Heat loss whilst in steady state

[smithy360]

Hi all,

I have a system which involves a ventilated box with a heat source located inside, if the heat source inside is say 1KW and I know it eventually reaches a steady state, in an ideal world it would reach this steady state by effectively ventilating 1KW of heat through the opening and assuming the boundaries of the box were adiabatic. However, obviously in the real world this isn't the case as there will be some heat loss from the container itself, dependent on material, if the heat loss through the fabric is relatively small, say 10W, how would I account for this heat loss. I should be more clear, if I am heating a box of fluid immersed in a large reservoir of ambient fluid held at a constant 20 degrees C and I know that if the box of fluid where perfectly insulated it would heat up the fluid in the container to 25 degrees C before reaching steady state as described above, i.e. as much heat gets vented as I am putting in. How would I determine the temperature reached in the container when accounting for the heat loss from the fabric? Naively I would say that as the heat loss is 1% of the heat flux going into the container I could just say that the temperature reached would be 99% of the 25 degrees C it is expected to reach. I say naively as I am not sure this is a fair assumption at all, is it better to say that now the flux going in, the 1KW, is now being balanced by the flux going out through the vent plus the heat loss, i.e. the vent flux is now equal to 990W?

Any help of guidance would be much appreciated, and I apologise in advance if this makes no sense!

 

[gsal]

I am having a hard time understanding your system, but I think you are on the right track...

If you have some kind of electric element in the middle of some kind of box and air is going in on one and and going out on the other end, then, yes, some heat is going to be lost through the box to the surrounding air and hence not all the heat generated by the electric element will be part of the air leaving the box.

The heat lost through the box to the surrounding air, though, will come from the air inside the box, right? This will happen more toward the exit where the air is hot, and not at the entrance, though...you know what I am saying?

This "steady state" that you talk about, though, is not your typical one where you could treat the air as being stationary and being heated from the center towards the surround box...instead, the air is always flowing and heated as it flows...

 

[smithy360]

Thanks for taking the time to reply. Sorry I know it was a little bit hard to understand as written. The system ends up in a steady state with a layer of hot air sitting on a layer of cool air, so the box has a simple two layer stratification. The flow in the box gets to the steady state by a balance in the flows through the openings, ambient air being drawn in the lower opening and hot air being exhausted through the top vent, and the flow from the plume emanating from the heat source at the base of the tank. In this way the temperature also reaches a steady state, all of the plumes energy goes into keeping the upper warm layer well mixed so it is of uniform temperature (still sat above the cooler ambient layer), and as said earlier the heat put into the upper layer is matched by the heat being extracted from the upper vent, hence keeping the temperature steady.

My question still remains on how to work out what the temperature of this upper layer will be in steady state but with additional heat loss through the container itself, if I calculate it as being 25 degrees C is it right to just say it will be 99% of that, or is a slightly more involved idea of now saying the plume heat flux entering the bottom of the upper layer is matched by the sum of the heat lost through the opening and the heat loss through the fabric of the upper layer (obviously only over the surface area in contact with the upper layer).

Thanks again.

 

[smithy360]

Just from thinking about it all logically I assume that I am correct in my thinking in terms of equating the relevant fluxes, it also seems to match up to some data I have so hopefully it is correct. Thanks again for the help and feel free to respond if my thinking is definitely not correct!

All the best.