So I know that conduction is transfer of thermal energy by direct contact via molecular collisions.
For conduction, $Q/t$ is the rate of heat flow and is heat current ($I$). My textbook says that the rate of heat flow is constant across any number of slabs between 2 heat reservoirs, and I understand why this is so because if I use electric current as an example, the current in constant through resistors of different ohms in a series circuit too.
But then, the textbook goes on to show how conservation of energy also explains why. It says that "If the rate of energy transfer were not steady across all slabs, the slab that conducted heat the fastest would become cold. A cold slab could not conduct heat to warmer slabs because heat moves from hot to cold."
I don't understand their explanation that they offered from a conservation of energy standpoint. Could you please clarify this for me? Why would the slab that conducted heat the fastest become cold if the rate of energy transfer were not steady?
For your reference, the equation for conduction is: $$\frac{Q}{t} = kA\frac{T[\text{hot}] – T[\text{cold}]}{L}$$