Legacy · Thermal validation

Infinite slab

Placement-temperature campaign. This is not the canonical slab: here the final adiabatic rise is $50\,^{\circ}\mathrm{C}$ , $T_{\infty}=20\,^{\circ}\mathrm{C}$ and the concrete has another diffusivity.

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

Input data

Item	Value
Thickness	$L=1.0\,\mathrm{m}$ , opposite faces at $T_{\infty}$
$T_{\max}$ point	$(0,\ L/2)$
$Q(t_{eq})$	$\Delta T=50\,^{\circ}\mathrm{C}$ , $a_1=40.10873\,\mathrm{h}$ , $c_1=1.54782$
$E_a/R$	$4000\,\mathrm{K}$
$T_{\mathrm{ref}}$	$20\,^{\circ}\mathrm{C}$
$T_0$	$20$ , $30$ or $40\,^{\circ}\mathrm{C}$
$T_{\infty}$	$20\,^{\circ}\mathrm{C}$
Concrete	$k=9\,\mathrm{kJ/(m\cdot h\cdot^{\circ}C)}$ ; $\rho=2400\,\mathrm{kg/m^3}$ ; $c_e=0.75\,\mathrm{kJ/(kg\cdot^{\circ}C)}$ ; $h^{2}=0.005\,\mathrm{m^2/h}$
Horizon	$t_f=480\,\mathrm{h}$
$C$ in the $Q$ column	$300\,\mathrm{kg/m^3}$

The adiabatic-FEM × isothermal-FEM comparison on this slab, at the three placement temperatures, is not part of the closed benchmark. The report leaves that check as a complement. This page closes analytical versus FEM, with the particular curve at $E_a/R=0$ .

Reference result

Regressed $\Delta T=50.00\,^{\circ}\mathrm{C}$ . $\beta=1.548$ .

$T_0$ (°C)	$\tau$ (h)	RMSE of $T(t)$ (°C)	$T_{\max}$ FEM / analytical (°C)
20	34.27	0.008	34.7 / 34.7
30	32.72	0.027	38.0 / 38.1
40	30.68	0.054	43.1 / 43.1

On the series, FEM peaks are $34.67\,^{\circ}\mathrm{C}$ ( $33.58\,\mathrm{h}$ ), $38.04\,^{\circ}\mathrm{C}$ ( $26.63\,\mathrm{h}$ ) and $43.09\,^{\circ}\mathrm{C}$ ( $17.53\,\mathrm{h}$ ).

Series t × Tmax × teq × Q(t)

No suffix: isothermal source. Suffix _particular: source of the analytical solution ( $t_{eq}=t$ ).

Report figures