Legacy · Thermal validation

Paste scale

Same $Q(t_{eq})$ as the homogeneous material, with no recalibration of $E_a/R$ . Heat is generated only in the paste. The aggregate is inert. Mean temperature must match the adiabatic rise of the homogeneous concrete ( $C=300\,\mathrm{kg/m^3}$ ).

Paper: Analytical and numerical validation of the thermochemical problem of early-age concrete · DOI 10.70271/rirc.v1n2a008

Input data

Item	Value
Unit batch	cement $1.00\,\mathrm{kg}$ ; aggregate $6.30\,\mathrm{kg}$ ; $w/c=0.667$
Specific mass	cement $3.00$ ; aggregate $2.70$ ; water $1.00\,\mathrm{kg/L}$
Concrete $C$	$300\,\mathrm{kg/m^3}$
Paste fraction	$30\%$
Paste $C$	$1000\,\mathrm{kg/m^3}$
Cell	square of side $L=0.05\,\mathrm{m}$
Aggregate	radius $r=0.944\,L$ (about $10\,\mathrm{cm}$ on the reference diameter)
Boundary	adiabatic
$T_0$ , $T_{\mathrm{ref}}$ , $E_a/R$	$25\,^{\circ}\mathrm{C}$ , $25\,^{\circ}\mathrm{C}$ , $4000\,\mathrm{K}$
$Q(t_{eq})$	the same two Hill terms as the homogeneous case

$L=0.05\,\mathrm{m}$ is an upper bound on the conduction path, not a field mix. The report does not split $k$ , $\rho$ and $c_e$ between paste and aggregate in this section. What is closed is the mix, the geometry, the single $Q(t_{eq})$ and the two temperature checks below.

Reference result

Check	Value in the report
Mean temperature	matches the homogeneous adiabatic rise
$\\|T_{\mathrm{paste}}-T_{\mathrm{aggregate}}\\|$	does not exceed $0.3\,^{\circ}\mathrm{C}$
Where the difference occurs	only on the rise, at the highest rate
At the peak and on cooling	uniform field

The report has no pointwise series of that $0.3\,^{\circ}\mathrm{C}$ difference. The file below is the mean temperature the heterogeneous model must recover. The marks $12\,\mathrm{h}\to 40\,^{\circ}\mathrm{C}$ , $24\,\mathrm{h}\to 49\,^{\circ}\mathrm{C}$ and the tail at $55\,^{\circ}\mathrm{C}$ are those of the homogeneous case.

Series t × Tmax × teq × Q(t)

serie_pasta_t_Tmed_teq_Q.csv

Tmax_C here is the reference mean temperature, not the paste core. teq_h uses $E_a/R=4000\,\mathrm{K}$ and $T_{\mathrm{ref}}=25\,^{\circ}\mathrm{C}$ along that mean. Q_kJ_kg is the homogeneous generation ( $C=300\,\mathrm{kg/m^3}$ in $\rho c_e\Delta T^{Q}/C$ ). In the model that $Q$ is applied in the paste; the aggregate generates no heat.

Report figures