Air flowing parallel to a $20m$ long, $2m$ high, $0\mathrm{.}20m$ thick wall with $Re=4{10}^4**x$ where $x$ is taken from leading edge of wall, $Pr=0\mathrm{.}7$; Wall temperature is maintained at $T_5,$ while air at $T_{}.$

For each of situation given below give an empirical correlation or equation to calculate $,$ and explain clearly why it is chosen, justification accounts to $50\%$ of grade.

a$.$ Heat transfer at the end of wall? $[10]$

b$.$ Heat transfer for the entire wall is required? $10$

c$.$ Heat transfer at a location four meter from leading edge of wall? $[10]$

d$.$ Heat transfer for the last $4$ meters of the wall? $[10]$

e$.$ Repeat $C$ above if first $2m$ are at air temperature while rest of plate at Ts$.[10]$