Oscillatory Behaviour of Transient Thermal Problems in Microelectronics

G. De Mey (Univ. of Ghent, Belgium), B. Więcek (Lodz Univ. of Techn., Poland), C. Hertleer, L. Van Langenhove (Univ. of Ghent, Belgium), V. Chatziathanassiou (Aristotle Univ. of Thessaloniki, Greece), M. Łoniewski, H. Madura (Military Univ. of Techn., Poland)

If an object is heated with a constant power source, the temperature will rise continuously towards a steady state value. In this contribution, the possibility of a temperature rise showing a damped oscillation will be analysed theoretically. It will be shown that such a phenomenon can be observed by a small change of the heat transfer equation describing the convective cooling. To model natural convection cooling, the simplest way is to use a constant heat transfer coefficient. This coefficient can also include the heat transfer by radiation toward the solid objects in the neighbourhood. A constant heat transfer coefficient means that, as soon as a surface has a higher temperature than the ambient air, the natural convection cooling starts immediately without any delay. For radiation, this is a reasonable assumption as radiation proceeds with the speed of light. For natural convection on the other hand this assumption is not so obvious. First of all, the heated surface has to warm up the nearest layers of the surrounding air. After that, the buoyancy force will move the warmed air upward and convection cooling can start. Hence, there will be a delay between the temperature rise and the heat removal by convection. In the next section, we present a small change in the classical heat transfer equation describing natural convection cooling.