Where the lengths, l, refer to the outside dimension of a cube and the subscripts refer to the outer and inner cubes.
In this improved model for designing a nested cooler system I assume that the effective area of a wall through which heat flows is proportional to the geometric mean of the inner and outer areas. This approximation is based on assuming spherical symmetry in heat flow.
For insulating cubical shells in series this results in:
Where
the lengths, l, refer to the
outside dimension of a cube and the subscripts refer to the outer and
inner cubes.
Assume that all film coefficients are equal to 1 BTU/hr-F-Ft2 , the walls are costructed of 2lb/cuft expanded polystyrene (K=.22 BTU-in/sqft-F-hr), the outer wall is two ft long and 1 in thick, the inner wall is 1 ft long, the inner temperature drop is 51F, and the outer temperature drop is 45F; solve the following for inner wall thickness:
The
result is that the thickness of the inner wall is very close to zero.
The presumed film coefficients of the inner wall dominate its
conductance.
The calculated heat loss for six such walls is only 216 BTU/hr. At that rate 24hrs would require melting about 6 lbs of eutectic brine ice.
The film coefficients have the greatest uncertanity in these estimates; experiments are therefore needed to verify these predictions.
Dmartin@newarts.com 2004 07 18 [Top]