The reinforced concrete foundation slab (4x6x1.2 m) with initial temperature of +10 °C is laid on the frozen ground (slab - concrete, base - sand, bedding - soil).
Plane problem of transient heat transfer.
Slab initial temperature Tslab = +10 °C
Soil temperature Tsoil = -5 °C
Air temperature Tair = -10 °C
Convection coefficient is 23 W/K·m2
Soil freezing depth is 1.3 m.
Planned hardening time is 1 week.
Resistance of the heating cables is constant.
Exothermic heat of the concrete Q = f(time, temperature)[W/m3] - a function of time under the average expected temperature.
Calculate temperature distribution in the slab during the hardening.
Temperature difference between the center and the surface of the slab is about 20 °C in average, which is within the project requirements.
During the calculation period the concrete temperature doesn't drop below 0 °C. Heating rate doesn't exceed of 5 °C/hour.
After 4 days the temperature in the center of the slab reaches its peak value of 47 °C.