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Model-based analysis of thermal insulation coatings

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Abstract

Thermal insulation properties of coatings based on selected functional filler materials are investigated. The underlying physics, thermal conductivity of a heterogeneous two-component coating, and porosity and thermal conductivity of hollow spheres (HS) are quantified and a mathematical model for a thermal insulation coating developed. Data from a previous experimental investigation with hollow glass sphere-based epoxy and acrylic coatings were used for model validation. Simulations of thermal conductivities were in good agreement with experimental data. Using the model, a parameter study was also conducted exploring the effects of the following parameters: pigment (hollow spheres) volume concentration (PVC), average sphere size or sphere size distribution, thermal conductivities of binder and sphere wall material, and sphere wall thickness. All the parameters affected the thermal conductivity of an epoxy coating, but simulations revealed that the most important parameters are the PVC, the sphere wall thickness, and the sphere wall material. The model can be used, qualitatively, to get an indication of the effect of important model parameters on the thermal conductivity of an HS-based coating and thereby be used as a specification tool or as a help in the planning of relevant experiments to conduct. Further work with the model must involve additional experiments to secure a general verification of important underlying model assumptions.

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Abbreviations

A :

Outer surface area of pipe (m2)

C :

Radiation number, 5.72 × 10−8 W/(m2·K4)

d p :

Hollow sphere diameter (m)

d po :

Base case diameter of hollow glass sphere (m)

D v,10% :

Hollow sphere diameter below which 10% of the total particle volume is present (m)

D v,50% :

Hollow sphere diameter below which 50% of the total particle volume is present (m)

D v,90% :

Hollow sphere diameter below which 90% of the total particle volume is present (m)

D y :

Outer diameter of steel pipe (m)

FC :

Forced convection

h y :

Heat transfer coefficient from coating surface to surrounding fluid [W/(m2·K)]

HS :

Hollow spheres

HGS :

Hollow glass spheres

k Air :

Thermal conductivity of air [mW/(m·K)]

k B :

Thermal conductivity of binder matrix in coating [mW/(m·K)]

\( k_{\text{B}}^{ \circ } \) :

Base case thermal conductivity of binder matrix in coating [mW/(m·K)]

k BSG :

Thermal conductivity of borosilicate glass [mW/(m·K)]

k C :

Thermal conductivity of insulation coating [mW/(m·K)]

k G :

Thermal conductivity of wall material of hollow spheres [mW/(m·K)]

\( k_{\text{G}}^{ \circ } \) :

Base case thermal conductivity of wall material of hollow spheres [mW/(m·K)]

k HS :

Thermal conductivity of hollow spheres [mW/(m·K)]

k HGS :

Thermal conductivity of hollow glass spheres [mW/(m·K)]

N :

Number of particle classes in hollow sphere size distribution

NC :

Natural convection

q :

Heat flux (W/m2)

PVC:

Pigment (hollow spheres) volume concentration (vol%)

T o :

Fluid (gas or liquid) temperature (K)

T steel :

Steel wall temperature (K)

T surface :

(Outer) coating surface temperature (K)

V Air :

Unit volume of air (m3)

v B :

Volume fraction of binder in coating

V B :

Volume of binder (m3)

V BSG :

Volume of borosilicate glass (m3)

V HGS :

Volume of hollow glass spheres (m3)

V i :

Volume fraction of particles present in a given size interval

V HS :

Volume fraction of hollow spheres in coating

ε :

Porosity of hollow spheres

ε E :

Emissivity of epoxy coating

δ :

Hollow sphere wall thickness (m)

Δq :

Reduction in heat loss (%)

ρ Air :

Density of air (kg/m3)

ρ BGS :

Density of borosilicate glass (kg/m3)

ρ HGS :

True density of hollow glass spheres (kg/m3)

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Acknowledgments

The author wishes to thank M.Sc. Stud. Maja Lind-Nielsen for conducting the SEM measurements at DTU CEN. Financial support by The Hempel Foundation is gratefully acknowledged.

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  1. Department of Chemical and Biochemical Engineering, Technical University of Denmark (DTU), Building 229, DK-2800 Kgs., Lyngby, Denmark

    Søren Kiil

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Kiil, S. Model-based analysis of thermal insulation coatings. J Coat Technol Res 11, 495–507 (2014). https://doi.org/10.1007/s11998-013-9562-7

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