In our case the Bejan number decreases with the increase of mass flow rate or Reynolds number of the multiphase fluids through a packed bed. However, if mass flow rate increases Nusselt number, ie, heat transfer coefficient increases. We are considering the heat transfer between the two fluids in co-current flow. As the the Nusselt number and Bejan number showing opposite trends in heat transfer coefficient values, should I consider that the higher Nusselt number and lower Bejan number prefers higher heat transfer between the two phases of the fluids passing through the packed bed. If, so then if i consider two different geometry (straight and bent) of same dimension and same fluids and same packed materials, which one should be the best geometry for the heat transfer applications? The best geometry should produce higher or lower values of Bejan number?
As the mass flow rate increases, Nu increases but Bejan number (Be) should be decreased because the Nu shows heat transfer rate whereas Be shows the irreversibilty because of heat transfer. So, it is obvious that the irreversibilty decreases as the heat transfer rate increases.
More explanation:
Be = ST/(ST+SP)
where ST is entropy generation because of heat transfer losses and SP is because of friction losses. Now, as the mass flow rate increases friction will increase which causes SP to be increased. Conversely, as the mass flow rate increases Nu increases which results in higher heat transfer thus reducing heat losses and causes ST to be reduced.
Also, I have noticed from one of my research papers published in heat and mass transfer (you can see my profile) that ST is 10 to 100 times greater than SP. So, it is clear that decreasing ST will reduce Be.
Thanks
Faraz Ahmad
According to Wikipedia (2019), Bejan number is the ratio of heat transfer irreversibility to total irreversibility due to heat transfer and fluid friction. Bejan number in convection (Be) is the combination of the Euler (Eu) and Reynolds (Re) numbers. In most cases, when Nusselt number is high and Bejan number is low, heat transfer is maximized.
https://en.wikipedia.org/wiki/Bejan_number
Awad, M. M. (2016). The science and the history of the two Bejan numbers. International Journal of Heat and Mass Transfer, 94, 101–103. doi:10.1016/j.ijheatmasstransfer.2015.11.073
Bejan number is a dimensionless number demonstrates the fraction of thermal entropy generation to the total entropy generation (thermal and frictional). Therefore, the Bejan number has no effect on heat transfer but rather is a description of the entropy generated by heat transfer and fluid friction. For any thermal system, when Bijan values are close to one, it is indicates that thermal entropy generation is predominant on the total entropy generation compared with frictional entropy generation.
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