A viscous fluid flows over an external flat surface of length $2\mathrm{.}5$ m at a velocity $q,$ as follows:

$T=250C$:$=1050k\frac{g}{m^3},=98510-6N.\frac{s}{m^2}$

The experimental measurements and related calculations det $,T=400C$:$,=974k\frac{g}{m}3,=47010-6N.\frac{s}{m^2}$

At $250C$:$h_{\text{a}\text{v}\text{g}}=2000\frac{W}{m^2}.K$ and at $400C,h_{\text{a}\text{v}\text{g}}=4200\frac{W}{m^2}.K$ mined the average heat transfer coefficients over the entire flat surface as follows:

$($a$)$ Determine the critical distance from the leading age where the flow is expected to transition from laminar to turbulent flow for the two conditions, i$.$e$.,$ at $250C$ and $400C.$

$($b$)$ What are the reasons the transition from laminar to turbulent flow occurs at different critical distances from the leading edge

$($c$)$ What are the reasons for the average heat transfer coefficient is significantly higher for the higher temperature.