X-Message-Number: 2011 Subject: cold room approximations; drawers Date: Tue, 23 Mar 93 11:56:26 EST From: Now that Bob Ettinger has pointed out that the curvature of a room that is small compared to its insulation causes it to radiate heat faster, the question arises, how to more accurately approximate the behavior of a real room? Brian Wowk used a spherical room. Here are two other possibilities: Option I: Do the same computation Brian Wowk did, but assume that cold is lost over the outside surface of the insulation rather than the inside surface. Intuitively, it seems that this approach will give a lower bound to the behavior of the real insulated room, but I can't prove it. In this model, the surface area asymptotically increases as the square of the insulation thickness, and the cold lost per square inch is inversely proportional to the insulation thickness. Thus in the limit the total cold lost is proportional to the insulation thickness, and it isn't clear that thicker insulation works better. So this approximation may be useless because it may give the result that no amount of insulation helps. Option II: Assume the insulation covering the room is a slab on each surface, a quarter cylinder on each edge, and an eighth of a sphere on each corner. Treat cold loss on the face with the simple linear approximation Brian used in his first program. Approximate cold loss at each corner as an eighth of the cold that would be lost from the center of a solid sphere with radius equal to the thickness of our insulation. Approximate cold loss along each edge as one fourth of the cold that would be lost per unit length from a long cylinder with radius equal to the thickness of the insulation and a cold wire down the center. The sphere approximation can use the same formula Brian posted for a hollow spherical room, except we have an inside radius of zero. The cylinder approximation will require repeating the derivation that Brian used for the hollow sphere, except with one less dimension. I have no intuition for whether this second option would overestimate or underestimate the cold lost from the room. I also have no intuition about whether people will be able to decipher my description without a diagram :-). Here's a top view of the model of the room which happens to look the same as a side view: .--------------. / \ | +------------+ | | | | | | | | | | | | | | | | | | +------------+ | \ / -------------- The inner square is the usable space, and the outer oval is the outer boundary of the insulation. The corners of the insulation should look like a quarter circle. (I'm not suggesting that anyone actually build it in this shape, I'm just suggesting that if we pretend it is built in this shape we can figure out how it would behave without too much work.) The approximation I'm suggesting essentially assumes perfect planar insulators added where the insulation changes shape: .--------------. / | | \ |--+------------+--| | | | | | | | | | | | | | | | | |--+------------+--| \ | | / -------------- Here there is good thermal contact between the corners of the cold room and the round-shaped insulation contacting the corner. Brian's original approximation simply multiplied the surface area of the inner room by the conductivity of the insulation, and it was equivalent to supposing the same perfect insulators are added in the same places, but there is no thermal contact between the edges and corners of the cold room and the edges and corners of the insulation. I don't know if any of this makes sense to the readers. Maybe email isn't the right place to describe it. It seems to me that doing a detailed finite element approximation before building the thing is a good idea. I'm hoping someone (Brian?) has the enthusiasm to modify Brian's program to implement either option I or option II or some better idea. I would do it myself except I have a thesis to write. :-). Another idea: Could we put the patients in drawers so we don't have to walk into a room with no oxygen? Maybe we could also have two or more independent LN2 dewars keeping the room cold, and some mechanism that makes it possible to remove them one at a time for servicing without walking into the room. Any practical implementation of this would have some sort of air lock mechanism for each drawer that would avoid sucking a lot of room-temperature air into the -130 degree cold room when you open a drawer. Tim Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=2011