$6-75$ For laminar boundary layers, it is reasonable to expect that $\frac{}{{}_t}$~~$P{r}^n,$ where $n$ is a positive exponent. Consider laminar boundary layer flow over a flat plate with air at $100C$ and $1$ atm $,$ where the thermal boundary layer thickness is approximately $15\%$ larger than the velocity boundary layer thickness. Determine the ratio of $\frac{}{{}_t}$ if the fluid is engine oil $($unused$)$ under the same flow conditions.