwang, CL., Knieper, P.J. & Fan, LT. Effects of viscous dissipation on heat transfer parameters for flow between parallel plates. Journal of Applied Mathematics and Physics (ZAMP) 16, 599–610 (1965). https://doi.org/10.1007/BF01590965

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  • DOI: https://doi.org/10.1007/BF01590965

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