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Wärme - und Stoffübertragung

, Volume 29, Issue 6, pp 355–359 | Cite as

Combined convection on a vertical slender cylinder in a micropolar fluid

  • I. A. Hassanien
  • M. A. Mansour
  • R. S. R. Gorla
Originalarbeiten

Abstract

An analysis is presented for the steady state mixed convective boundary layer flow of a micropolar fluid along vertical slender cylinders. The governing equations have been solved numerically. Results for the friction factor, Nusselt number as well as the details of flow and temperature fields are displayed for a range of values of the transverse curvature and material parameters for the micropolar fluid. It is observed that micropolar fluids display drag reduction as well as heat transfer rate reduction when compared to Newtonian fluids.

Keywords

Heat Transfer Convection Boundary Layer Nusselt Number Friction Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

cf

friction factor

cp

specific heat [J Kg−1 K−1]

f

dimensionless stream function

g

gravitational acceleration [m s−2]

Gr, Gr

Grashof number

h

local heat transfer coefficient [Wm−2 K−1]

j

micro-inertia per unit mass [m2]

k

thermal conductivity [Wm−1 k−1]

K

Vortex viscosity [Kg m−1 s−1]

L

total length of cylinder [m]

N

angular velocity [s−1]

Nux

local Nusselt number

q

heat flux [Wm−2]

r

radial coordinate [m]

R

Radius of cylinder [m]

Re

Reynolds number (based onR)

Rex

Reynolds number (based onx)

T

Temperature [K]

u, v

velocity components inx, y direction respectively [m s−1]

U

free steam velocity [m s−1]

x

longitudinal coordinate [m]

z

constant defined in equation (10)

Greek symbols

α

thermal diffusivity [m2 s−1]

β

thermal expansion coefficient [K−1]

ε

transverse curvature parameter

η

pseudo-similarity variable

θ

dimensionless temperature

λT,λq

buoyancy parameters

ν

kinematic viscosity [m2 s−1]

γ

spin-gradient viscosity [kg m s−1]

ρ

density [kg m−3]

ξ

dimensionless parameter,x/R

ρ

density of fluid [Kg m−3]

τ

shear stress [N/m2]

ψ

stream function

Δ, λ, B

material parameters

Subscripts

ambient condition

f

properties of fluid

q

constant wall heat flux

T

constant wall temperature case

w

wall condition

Mischkonvektion an einem senkrechten schlanken Zylinder in einem mikropolaren Fluid

Zusammenfassung

Die Untersuchung bezieht sich auf stationäre Mischkonvektion in der Grenzschicht einer mikropolaren Flüssigkeit entlang eines senkrechten schlanken Zylinders. Die bestimmenden Gleichungen wurden numerisch gelöst. In einem gewissen Bereich des Krümmungsverhältnisses und der Stoffparameter des mikropolaren Fluids werden Ergebnisse für den Widerstandsbeiwert, die Nusselt-Zahl sowie Besonderheiten des Strömungs- und Temperaturfeldes mitgeteilt. Wie sich zeigte, weisen mikropolare Fluide gegenüber Newtonschen Fluiden sowohl geringeren Widerstand als auch niedrigere Wärmeübertragungsintensität auf.

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References

  1. 1.
    Eringen, A. C.: Theory of Micropolar Fluids. J. Math. Mech. 16 (1966) 1–18Google Scholar
  2. 2.
    Eringen, A. C.: Theory of Thermomicrofluids. J. Mathematical Analysis and Applications 38 (1972) 480–496CrossRefGoogle Scholar
  3. 3.
    Gorla, R. S. R.: Thermal Boundary Layer of a Micropolar Fluids at a Stagnation Point. Int. J. Engineering Science 18 (1980) 611–617CrossRefGoogle Scholar
  4. 4.
    Jena, S. K.; Mathur, M. N.: Similarity Solutions for Laminar Free Convective Flow of a Thermomicropolar Fluid Past a Non-Isothermal Vertical Plate. Int. J. Engineering Science 19 (1981) 1431–1439CrossRefGoogle Scholar
  5. 5.
    Gorla, R. S. R.; Schoren, W. R.; Takhar, H. S.: Natural Convection Boundary Layer Flow of a Micropolar Fluid over an Isothermal Cone. Acta Mechanica 61 (1986) 139–152CrossRefGoogle Scholar
  6. 6.
    Gorla, R. S. R.; Lin, P.; Yang, A.: Asymptotic Boundary Layer Solutions for Mixed Convection from a Vertical Surface in Micropolar Fluids. Int. J. Engineering Science 28 (1990) 525–533CrossRefGoogle Scholar
  7. 7.
    Cebeci, T.; Bradshaw, P.: Momentum Transfer in Boundary Layers. Hemisphere Publishing Col, Washington D.C., 1977Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • I. A. Hassanien
    • 1
  • M. A. Mansour
    • 1
  • R. S. R. Gorla
    • 1
  1. 1.Department of Mechanical EngineeringCleveland State UniversityClevelandUSA

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