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Friction factor and Nusselt number in annular flows with smooth and slotted surface

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Abstract

The purpose of this experimental work is to study the effect of slot depth to width ratio, rotational motion and inlet velocity on friction factor and Nusselt number in an annular flow between two concentric cylinders with smooth and slotted surface. The heated outer surface is stationary and the unheated inner one is rotating. This configuration is popular in industrial applications such as internal air system of gas turbine engines, cooling of rotating machinery, techniques of chemical vapor deposition and solidification of pure metals. The results show that the ratio of average slotted surface friction factor to that of the smooth one enhances by increasing the slot depth to width ratio and that is more significant at higher effective Reynolds numbers. Furthermore, ratio of local Nusselt number of the slotted surface to that of the smooth one is nearly equal to 1.2 along 60% of first part of channel length and afterwards increases sharply. The main interest of this work is to present a correlation formula for the local Nusselt number as a function of the effective Reynolds number, the slot aspect ratio and the local axial position.

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Abbreviations

A :

surface area, m2

a :

groove pitch, m

b :

groove depth, m

c :

groove width, m

D :

diameter, m

e :

air gap between two cylinders, m

f :

friction factor

h :

heat transfer coefficient, W/m2. K

I :

Ampere, A

k :

Thermal conductivity, W/m. K

L :

channel length, m

N :

Number of axial slots

Nu:

Nusselt number

p:

Pressure, kPa

\( \dot{q} \) :

heat transfer rate, W

r:

r-direction

R:

cylinder radius, m

Re:

Reynolds number

T:

temperature, C

Ta:

Taylor number

u:

axial velocity, m/s

V:

Velocity, m/s

x:

general variable

ν :

kinetic viscosity

Δ :

(Difference)

Ω:

rotational speed, rad/s

1:

inner

2:

outer

a:

axial, ambient

eff:

effective

h:

hydraulic

in:

inlet

s:

smooth

w:

wall

__:

average

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Authors and Affiliations

  1. School of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, Tehran, Iran

    A. Nouri-Borujerdi & M. E. Nakhchi

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  1. A. Nouri-Borujerdi
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  2. M. E. Nakhchi
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Correspondence to A. Nouri-Borujerdi.

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Nouri-Borujerdi, A., Nakhchi, M.E. Friction factor and Nusselt number in annular flows with smooth and slotted surface. Heat Mass Transfer 55, 645–653 (2019). https://doi.org/10.1007/s00231-018-2445-9

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