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Heat and Mass Transfer

, Volume 46, Issue 11–12, pp 1379–1394 | Cite as

Comparison of geometry dependent resistance models with conventional models for estimation of effective thermal conductivity of two-phase materials

  • A. P. Senthil Kumar
  • V. Prabhu Raja
  • P. KarthikeyanEmail author
Original

Abstract

The geometry dependent resistance models are used to estimate the effective thermal conductivity of two-phase materials based on the unit cell approach. The algebraic equations are derived based on isotherm approach for various geometries. The effective thermal conductivity of the above models are found and compared with experimental data with a minimum and maximum deviation of ±3.976 and ±19.55%, respectively. The present models are good agreement with experimental results.

Keywords

Effective Thermal Conductivity Composite Layer Total Resistance Conventional Model Conductivity Ratio 
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.

List of symbols

a

Length of the square, octagon and hexagon cylinders or diameter of the circular cylinder

c

Width of the connecting plate in the square, circular, octagon and hexagon cylinders

K

Non-dimensional thermal conductivity of the two-phase materials (keff/kf)

keff

Effective thermal conductivity of two-phase materials (W/mK)

kf

Fluid or continuous thermal conductivity (W/mK)

ks

Solid or dispersed thermal conductivity (W/mK)

ksf

Equivalent thermal conductivity of a composite layer (W/mK)

R

Thermal resistance (m2K/W)

l

Length of the unit cell (m)

Greek symbols

α

Conductivity ratio (ks/kf)

δ

Height of the circular cylinder shown in Fig. 2

ε

Length ratio (a/l)

Φ

Ratio of equivalent thermal conductivity of a composite layer to the fluid or continuous thermal conductivity (ksf/kf)

θi

Angle defined in circular cylinder model (Fig. 2b)

θc

Angle defined in circular cylinder model (Fig. 2b)

λ

Contact ratio (c/a)

υ

Concentration

ς

Connecting plate height to the length of the unit cell in the circular cylinder (δ/l)

ζ

Non-dimensional thermo-physical parameter, \( \left( {{\frac{1}{\alpha }} - 1} \right)\varepsilon \)

Subscripts

B–M

Brailsford and Major

Brug

Bruggeman

cir

Circular

Devi

Deviation

eff

Effective

exp

Experimental

Had

Hadley

hex

Hexagon

Lid

Litchnecker

octa

Octagon

Pand

Pande

R–M

Raghavan–Martin

Squ

Square

Z–S

Zehner–Schlunder

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • A. P. Senthil Kumar
    • 1
  • V. Prabhu Raja
    • 1
  • P. Karthikeyan
    • 2
    Email author
  1. 1.Department of Mechanical EngineeringPSG College of TechnologyCoimbatoreIndia
  2. 2.Department of Automobile EngineeringPSG College of TechnologyCoimbatoreIndia

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