The influence of heat capacity and its spatial distribution on the transient wall thermal behavior under the effect of harmonically time-varying driving forces

An analysis was developed for the theoretical investigation of heat capacity and of the effects of its spatial distribution on the thermal behavior of structural walls of uniform thermal resistance. The numerical solution of the governing differential equations under the appropriate initial and boundary conditions, allows the prediction of the time-varying heat flux during the transient heating of walls until quasi steady-state conditions are developed asymptotically. It is derived that as far as the fundamental physical behavior of a clear wall section is concerned, although the time depended heat flux is effectively damped and phased out as the wall heat capacity increases, the average quasi steady-state heat flux is constant, irrespectively of wall heat capacity, incident solar radiation intensity, radiation absorption at the exterior wall surface and particular weather conditions defining wall heat loss or gain. However, even though the average quasi steady-state heat flux is constant irrespectively of the wall heat capacity, its time depended value during the development of transient is strongly influenced by the spatial distribution of heat capacity at a direction perpendicular to the wall plane, something which is determined by the wall time constant.