Dynamics of three-dimensional temperature field in electrical system of floor heating

In the paper dynamics of a three-dimensional temperature field in the system of direct floor heater was investigated. A step response (heating on curve) and local and global time constants of the device were determined. Then, a spatial–temporal distribution of the field in the system controlled by the on–off regulator was found. The mathematical model of heat propagation was a non-homogeneous and homogeneous equation of a three-dimensional diffusion with an adequate set of boundary conditions. Four methods were applied for the solution of the above: superposition of states (coupled with separation of variables), finite elements, criterion of an averaged time constant and superposition of step characteristics. It was found that time profiles of the temperature depend very strongly on the position of an observing point. All relations were processed numerically. The obtained results are presented in a graphic form. A physical interpretation of the achieved solutions is included.