The factor \(j_{\mathrm{D}}\) is also used in the correlation. This is defined as

\[j_{\mathrm{D}}=S t(S c)^{2 / 3}=\frac{k_{\mathrm{m}}}{v_{\text {ref }}}(S c)^{2 / 3}\]

where \(S t\) is the Stanton number for mass transfer. Show that the following correlations apply for a flat plate:

\[j_{\mathrm{D}}=0.664 R e^{-1 / 2}\]

for laminar flow, and

\[j_{\mathrm{D}}=0.037 R e^{-0.2}\]

for turbulent flow.