I was thinking about Fourier's Law in heat transfer today and for some reason I am just not understanding the relationships it gives us. Fourier's tells us that if the heat transfer rate is kept constant, then a larger thermal conductivity provides a smaller temperature gradient.
I am confused about the physical reason behind this or I am just misunderstanding the definition of thermal conductivity.
I thought that since thermal conductivity is ease of heat transfer through a material then a high thermal conductivity would mean heat is easily transferred so one side of the material is at a much temperature than the other and a large temperature gradient is created. In fact, this is actually the opposite