The thermal model of the filament developed in this chapter assumed that the only heat-loss path was conduction down the filament. In practice, about 15% of the total heat loss is through the air gap. How does the steady-state parabolic heat-flow solution change if one adds a heat conduction path through the air gap? (You can explore this either with analytical methods or with a modification of the finite-difference solution of Section 12.4.1.)