Can you calculate energy required to maintain heating element?

[tsx387]

Regarding a 12v source, is there a way to calculate how much energy is required to maintain a certain temperature through an element? Meaning if you want to maintain an element temperature of 35 F how much energy will it consume using 12v? How will the ambient temperature affect this equation? How much more energy will the element require if the ambient temperature is below 0?

 

[spaceboy033]

Is this a hands on project, or strictly pen+paper?

First you would want to determine the resistance of the element. Note that the element may or may not be ohmic over the range of currents you are considering. If you have the element in front of you, hook up an ammeter and take some data points at varying voltages. If all you have is a book, start looking up some resistivities of the materials you have, and measure lengths+widths of the "wire" making up the element. Ultimately, you should be able to determine the power loss from resistance using your V=IR and P=I^2R formulas.

Next thing to consider is the heat exchange. To model this, perhaps you could start with the heat equation and make some assumptions: consider the problem to be one-dimensional. If you know how to solve a differential equation, identify your boundary conditions, and solve. Otherwise, the solutions to the 1D heat equation are well known and can be looked up. As the for the dissipative constant, k, this is also material dependent and will either need to be looked up or determined from hands on measurements.

Good luck,
Ben