I'm not sure I fully understand the difference between thermal conductivity and thermal diffusivity as thermal properties of a material and would appreciate if anyone could clarify. I understand thermal diffusivity is for a transient case and conductivity is for steady state. This is what I've understood of the two parameters: conductivity: rate at which heat flows through a material when one side is hot and the other is cold [W/mK] diffusivity: a measure of how long it takes for a temperature pulse to traverse a certain thickness when a heat source is briefly applied to one side of a material. [m^{2}/s] If a material has high conductivity, wouldn't it automatically have low diffusivity as well? In this case why is there a need to define both of these? Also in terms of design, if say a saucepan needs a material with high conductivity to ensure the heat from the stove is transferred through the base of the saucepan and to the food. It would also need a low diffusivity as well so that the material gets heated quickly.
Not necessarily. thermal diffusivity = (thermal conductivity) / (density times specific heat) specific heat is defined as energy needed to heat a unit mass of material by one degree, so (density times specific heat) is the energy to heat a unit volume of material by one degree. As you said, for steady state heat conduction the heat capacity is irrelevant (because the temperature isn't changing), and the rate of heat flow only depends on the thermal conductivity. But for a non-steady state, you also need to consider the amount of energy it takes to heat up the material itself. If different materials have the same thermal conductivity, the one with the lowest (density times specific heat) will get to a steady state condition fastest, and that material will have the highest thermal diffusivity.