# 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.

## Keywords

Friction factor Nusselt number Annular flow Smooth and slotted surfaces## Nomenclature

*A*surface area, m

^{2}*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/m

^{2}. 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

## Greek letters

*ν*kinetic viscosity

*Δ*(Difference)

- Ω
rotational speed, rad/s

## Subscripts

- 1
inner

- 2
outer

- a
axial, ambient

- eff
effective

- h
hydraulic

- in
inlet

- s
smooth

- w
wall

- __
average

## Notes

## References

- 1.Lappa (2012) Rotating Thermal Flows in Natural and Industrial Processes, John Wiley and SonsGoogle Scholar
- 2.Matsuo S and Kiuch M (1983) Low temperature chemical vapor deposition method utilizing an Electron cyclotron resonance plasma, Japanese journal of applied physics, 22(4), Part 2Google Scholar
- 3.Vivès C (1988) Effects of a forced Couette flow during the controlled solidification of a pure metal. Int J Heat Mass Transf 31(10):2047–2062CrossRefGoogle Scholar
- 4.Ali ME, Weidman PD (1990) On the stability of circular Couette-flow with radial heating. J Fluid Mech 220:53–84CrossRefzbMATHGoogle Scholar
- 5.Snyder HA, Karlsson SK (1964) F, experiments on the stability of Couette motion with a radial thermal gradient. Phys Fluids 7:1696CrossRefGoogle Scholar
- 6.Sorour MM, Coney JER (1979) The effect of temperature gradient on the stability of flow between vertical concentric rotating cylinders. J Mech Eng Sci 21:403–409CrossRefGoogle Scholar
- 7.Lepiller V, Goharzadeh A, Prigent A, Mutabazi I (2008) Weak temperature gradient e ffect on the stability of the circular Couette flow. Eur Phys J B 61:445–455CrossRefGoogle Scholar
- 8.Ball KS, Farouk B (1989) A flow visualization study of the effects of buoyancy on Taylor vortices. Phys Fluids A 1:1502–1507CrossRefGoogle Scholar
- 9.Lopez JM, Marques F, Avila M (2013) The Boussinesq approximation in rapidly rotating fluids. J Fluid Mech 737:56–77MathSciNetCrossRefzbMATHGoogle Scholar
- 10.Shi L, Rampp M, Hof B, Avila M (2015) A hybrid MPI-OpenMP parallel implementation for pseudospectral simulations with application to Taylor–Couette flow. Comput Fluids 106:1–11MathSciNetCrossRefzbMATHGoogle Scholar
- 11.Nachouane AB, Abdenour A, Friedrich G and Vivier S (2015) Numerical approach forthermal analysis of heat transfer into a very narrow air gap of a totally enclosed permanent magnet integrated starter generator, conference of ECCE, Montreal CanadaGoogle Scholar
- 12.Kawata T, Henrik Alfredsson P (2016) Turbulent rotating plane Couette flow: Reynolds and rotation number dependency of flow structure and momentum transport. Physical Review Fluids 22:34402CrossRefGoogle Scholar
- 13.Biage M, Campos JCC (2003) Visualization study and quantitative velocity measurements in turbulent Taylor-Couette flow by phantomm flow tagging: a description of the transition to turbulence. J Braz Soc Mech Sci Eng 25(4):378–390CrossRefGoogle Scholar
- 14.Jakoby R, Kim S, Wittig S (1999) Correlations of the convection heat transfer in annular channels with rotating inner cylinder. Journal of Engineering Gas Turbines Power 121(4):670–677CrossRefGoogle Scholar
- 15.Nouri-Borujerdi A, Nakhchi M (2017) Optimization of the heat transfer coefficient and pressure drop of Taylor-Couette-Poiseuille flows between an inner rotating cylinder and an outer grooved stationary cylinder. Int J Heat Mass Transf 108:1449–1459CrossRefGoogle Scholar
- 16.Nouri-Borujerdi A, Nakhchi M (2017) Heat transfer enhancement in annular flow with outer grooved cylinder and rotating inner cylinder: review and experiments. Appl Therm Eng 120:257–268CrossRefGoogle Scholar
- 17.Lee YN, Minkowycz W (1989) Heat transfer characteristics of the annulus of twocoaxial cylinders with one cylinder rotating. Int J Heat Mass Transf 32:711–722CrossRefGoogle Scholar
- 18.Bouafia M, Bertin Y, Saulnier JB, Ropert P (1998) Analyse expérimentale des transferts de chaleur en espace annulaire étroit et rainuré avec cylindre intérieur tournant. Int J Heat Mass Transf 41(10):1279–1291CrossRefGoogle Scholar
- 19.Coleman HW, Steele WG (2009) Experimentation, validation, and uncertaintyanalysis for engineers, John Wiley & SonsGoogle Scholar
- 20.Gardiner SRM, Sabersky R (1978) Heat transfer in an annular gap. Int J Heat Mass Transf 21:1459–1466CrossRefGoogle Scholar
- 21.Kuzay T, Scott C (1977) Turbulent heat transfer studies in annulus with inner cylinder rotation. J Heat Transf 99:12–19CrossRefGoogle Scholar
- 22.Jalil JM, Hanfash A-JO, Abdul-Mutaleb MR (2016) Experimental and numerical study of axial turbulent fluid flow and heat transfer in a rotating annulus. Arab J Sci Eng 41:1857–1865MathSciNetCrossRefzbMATHGoogle Scholar