By using the principle of dimensional consistency, what is the correct dimension for thermal conductivity in the SI?

from Fourier law,

q = - K (∆T/L)

but q = Q/A,

hence,

K = (QL) / (AΔT)

Q = Joules/s = ML²/T³

L = L

A = L²

∆T = Kelvin = K

since K = (QL) / (AΔT)

substitute the fundamental units into the above equation we have

K = (ML²/T³) (L) / (L²K) = ML³/T³L²K = ML/T³K

the thermal conductivity, K dimensionality = ML/T³K

or mass lenght per cube unit seconds per Kelvin