Legacy · Thermal validation

Cylindrical shaft

One isothermal calibration, three placement temperatures. What changes with $T_0$ is the time parameter of the particular curve and $T_{\max}$. The regressed amplitude stays at $50\,^{\circ}\mathrm{C}$.

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

Input data

The report states the source as a rise $\Delta T^{Q}$, not as a cement content. Q_kJ_kg uses $C=300\,\mathrm{kg/m^3}$, the interconversion consumption, only to close the unit. A code that integrates in °C uses $\Delta T^{Q}=Q\,C/(\rho c_e)$.

The analytical route regresses the particular curve with $E_a/R=0$. The input $Q(t_{eq})$ is not recalibrated.

Reference result

From the report. Regressed $\Delta T$ stays at $50.00\,^{\circ}\mathrm{C}$ (deviation under $0.01\%$). $\beta=1.549$.

The largest error in the geometry × $T_0$ matrix is this shaft at $40\,^{\circ}\mathrm{C}$. On the series of this page the FEM peaks are $43.31\,^{\circ}\mathrm{C}$ ($42.07\,\mathrm{h}$), $52.39\,^{\circ}\mathrm{C}$ ($27.28\,\mathrm{h}$) and $62.85\,^{\circ}\mathrm{C}$ ($18.48\,\mathrm{h}$).

The shaft FEM file did not store the generation column. In the particular series, Q_kJ_kg was rebuilt from the regressed Hill law ($\Delta T$, $\tau$, $\beta$) of each placement.

Series t × Tmax × teq × Q(t)

No suffix: Tmax_C is the FEM axis temperature, teq_h uses $E_a/R=4000\,\mathrm{K}$ and $T_{\mathrm{ref}}=20\,^{\circ}\mathrm{C}$, Q_kJ_kg is the $50\,^{\circ}\mathrm{C}$ isothermal calibration at that $t_{eq}$.

• T0 = 20 °C
• T0 = 30 °C
• T0 = 40 °C

Suffix _particular: teq_h $=t$ and Q_kJ_kg is the particular curve ($E_a/R=0$) used by the analytical solution.

• particular, 20 °C
• particular, 30 °C
• particular, 40 °C

Report figures