... configuration.¹

This is only true for the steady-state configuration. If the problem were dynamic, the flux across a position may vary as the system settles toward an equilibrium configuration.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

....²

The true diffusive flux would be -khq_x where h is the height of the hallway, but the height of the hallway is constant so we can fold this into the parameter k. In problem #2, the height changes, so we need to keep track of h(x).

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.