Numerical solution of unsteady three-dimensional heat transfer during space cooling using ceiling-embedded piping

A finite-difference procedure is presented for solving unsteady, three-dimensional heat-transfer problems for cooling buildings by the use of cold water flowing within regularly arranged pipes embedded in the ceiling slab. Our procedure is based on solution of the three differential equations for heat conduction within the ceiling slab, convection cooling with water and the indoor energy balance. Inaccuracies in previously used procedures for steady, one- or two-dimensional flows may distort the results considerably.