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Temperature dependency of the thermal conductivity of porous heat storage media

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Abstract

Analyzing the variation of thermal conductivity with temperature is vital in the design and assessment of the efficiency of sensible heat storage systems. In this study, the temperature variation of the thermal conductivity of a commercial cement-based porous heat storage material named – Füllbinder L is analyzed in saturated condition in the temperature range between 20 to 70°C (water based storage) with a steady state thermal conductivity and diffusivity meter. A considerable decrease in the thermal conductivity of the saturated sensible heat storage material upon increase in temperature is obtained, resulting in a significant loss of system efficiency and slower loading/un-loading rates, which when unaccounted for can lead to the under-designing of such systems. Furthermore, a new empirical prediction model for the estimation of thermal conductivity of cement-based porous sensible heat storage materials and naturally occurring crystalline rock formations as a function of temperature is proposed. The results of the model prediction are compared with the experimental results with satisfactory results.

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Notes

  1. http://www.schwenk-zement.de/

  2. IGLU is an analysis, modeling and assessment of an intelligent and environmentally friendly geothermal long-term heat storage system project funded by the German Federal Ministry of Economy and Energy (BMWi)

  3. For predicting the variation of thermal conductivity with temperature of single-phased solids such as rock forming minerals, \( {\lambda}_{T_o} \) is identical with λ dom (W m−1 K−1) in Eq. (12), and hence the use of Eqs. (13–16) is not necessary

Abbreviations

A & B :

Constants related to the phonon scattering properties of a medium [1]

A’ & B′ :

Empirical constants of Zoth and Hanel [1] model

b :

Temperature coefficient of thermal conductivity of Kukkonen et al. [2] model

b 0 , b 1 & b 2 :

Fitted constants for the SH-1 transient needle probe

c :

Specific heat capacity of a medium

C :

Constant related to the radiative heat transfer properties of a medium

C′ :

Solid matrix texture dependent constant of Johansen [3] model

D :

Thermal diffusivity of a medium

Ei :

Exponential integral

G s :

Specific gravity of solids of a medium

K e :

Kersten’s number of Johansen [3] and Côté and Konrad [4] models

m :

Empirical coefficient of Aurangzeb et al. [5] model

n :

Porosity of a medium

q :

Phonon scattering coefficient of the proposed new model

q h :

Heat flux

Q :

Constant rate of application of heat for the TR-1 and SH-1 transient probes

r :

Distance between heater and temperature sensor for the TR-1 transient probe

r h :

Distance between the two needles of the SH-1 transient probe

S p :

Height of specimen in the steady state apparatus.

S r :

Degree of saturation of a medium

S v :

Height of the reference plate in the steady state apparatus

S 23 :

Distance between the bottom (cooling) and reference disc thermocouples in the steady state apparatus

S 12 :

Distance between the top (heating) and reference disc thermocouples in the steady state apparatus

t :

Duration of heating for the TR-1 transient needle probe

t h :

Duration of heating for the SH-1 transient needle probe

T :

Medium temperature

T 1 :

Temperature of the top (heating) plate in the steady state apparatus

T 2 :

Temperature of the reference plate in the steady state apparatus

T 3 :

Temperature of the bottom (cooling) plate in the steady state apparatus

T av :

Temperature at the center of a specimen (average temperature of a specimen) in the steady state apparatus

T 0 :

Temperature at the start of measurement (at time 0) for the SH-1 probe

T max :

Maximum temperature considered in a study

T o :

Reference temperature

ΔT :

Temperature response of the source over time for the TR-1 transient probe

u a :

Pore-air pressure in a medium

u w :

Pore-water pressure in a medium

V :

Bulk volume of a medium

VF m,k :

Volumetric fraction of the kth constituent mineral of a medium

V s :

Volume of solids of a medium

V v :

Volume of voids of a medium

W dry :

Dry bulk weight of a medium

WF m,k :

Weight fraction of the kth constituent mineral of a medium

w sat :

Saturated moisture content of a medium

W sat :

Saturated bulk weight of a medium

θ :

Volumetric water content of a medium

κ :

Matrix texture dependent parameter of the Côté and Konrad [4] model

λ :

Temperature dependent thermal conductivity of a specimen

λ a :

Thermal conductivity of air at a reference temperature T o

λ c :

Thermal conductivity of calcite at a reference temperature T o

λ d :

Dry thermal conductivity of a medium at a reference temperature T o

λ dom :

Thermal conductivity of the dominant mineral of a medium at a reference temperature T o

λ exp :

Experimental thermal conductivity as used in the Aurangzeb et al. [5] model

λ f :

Thermal conductivity of the fluid phase at a reference temperature T o

λ l :

Lattice (phonon) thermal conductivity

λ m,k :

Thermal conductivity of the kth constituent mineral of a medium at a reference temperature T o

λ ncg :

Thermal conductivity of hardened neat cement grout at a reference temperature T o

λ o :

Thermal conductivity at a reference temperature of the Kukkonen et al. [2] model

λ p :

Thermal conductivity of a specimen obtained using the steady state method

λ r :

Radiative thermal conductivity

λ s :

Thermal conductivity of the solid phase at a reference temperature T o

λ sat :

Saturated thermal conductivity of a medium at a reference temperature T o

\( {\lambda}_{T_o} \) :

Predicted thermal conductivity of a medium at a reference temperature T o of the new proposed model

\( {\left({\lambda}_{T_o}\right)}_{exp} \) :

Measured thermal conductivity of a medium at a reference temperature T o

\( {\left({\lambda}_{T_{max}}\right)}_{exp} \) :

Measured thermal conductivity of a medium at the maximum T max temperature considered in the study

λ v :

Thermal conductivity of the reference plate in the steady state apparatus

λ w :

Thermal conductivity of water at a reference temperature T o

ρ :

Density of a medium

ρ c :

Density of calcite mineral

ρ d :

Bulk dry density of a medium

ρ m,k :

Density of the kth constituent mineral of a medium

ρ ncg :

Density of hardened neat cement grout

ρ s :

Density of the solids of a medium

ρ sat :

Bulk saturated density of a medium

ρ w :

Density of water

ψ m :

Matric suction of a medium

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Acknowledgements

The authors would like to acknowledge the financial support provided by the German Federal Ministry for Economic Affairs and Energy (BMWi) under Grant numbers 0325547B (Project IGLU) and 03ET6122A (Project ANGUS II) as well as the support of Project Management Jülich.

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  1. Marine and Land Geomechanics and Geotechnics, Kiel University, Kiel, Germany

    Henok Hailemariam & Frank Wuttke

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Hailemariam, H., Wuttke, F. Temperature dependency of the thermal conductivity of porous heat storage media. Heat Mass Transfer 54, 1031–1051 (2018). https://doi.org/10.1007/s00231-017-2204-3

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