Unsteady state temperature fields in a slab induced by line sources

Solutions for the unsteady state temperature fields and heat fluxes from the surfaces due to single or multiple line sources in a slab and in a semi-infinite solid are derived by using integral transform techniques. The convective boundary condition (boundary condition of the third kind) is applied at the surfaces. Responses to a step change in the coil power are given. Also a cyclic case is studied, in which power in coils is alternately switched on and off as described by a cyclic square wave function. As an application the use of a floor or a wall as storage of heat from electric cables is discussed and equations applicable for dimensioning of the heat storage system and simulation of operation are given. The temperature isotherms generated by a line source are approximately circular in the vicinity of the line source. Based on this an approximate method to calculate heat losses in steady state from single or several pipes in a slab or ground with convective heat transfer at surface is illustrated.