Upon inspecting the supplementary material provided form the above paper, most recently, regrettably some issues were found which are better to be modified and corrected for a much improved experience of the researchers who may like to follow the analysis. Of course these do not affect what are written in the actual paper. The modifications/corrections in the supplementary file are described here.

Following on from Eq. (S5) in supplementary data, the left side vertical axis in Fig. S1 in supplementary data should be marked as (II – I)/Re, which was (II – I) that was incorrect. Following on from Eqs. (S7) and (S8) in supplementary data, Eq. (S9) in supplementary data should have a Re in the equation, it was missing in the originally submitted file. Eq. (S9) has thus been modified to include the Re:

Fig. S2 in supplementary data has similar issue that the left side vertical axis should be labelled as (III – I)/Re, not (III – I). Anyway Figs. S1 and S2 have been modified to be consistent with the equations outlined.

There can be a confusion created with the term R_o used in the original supplementary material. As such the first paragraph has been modified which now reads as: Historical experimental measurements have validated, for a wide range of Re(s), that the similarity solution to the velocity profiles of the plate flow is excellent. It is, however, very useful to correlate the result using a parabolic formula $u/U_{\infty }=1-{\left(r/R\right)}^2$, instead, where U_∞ is the velocity of the bulk fluid in plate flow and R may be taken as the boundary layer thickness of laminar region at x (m). $r/R=1-\eta /R_o$, where η is the dimensionless transformation variable. R_o is taken as 3.67, beyond which u is considered to be U_∞ (with a difference of less than 0.01 of the U_∞).

In addition, it was found that Fig. S3 in supplementary data has different vertical axis opposite in location with that in Figs. S1 and S2 making it inconvenient to compare among them. It has been modified also (see below). Here (V – IV)/5000 is plotted in Fig. S3 so to have similar axis as in Figs. S1 and S2 for the ease to compare (also refer to Eqs. (S12) and (S13) in supplementary data).

For plate flow, the local Reynolds number equivalence γ was about 151.5, which should have been about 154.6 as in the results section. So is in the supplementary data.

Supplementary data to this article can be found online at https://doi.org/10.1016/j.eng.2025.06.008.