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

Explanation:

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

i believe the answer would be:

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