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

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## 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## 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 (k

_{eff}/k_{f})- k
_{eff} Effective thermal conductivity of two-phase materials (W/mK)

- k
_{f} Fluid or continuous thermal conductivity (W/mK)

- k
_{s} Solid or dispersed thermal conductivity (W/mK)

- k
_{sf} Equivalent thermal conductivity of a composite layer (W/mK)

- R
Thermal resistance (m

^{2}K/W)*l*Length of the unit cell (m)

## Greek symbols

- α
Conductivity ratio (k

_{s}/k_{f})- 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 (k

_{sf}/k_{f})- θ
_{i} Angle defined in circular cylinder model (Fig. 2b)

- θ
_{c} 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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