Periodic steady-state heat transfer in cooling panels

Abstract

A slab is considered to be exchanging heat internally with a fluid flowing through pipes embedded in the slab and externally by convection and radiation with the ambient surroundings in a periodic fashion. In practice, such cases are encountered in panel cooling of buildings, in which the heat produced within or inserted into a room is absorbed by a cold fluid flowing through pipes imbedded in the roof slab of the room. A method is developed for predicting the performance of such systems, which is based on a finite-difference solution of the transient two-dimensional heat conduction differential equation within the roof slab containing the cooling pipes. The boundary conditions on the upper surface are periodic, i.e., it is assumed that the daily cycle of the ambient temperature and the incident solar radiation are repeated on consecutive days, thus leading to a periodic steady-state solution. In the case of floor slabs, the problem becomes steady-state unless intermittent operation is to be examined. A parametric study is presented, in which the effect is examined of the most important parameters, including the pipe spacing and the cooling fluid temperature.