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An analysis for friction and heat transfer characteristics of power-law non-Newtonian fluid flows past bodies of arbitrary geometrical configuration

Eine Analyse der Reibung und des Wärmeübergangs in Strömungen strukturviskoser, nicht Newtonscher Fluide hinter Körpern verschiedener Geometrien

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Abstract

A general integral solution procedure has been suggested for the analysis of the forced convective heat transfer to the power-law-non-Newtonian fluids from bodies of arbitrary geometrical configuration. Both the free stream velocity and wall temperature are allowed to vary in arbitrary fashion. The set of governing equations has been eventually reduced to a pair of characteristic equations: one first order ordinary differential equation and another integral equation, which can readily be solved, once the power-law exponent, body geometry, external velocity distribution and wall temperature distribution are specified. Comparison of the calculated results with available experimental data and series expansion solutions suggests an excellent performance of the present approximate solution procedure.

Zusammenfassung

Es wird eine generelle Methode für eine integrale Lösung zur Analyse des Wärmeübergangs bei Zwangskonvektion für strukturviskose, nicht Newtonsche Fluide vorgeschlagen, die Körper unterschiedlicher geometrischer Konfiguration umströmen. Sowohl die Freistrahlgeschwindigkeit als auch die Wandtemperatur können beliebig variieren. Der die Vorgänge beschreibende Gleichungssatz wurde schließlich auf ein Paar charakteristische Gleichungen reduziert, nämlich eine gewöhnliche Differentialgleichung erster Ordnung und eine Integralgleichung, die sofort gelöst werden können, wenn der Exponentialansatz für das strukturviskose Verhalten die Geometrie des umströmten Körpers, die Verteilung der Anströmgeschwindigkeit und die Verteilung der Wandtemperatur spezifiziert sind. Ein Vergleich der berechneten Ergebnisse mit verfügbaren Messungen und anderen Lösungen zeigt ein ausgezeichnetes Verhalten der vorliegenden Näherungslösungs-Methode.

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Abbreviations

C, D, E, G, H :

boundary layer shape factors

Cfx :

local skin friction coefficient

Cp :

specific heat

f,ft :

velocity and temperature profiles

I, It :

functions associated with the deviation from unity

k :

thermal conductivity

K :

multiplicative constant in the power-law model

m :

function describing the external flow velocity

mt :

exponent for the wall temperature variation

n :

power-law exponent

Nux :

local Nusselt number

Prx :

Prandtl number

Rex :

Reynolds number

T, Δ Tw :

temperature, and wall-ambient temperature difference

u, v :

velocity components in thex andy directions

x, y :

boundary layer coordinates

δ, δt :

viscous and thermal boundary layer thicknesses

ζ :

boundary layer thickness ratio

η, ηt :

dimensionless variable in they direction

Λ :

shape factor associated with the curvature off at the wall

ξ :

shape factor associated with the boundary layer thickness

e :

boundary layer edge

t :

thermal boundary layer

w :

wall

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Authors and Affiliations

  1. Dept. of Energy and Mechanical Engng., Shizuoka University, 432, Hamamatsu, Japan

    A. Nakayama &  H. Koyama

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  1. A. Nakayama
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  2. H. Koyama
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Nakayama, A., Koyama, H. An analysis for friction and heat transfer characteristics of power-law non-Newtonian fluid flows past bodies of arbitrary geometrical configuration. Wärme- und Stoffübertragung 22, 29–36 (1988). https://doi.org/10.1007/BF01001569

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