Understanding a Sealed Container with a Heater & Fan

[Logan Fife]

Hi, I would really like some insight here, I don't know what I'm doing! also, sorry if i get the terms wrong and miss the obvious, this isn't my field.

I will try to keep this short:
I think that if you have a solid object, with a Heating element in the centre, and the surface in ambient temperature, then any point inside that object will have a steady state temperature determined only by the difference between the element and the ambient, with some coefficient related to position. (like the midpoint of a rod will always be half way between its to ends).

can this idea be carried over to a sealed container with a fan/heater inside, and the ambient heat-sink on the outside? meaning, say ambient was 20°, and my fan heater was putting out 40°. if I pick a random point and measure its SS temp as 25°, will that point always have a SS temperature given by the formula

ambient + (heater - ambient)/4

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I'm thinking mainly of forced convection, where the airflow stays the same but the heater and ambient temperatures vary. I don't think pressure would have much to do with it, because the container is very sealed. I suppose the question is will the airflow from the heater have a different pattern depending on its temperature? if it is the same pattern for all temperatures, then the heatflow will be along the same paths, and behave like a solid object.

is this model likely to work out? what assumptions have i made? is there a better (and still simple) model? thanks very much!

edit: is there a better place for this question? Mechanical Engineering perhaps, or even Classical Physics?

 

[David Grider]

"Hi, I would really like some insight here, I don't know what I'm doing! also, sorry if i get the terms wrong and miss the obvious, this isn't my field.

I will try to keep this short:
I think that if you have a solid object, with a Heating element in the centre, and the surface in ambient temperature, then any point inside that object will have a steady state temperature determined only by the difference between the element and the ambient, with some coefficient related to position. (like the midpoint of a rod will always be half way between its to ends)."

This is mostly accurate as far as you have gone (and assuming that enough time has passed to reach a steady state equilibrium. You may have assumed that the outside temperature will be at ambient temperature, however, which is an unlikely assumption.
The heat transfer is straightforward in a homogeneous material and proportional to the heat transfer coefficient for that material, and the delta T (temperature difference) across the material. The situation becomes much more complicated when you wish to consider what happens at a transition to another material, or the change from conduction in the solid to convection in air (ambient?). As you might imagine, "natural" convection currents will transfer heat at a different rate from forced convection (produced by a fan - which will speed the heat transfer - and at different rates depending on the velocity -see laminar vs turbulent heat transfer). For most situations of interest, the design of the airflow in the box, the heat transfer to the box, and the cooling of the box by the ambient surroundings are easier to set up and measure than to try to calculate. Typically conduction is much more straightforward than convection.