The Stefan-Boltzmann law has to do with radiation of black bodies, the Weins law and other concepts related to heat radiation (infrared) and other types of electromagnetic radiation, among other very abstract concepts. All of this is very well documented and can be consulted in the internet. This article has to do with a very simple, totally new application used to keep your enchiladas (I mean your food) hot: A ceramic microwaveable HEAT RETENTIVE PLATE or heat retaining plate what do you prefer?.

What happens if you enclose a disk of very efficient microwave absorbing material in a tight cavity transparent to microwaves like ceramic and preheat it in a 1200 Watts microwave oven for lets say one minute?: That hypothetical disk will get very hot and will radiate in the infrared wave length (if it gets too hot (Like red hot) it will even radiate in the visible zone of the electromagnetic spectrum. Fortunately we can regulate the preheating time.

Now lets say that this disk which I will call heater is in minimum physical contact with the walls of the cavity (separated by pointed bosses), if the cavity is sealed while hot it will form a semi vacuum, so the heat losses will be mainly by radiation since the semi vacuum will minimize also the heat losses by convection.

Now, since the cavity is very tight, part of the radiation of the heater will be reflected and the inside of the cavity (or space in the cavity) will reach a temperature very close to the temperature of the hot body (the heater).

According to the Stefan-Boltzmann formula, the net radiated power is equal to the emissivity multiplied by the Stefans constant, multiplied by the area, multiplied by -here comes the good part- the difference of the heaters temperature minus the surrounding temperature, both at the fourth power (in Kelvin degrees).

Bottom line:

The difference of temperatures have a large bearing (or weight) in the formula since they are at the fourth power. The radiation of the heater will be limited, If this heat storage device is incorporated in the design of a ceramic plate, your food will stay hot. The emissivity of the heater and absorption coefficient of the walls of the cavity can also be manipulated for better control

How to keep the plate from breaking due to thermal shock is another story I have solved the problem. For more information look for HEAT RETENTIVE PLATES in the internet.

By the way, I invented them.
Juan J. Ramirez
El Paso, TX