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Heat transfer for non-Newtonian laminar flow in internally finned pipes with uniform temperature

Wärmeübergang bei nicht-Newtonscher Laminarströmung in innenberippten Rohren gleichförmiger Temperatur

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Abstract

An analysis is presented for fully developed laminar convective heat transfer of non-Newtonian power-law fluids in pipes with internal longitudinal fins and uniform outside wall temperature. The governing momentum and energy equations have been solved numerically, with the influence of fin conductance. The distributions of fin temperature, fluid temperature and local heat flux (both at finned and unfinned surfaces) are presented. These are shown to be strongly dependent on finned pipe geometry, fluid flow behavior index and the fin conductance. Values of overall Nusselt number indicated significant heat transfer enhancement over finless pipes. The flow behavior index affects the no. of fins which maximizes the overall Nusselt number.

Zusammenfassung

Die Untersuchung bezieht sich auf den konvektiven Wärmeübergang nicht-Newtonscher Potenzgesetz-Fluide in innenberippten Rohren bei vollausgebildeter Laminarströmung und gleichförmiger Außenwandtemperatur. Die Grundgleichungen für Impuls und Energie wurden numerisch unter Berücksichtigung der Rippenleitfähigkeit gelöst. Dargestellt sind die Verläufe der Rippen- und Fluidtemperatur sowie des lokalen Wärmeflusses, sowohl an berippten wie unberippten Flächen. Sie werden entscheidend von der Rippengeometrie, der Rippenleitfähigkeit und dem Viskositäts-index beeinflußt. Die gemittelten Nusselt-Zahlen zeigen, daß sich durch Berippung eine erhebliche Steigerung des Wärmeübergangs erreichen läßt. Die Anzahl der Rippen für welche die gemittelte Nusselt-Zahl einen Maximalwert erreicht, ist eine Funktion des Viskositätsindex.

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Abbreviations

A f :

dimensionless flow are of the pipe, Eq. (11)

a f :

flow area of the pipe

C p :

specific heat capacity of fluid

H :

dimensionless fin height,h/r 0

h :

fin height

\(\bar h\) :

average heat transfer coefficient at solid-fluid interface

K :

fin conductance parameter, βk s /k f

k f :

thermal conductivity of fluid

k s :

thermal conductivity of fin

M :

number of fins

m :

consistency index for non-Newtonian power-law fluids

n :

flow behavior index

Nu :

Nusselt number, Eqs. (14) and (15)

p :

pressure

Q :

total heat transfer rate at solid fluid interface

\(\bar q\) :

average heat flux,Q/[2M(αr 0+h)]

q f :

local fin heat flux

\(\bar q_f \) :

average fin heat flux

\(\bar q_w \) :

average heat flux at outer pipe-wall,Q/(2πr 0)

q θ :

local heat flux at unfinned surface

\(\bar q_\theta \) :

average heat flux at unfinned surface

r :

radial coordinate

r 0 :

radius of pipe

\(\bar r\) :

dimensionless radial coordinater/r 0

\(\bar r_i \) :

dimensionless radial coordinate at tip of fin

T :

temperature

T b :

bulk temperature

T w :

tube wall temperature

u :

dimensionless velocity

u b :

dimensionless bulk velocity

u z :

axial velocity

z :

axial coordinate

α:

half the angle between the flanks of two adjacent fins

β:

half the angle subtended by a fin

γ:

half the angle between the center-lines of two adjacent fins

η:

apparent viscosity of non-Newtonian power law fluid, Eq. (2)

θ:

angular coordinate

ϕ:

dimensionless temperature, Eq. (9)

φ b :

dimensionless bulk temperature

References

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Authors and Affiliations

  1. Mechanical Power Engineering Department, Menonfia University, Shebin El-Kom, Egypt

    A. S. Hegazy &  M. H. Embaby

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  1. A. S. Hegazy
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  2. M. H. Embaby
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Hegazy, A.S., Embaby, M.H. Heat transfer for non-Newtonian laminar flow in internally finned pipes with uniform temperature. Heat and Mass Transfer 30, 361–367 (1995). https://doi.org/10.1007/BF01463927

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