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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.

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Franz Roman
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  • 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 Jan 10 '24 at 13:51
  • Which nusselt correlation are you using? – Sami Safarini Jan 10 '24 at 14:13

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It could be that the flow is not fully developed as is the case for laminar flow and it could be the length you have is not enough for it to be so, have you considered a transition value between the two Re values? i.e. Re reduces by 2000 points every 0.1m of length.

Sami Safarini
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  • The reasoning is that turbulence tends to help with convective heat transfer. – Sami Safarini Jan 10 '24 at 14:17
  • Yes, thanks. I was actually using an equation for fully developed laminar flow. For developing flow I had not found an equation which is best for a computer program. But using an appropriate value for developing flow gives better results. – Franz Roman Jan 10 '24 at 20:59
  • Is the method called Reynold-Colburn by any chance?, Reynold analogy has something in it for turbulent flow. – Sami Safarini Jan 11 '24 at 14:12