sleeplessfreek :
i am about to do an experiment on shapes and how their surface area relates to the amount of heat loss. I am wondering if a sphere is the ideal shape because of it has minimal surface area while having the greatest volume. The goal of my assignment is to design and build a prototype (can be a model) of an aspect for water heating in a solar home(meaning it has to be energy efficient). This design has to be innovative which is why i chose a sphere (since it SHOULD reduce heat loss compared to commercial cylinders). Any feedback would be great thanks!
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{ 5 comments }
I would agree that minimum surface area for a given volume has to give the minimum heat loss if maximum heat loss occurs through the surface. Sounds to be quite innovative. Good luck.
Yes a sphere should have less heat loss due to less surface area. However it is harder and therefore more costly to make than a cylinder and in the same diameter space you can fit a larger volume cylinder.
I would bet that the type and quantity of insulating material is more important that the general shape within reason.
most of the answers are covering it well…..
Nice Hint : avoid sharp shapes & any shape with edges , because any edge a flux gets concentrated at it , if that was shear flux , thermal , stresses or whatever…….
and as u c among them sphere is the best
Yes, a sphere is the best shape.
But you may run into problems when it comes to the “real world”. There has to a compromise when true science and reality meet. I understand what you are trying to do, but who would buy a sphere hot water tank? Go look at your own hot water tank and figure how big it would be if it was a sphere holding the same amount of water.
I wonder if would be a good idea to have two or more smaller spheres stacked on top of each other instead of one big tank.
The volume of a sphere of radius r i s (4/3)pi r^3 and its surface area is 4pi r^2. The volume over area ratio is r/3.
The volume of a cube of 2r sides is (2r)^3 and its surface area is 6(2r)^2. The Volume over area ratio is still r/3.
The above shows that there is no advantage using a spherical container over that of a cubical container in terms of heat loss.
A spherical container would be more difficult to fabricate, however the thickness of the material needed to make one is less than that of a cubical container. But that is another matter.