Heat and Mass Transfer

, Volume 54, Issue 4, pp 1031–1051 | Cite as

Temperature dependency of the thermal conductivity of porous heat storage media

  • Henok HailemariamEmail author
  • Frank Wuttke


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.

List of symbols

A & B

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

A’ & B′

Empirical constants of Zoth and Hanel [1] model


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

b0, b1 & b2

Fitted constants for the SH-1 transient needle probe


Specific heat capacity of a medium


Constant related to the radiative heat transfer properties of a medium


Solid matrix texture dependent constant of Johansen [3] model


Thermal diffusivity of a medium


Exponential integral


Specific gravity of solids of a medium


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


Empirical coefficient of Aurangzeb et al. [5] model


Porosity of a medium


Phonon scattering coefficient of the proposed new model


Heat flux


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


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


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


Height of specimen in the steady state apparatus.


Degree of saturation of a medium


Height of the reference plate in the steady state apparatus


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


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


Duration of heating for the TR-1 transient needle probe


Duration of heating for the SH-1 transient needle probe


Medium temperature


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


Temperature of the reference plate in the steady state apparatus


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


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


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


Maximum temperature considered in a study


Reference temperature


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


Pore-air pressure in a medium


Pore-water pressure in a medium


Bulk volume of a medium


Volumetric fraction of the kth constituent mineral of a medium


Volume of solids of a medium


Volume of voids of a medium


Dry bulk weight of a medium


Weight fraction of the kth constituent mineral of a medium


Saturated moisture content of a medium


Saturated bulk weight of a medium


Volumetric water content of a medium


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


Temperature dependent thermal conductivity of a specimen


Thermal conductivity of air at a reference temperature T o


Thermal conductivity of calcite at a reference temperature T o


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


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


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


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


Lattice (phonon) thermal conductivity


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


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


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


Thermal conductivity of a specimen obtained using the steady state method


Radiative thermal conductivity


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


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


Thermal conductivity of the reference plate in the steady state apparatus


Thermal conductivity of water at a reference temperature T o


Density of a medium


Density of calcite mineral


Bulk dry density of a medium


Density of the kth constituent mineral of a medium


Density of hardened neat cement grout


Density of the solids of a medium


Bulk saturated density of a medium


Density of water


Matric suction of a medium



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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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Marine and Land Geomechanics and GeotechnicsKiel UniversityKielGermany

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