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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
Original

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.

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

b

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

b0, b1 & b2

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

Gs

Specific gravity of solids of a medium

Ke

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

qh

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

rh

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

Sp

Height of specimen in the steady state apparatus.

Sr

Degree of saturation of a medium

Sv

Height of the reference plate in the steady state apparatus

S23

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

S12

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

th

Duration of heating for the SH-1 transient needle probe

T

Medium temperature

T1

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

T2

Temperature of the reference plate in the steady state apparatus

T3

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

Tav

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

T0

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

Tmax

Maximum temperature considered in a study

To

Reference temperature

ΔT

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

ua

Pore-air pressure in a medium

uw

Pore-water pressure in a medium

V

Bulk volume of a medium

VFm,k

Volumetric fraction of the kth constituent mineral of a medium

Vs

Volume of solids of a medium

Vv

Volume of voids of a medium

Wdry

Dry bulk weight of a medium

WFm,k

Weight fraction of the kth constituent mineral of a medium

wsat

Saturated moisture content of a medium

Wsat

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

λa

Thermal conductivity of air at a reference temperature T o

λc

Thermal conductivity of calcite at a reference temperature T o

λd

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

λdom

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

λexp

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

λf

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

λl

Lattice (phonon) thermal conductivity

λm,k

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

λncg

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

λo

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

λp

Thermal conductivity of a specimen obtained using the steady state method

λr

Radiative thermal conductivity

λs

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

λsat

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

λv

Thermal conductivity of the reference plate in the steady state apparatus

λw

Thermal conductivity of water at a reference temperature T o

ρ

Density of a medium

ρc

Density of calcite mineral

ρd

Bulk dry density of a medium

ρm,k

Density of the kth constituent mineral of a medium

ρncg

Density of hardened neat cement grout

ρs

Density of the solids of a medium

ρsat

Bulk saturated density of a medium

ρw

Density of water

ψm

Matric suction of a medium

Notes

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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© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Marine and Land Geomechanics and GeotechnicsKiel UniversityKielGermany

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