The weight of the insulation in a spacecraft may be more important than the space required. Show analytically that the lightest insulation for a plane wall with a specified thermal resistance is the insulation that has the smallest product of density times thermal conductivity.
GIVEN
Insulating a plane wall, the weight of insulation is most significant
FIND
Show that lightest insulation for a given thermal resistance is that insulation which has the
smallest product of density (?) times thermal conductivity (k)
ASSUMPTIONS
One dimensional heat transfer through the wall
Steady state conditions
The resistance of the wall (Rk), is.
where
L = the thickness of the wall
A = the area of the wall
The weight of the wall (w) is
Solving this for L
Substituting this expression for L into the equation for the resistance
Therefore, when the product of ? k for a given resistance is smallest, the weight is also smallest.
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