# Heat transfer in air gaps between slabs

I am working on the modelling of heat transfer in a storage unit consisting of a number of slabs contained inside a rectangular duct. A hand made sketch of the storage is below, as seen from above. The idea is that the air comes to the slab bank with a certain velocity, here 0.75 m/s. Calculating the Reynolds number gives in this case around 13330. Then the air is forced through the gaps between slabs. In this case the slabs are 1.3 cm thick and the gaps are 1 cm thick. Air is accelerated to about 1.7 m/s. Calculating the Reynolds number in the gaps gives about 2200. If I use a Nusselt number correlation for laminar flow in the gaps, where heat transfer takes place, my calculations don't fit well to my experiment. The slabs are relatively short, only 0.5 m long. My calculations result in much slower heat transfer. I think this is due to the fact that the air upstream of the slabs is turbulent, and as it enters the gaps it should become laminar, but for a good part of the slab length (or all of it) the flow is not really laminar so the Nusselt correlation is too conservative. I was wondering if somebody knows of correlations (and the source) for this particular case.

• Regardless of the formulas, a numeric model that matches reality is the correct one. Focus on mass flow rate through the system and then track the energy. Remember that air that loses heat will tend to get more dense- so what are the densities before and after? What is the pressure distribution at slabs leading and trailing edges? Pressure can also cause increases in density.
– Abel
Commented Jan 10 at 13:51
• Which nusselt correlation are you using? Commented Jan 10 at 14:13