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A prediction model using response surface methodology based on cell size and foam density to predict thermal conductivity of polystyrene foams

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Abstract

Polymeric foams are one of the most important insulating materials due to their low thermal conductivity. The comprehensive investigation of the thermal behavior of these materials is experimentally difficult, costly, and time-consuming. In this study, a step-wise approach is used in order to predict thermal conductivity of the polymeric foams. The results demonstrate that two different models estimate the thermal conductivity of the polystyrene foams with cell sizes smaller than 100 μm and larger than 100 μm with an error almost smaller than 10%. According to these theoretical models, a comprehensive investigation is performed on the thermal-insulation performance of polystyrene foams. The results indicate that the thermal conductivity reduces by decreasing the cell size but there is an optimum foam density for achieving the smallest thermal conductivity. The effects of foam density and cell size are studied on the different mechanisms of thermal conductivity. In the following, a new approach is offered based on the cell size and the foam density using response surface method (RSM). The reliability of the proposed regression model is checked not only using analysis of variance (ANOVA) tool of RSM but also in comparison to empirical results.

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Abbreviations

ϵ VF :

Void fraction

K n :

Knudsen number

λ gas :

Bulk gas conductivity, 0.026 W/mK

λ solid :

Bulk solid conductivity, W/mK

l mean :

Mean free path, 70 nm for air

φ c :

Cell size, μm

φ :

Expansion ratio

N:

Cell density, cell.cm−3

f s :

Strut fraction

V struts :

Volumetric fraction of struts

V walls :

Volumetric fraction of cell walls

φ s :

Strut diameter, μm

d w :

Cell wall thickness, μm

n:

Effective index of refraction

T:

Temperature, K

K R :

Rosseland mean extinction coefficient, m−1

K struts :

Extinction coefficient of struts, m−1

K walls :

Extinction coefficient of cell walls

K Solid :

Extinction coefficient of solid polymer, m−1

β :

Efficiency of the energy transfer between gas molecules and cell walls

λ:

Thermal conductivity

ρ :

Density

σ :

Stefan-Boltzmann constant

t:

Total

s:

Solid

g:

Gas

r:

Radiation

f:

Foam

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Authors and Affiliations

  1. Department of Mechanical Engineering, Urmia University, Urmia, Iran

    Rezgar Hasanzadeh, Taher Azdast, Ali Doniavi & Milad Rostami

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  1. Rezgar Hasanzadeh
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  2. Taher Azdast
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  3. Ali Doniavi
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  4. Milad Rostami
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Correspondence to Ali Doniavi.

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Hasanzadeh, R., Azdast, T., Doniavi, A. et al. A prediction model using response surface methodology based on cell size and foam density to predict thermal conductivity of polystyrene foams. Heat Mass Transfer 55, 2845–2855 (2019). https://doi.org/10.1007/s00231-019-02628-8

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  • DOI: https://doi.org/10.1007/s00231-019-02628-8

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