A practical application of the Stefan-Boltzmann law
The Stefan-Boltzmann law has to do with black body radiation, Wein’s law and other concepts related to thermal (infrared) radiation and other types of electromagnetic radiation, among other very abstract concepts. All this is very well documented and can be consulted on the internet.
This article is about a very simple and brand new app to keep your enchiladas (I mean your food) warm:
A microwave safe ceramic HEAT RETENTION PLATE or heat retention plate, which do you prefer?
What happens if you enclose a disk of a highly efficient microwave absorbing material in a microwave-transparent, airtight cavity like ceramic, and preheat it in a 1200-watt microwave oven for, say… a minute:
That hypothetical disc will get very hot and will radiate in the infrared wavelength (if it gets too hot (like red hot) it will even radiate in the visible part of the electromagnetic spectrum. Fortunately we can regulate the preheating time.
Now let’s say this disc which I’ll call a heater is in minimal physical contact with the cavity walls (separated by sharp protrusions), if the cavity is sealed hot it will form a semi-vacuum, so heat losses will be mainly by radiation since that the semi-vacuum will also minimize convective heat losses.
Now since the cavity is very narrow, some of the radiation from the heater will be reflected and the interior 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 Stefan constant, multiplied by the area, multiplied by – here comes the good part – the temperature difference of the heater minus the ambient temperature, both in the fourth power (in degrees Kelvin).
Bottom line:
The temperature difference has a great influence (or weight) on the formula since they are at the fourth power. Radiation from the heater will be limited. If this heat storage device is incorporated into the design of a ceramic plate, your food will stay warm.
The emissivity of the heater and the absorption coefficient of the cavity walls can also be manipulated for better control.
How to prevent the plate from breaking due to thermal shock is another story, I have solved the problem. For more information look for HEAT RETENTIVE PLATES on the internet.
By the way, I invented them.
Juan J. Ramirez
El Paso, Texas
