= Thermal conductivity
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<Thermal conductivity> is the material response coefficient in <Fourier's law>. For an <isotropic> material it is a <scalar> $k$, with units $\mathrm{W\,m^{-1}\,K^{-1}}$; larger positive $k$ means a larger conductive <heat flux> for the same <temperature gradient>. It can depend on <temperature> and composition. Direction-dependent response in an <anisotropic> material is described by a <thermal conductivity tensor>. The two worked examples use stipulated positive constants, rather than measured values for named materials.
<Thermal conductivity> describes material response, whereas <thermal resistance> also includes geometry: for the steady bar, $R_{\rm th}=L/(kA)$. Doubling $k$ at fixed <length>, cross-sectional <area> and end <temperatures> halves <thermal resistance> and doubles the rate of <heat transfer>. Doubling <length> changes <thermal resistance> without changing the material's <thermal conductivity>. This distinction lets a designer improve cooling either by choosing a higher <thermal conductivity> or by shortening and widening the path. It also explains why the less conductive layer in <thermal resistance> takes the greater <temperature> drop.
<Thermal diffusivity> answers a different question: how rapidly a <temperature> disturbance spreads. Its usual model $\kappa=k/(\rho c_p)$ also involves <mass density> $\rho$ and <specific heat capacity> $c_p$, so equal <thermal conductivities> need not imply equal rates of warming.
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