Hello,

I'm currently modelling a micro heater sitting in air. I was concerned with, up until recently, temperatures up to 100'c. Now, I'm making devices that go up to 1000'c. I've been using boussinesq's theory for the 100'c model. My question is, as a rule of thumb, what temperature differences, in air, does the boussinesq approximation start to fall apart at? Also, for the 100'c model I've only been using conduction and convection as modes of heat transport. When should you start using radiation? It's my understanding that radiation becomes the dominant mode of heat transport at high temperatures. Basically I'll be making different models of heaters of different temperatures and would like to save on computation time.

Regards,

MW

"It's my understanding that radiation becomes the dominant mode of heat transport at high temperatures" This is a wrong conclusion, to see this by yourself, take the simple insulated pipe model (All heat transfer book explain this problem) and change the numbers etc.. Radiation heat transfer at moderate surface temperatures is more than the convection part (unless you are using a forced convection system), The Boussinesq approximation is valid as long as the temperature differences(not the temperature level)in your system are moderate

Hello,

Thanks for the reply. Sorry, I forgot to mention that the heaters are sitting in air at room temperature, with no forced convection. I understand that it's to do with temperature difference rather than temperature level. So, roughly, at the most you would see a temperature difference of 1000'c.

Another reason that I ask this is because my numerical model is giving me temperatures and fluid velocitys that are not possible. My results for temperature were much higher than the melting temperature of the device. My results for velocity were above 1 m/s (the device is 20 micrometers squared). As you can see those are ridiculous answers.

In my model, I assign power density rather than a temperature. I obtain my power density (W/m^3) from experimental work. The point of the model is to obtain the results for fluid flow and temperature. At low power densitys, my model gives me accurate results and have been verified against a published paper and on top of that seem entirely reasonable. So, I came to the conclusion that at the higher temperatures, boussinesq approximation is no longer valid and gives unrealistic convective heat transfer. And also, because the model is not using radiation it is losing another method of heat transfer. Any thoughts on this?

You are absolutely correct... at the temperature difference and absoulute temperature u r operating u have to use the incompressible ideal-gas law and also include radiation in ur model... but including radiation will increase the computational time considerably.