Problem $2$: Thermal and Momentum Boundary Lavers $(50$ Points$)$

In this problem, you will evaluate the shear stresses and heat fluxes at different locations along a flat plate resulting from water flowing over it$.$

Water at $35$ C is flowing over a flat plate of length $1$ m that is being maintained at $\backslash (\backslash$mathbf$\{85\}\backslash$mathrm$\{$C$\}\backslash ).$

The velocity of water is $\backslash (0\mathrm{.}5\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$

Your goal is to compute the wall shear stress and heat fluxes at different distances from the leading edge of the plate.

The thermo$-$physical properties of water are given in the table below.

Scaling Analysis: For each fluid, assuming a linear variation in velocity and temperature across the boundary layer, estimate the shear$-$stresses and heat fluxes at distances of: $0\mathrm{.}9$ m from the leading edge.

Please show all steps in your calculations!

Total $=2$ fluxes $($shear stress, heat flux$)$