Why does increasing heat conductivity decrease Nusselt number?

Question

Normally we expect that when heat conductivity(k) increases heat transfer is also increases. But for fluids increasing k decreases Nusselt number. My senses tell that using high conductive fluid cause higher heat transfer but description of Nusselt number tells opposit of it. What am I missing?

Answer 1

You are missing that $$h=k\frac{Nu}{L}$$where L is the characteristic length. So, for a given value of the Nusselt number, increasing the thermal conductivity corresponds to an increase in the heat transfer coefficient. In any of the correlations that are out there, if you express Nu as a function of the Reynolds number and Prantdl number, and then solve for the heat transfer coefficient, you will always find that h increases with k.