Question $3)[50$ Pts$]$

A $3-$m long flat plate is exposed to a steady incompressible laminar flow of water having a density of $1000k\frac{g}{m^3}$ and a viscosity of $0\mathrm{.}001$ Pa$*$s$.$ See the following figure. According to the following figure, the $x$ direction represents the direction of flow while the $y-$axis represents the direction normal to the flow. The heat transfer properties of water are: Specific heat : $4186\frac{J}{kg*K}$ and Thermal conductivity : $0\mathrm{.}606\frac{W}{m*K}$ The freestream velocity is $1\mathrm{.}5\frac{m}{s}.$ The plate is present at $25C$ while the bulk of the fluid is present at $70C.$Assume constant physical properties.

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Calculate:

A$)$ The Reynolds number at $x=3m[5Pts]$

B$)$ The friction coefficient using the Blasius solution at $x=3m[5$ Pts$]$

C$)$ Momentum Diffusivity $[5$ Pts$]$

D$)$ The Prandtl Number $[5$ Pts$]$

E$)$ The local Nusselt number at at $x=3m$ using the Sieder$-$Tate correlation. $[5$ Pts$]$

F$)$ The convective heat transfer coefficient at at $x=3m[5Pts]$

G$)$ What is the velocity at $y=0?[5$ Pts$]$

H$)$ What is the temperature at $y=0?[5$ Pts$]$

I$)$ What is the effect of increasing the velocity on the convective heat transfer coefficient and the friction coefficient? $[10$ Pts$]$