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     Chris Bailey (c_bailey) Member Username: c_bailey Post Number: 8 Registered: 01-2010 |
I need help with the equations that describe thermoelectricity here. FlexPDE is probably correctly doing whatever I am telling it to. This attached descriptor file is intended to model a thermocouple whose junction is in contact with a heated (or cooled) slab of diamond, whose thermal conductivity is practically perfect. When the entire junction is isothermal, the voltage difference at the far ends of the thermocouple (at a reference temperature) should match the NIST polynomial, and it does within a couple percent or so. The voltage difference should be more interesting if the junction's step shape extends over more length than the heated diamond slab, which is the motivation for this analysis. I have encountered a bizarre special thermocouple made with a very large area extended junction, which the manufacturer claims will average the temperature over this area, apparently misunderstanding that thermocouples generate their output voltage entirely at the junction itself. Clearly their device will not average the temperature, but we need to calculate what it actually does do. There are two things that look wrong to me, although this descriptor gives the expected voltage result in the case where the junction is small and isothermal. The first thing that looks wrong is that in my equation for "Volt", the first term is for Ohm's law, and yet with a factor for conductivity in it, the end result is obviously wrong by orders of magnitude. I discovered that eliminating the conductivity factor in the first term gives a result that looks good. Maybe my discovery is a red herring.... The second thing that looks wrong is that electrical current appears to travel outward on the legs, whereas the only place it should be circulating is right around the junction if the junction is not isothermal, in which case different parts of the junction would be acting as thermoelectric generators and heat pumps. Though this descriptor now defines a high impedance thermocouple type application, I would like this model to also allow for forcing currents to flow by adding voltage value boundary conditions (notice that one is commented out). Real physical thermocouples can also be operated as thermogenerators and heat pumps, and exploring this is useful in my application. I think I misunderstand the equations, which I pieced together from literature articles about thermoelectric generators, Peltier heat pumps, and thermocouples. I guess there are other clues here that I am missing, too. My equations are: EQUATIONS ! Heat conduction and Thomson effect and resistive heating terms sum to zero Temp: k*div(grad(Temp)) + Thomson*Conduct*dot(grad(Volt),grad(Temp)) + Conduct*(magnitude(grad(Volt)))^2 = 0 ! Electrical conduction and Seebeck effect terms sum to zero Volt: div(grad(Volt)) + Seebeck*div(grad(Temp)) = 0 ! Think first term should be multiplied by "Conduct" but get correct looking result by eliminating that factor ??????? Any help or insights would be most welcome! Thanks!
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Thermocouple descriptor