The better box model: An analytical estimation of temperature and flow in a free convection air cooled electronics enclosure

A model is described to enable quick estimation of temperatures and air flow in electronic products that are cooled by free convection. Constituting elements are the size and shape of the box-like enclosure, internal heat dissipation, location and hydraulic resistances of inlet and exhaust vents, and of the main internal air path. The model proved to be very useful in the early product development stages to assist in making various fundamental design choices. It is the synthesis from two different analytical models: the first analytical model describes a box shaped product enclosure, the so-called ldquosimple boxrdquo model. This model estimates the air temperature inside and the average temperature of the enclosure itself, provided that the airflow through the product is known. In a free convection cooled enclosure, this air flow is not known a priori, because the flow itself depends on the temperature rise of the air. The second simplified analytical model estimates the air flow through the box as a function of the temperature rise of the air for a free convection situation. Combination of the first and the second model yields a model for the estimation of both free convection airflow and temperatures, the so-called ldquobetter boxrdquo model. This better box model is implemented into a commercial spreadsheet program, and results are compared with CFD and measurements on different flat TVs. The model works well to describe the main thermal and flow aspects of a first rough product idea. Apart from the obvious use to assess the thermal feasibility of a free convection cooled system, the insight in the power balance and the main hydraulic resistances also proves to be very useful in the identification of improvement opportunities in the thermal architecture of the product.