Modelling the thermal pattern of a statue or column exposed to periodic lighting conditions

In the case of monuments, the thermal effects due to periodic lighting conditions in the long run may be very dangerous. In this article the thermal response of a column or a statue cylindrically shaped and subjected to periodic lighting conditions is studied. Two sources are considered: in the first the intensity is time dependent according to a sinusoid (i.e. diffuse solar radiation from a skylight or window or partially closed outdoor environments); in the second according to a square-wave law (i.e. spot-light switched on and off). The model shows some characteristic features as a function of a dimensionless parameter ?, expressed as the ratio between the radius of the cylinder and its penetration depth, which takes into account the thermal properties of the substance and the lighting period. For high values of ?, the amplitude is poorly dependent on azimuth. The shadowed part is practically insensitive to the azimuth variation. For small values of ? the amplitudes of the thermal wave are very large, causing enhanced thermohydrometric cycles on the bodies. The phase lags between the different point depths increase with ?. The phase lags behave differently in three zones of the cylinder: i) the part facing the light, ii) the two transition zones, iii) the shadowed part. For small lighting durations and small ? the switching on or off of artificial light causes sudden and dangerous variations of temperature. Some hours after the switching off, all the surface of a cylinder with small ? reaches a homogeneous temperature. The mathematical analysis of the thermal behaviour of a cylinder shows how a physical simulation can be made, by changing radius, substance and lighting period, separately or together.