Question about the Surface Nusselt Number calculation
 

Hi, I‘m doing a simulation about the natural convection in a square cavity, set the thermal conductivity of air at 293 K . when at post-processing, I need the Surface Nusselt number Nu= q*L/(T_wall-T_ref)/k. I get the T_ref = 290 K by the mass-weighted average of fluid's static temperature. I wonder whether the thermal conductivity k needs to use the value at 290 K rather than at 293 K? Thanks a lot.

It depends... But it's unlikely to evaluated at the reference temperature. It's more likely to be at the wall temperature or film temperature. But some people do use the reference temperature for convenience. There's volumes written on this topic.

You need to consult your favorite handbook for this situation or use the same method as whatever you might be comparing your Nu with. It could be anything.