Consider airflow over a plate surface maintained at a temperature of $220C.$ The temperature profile of the airflow is given as

$T(y)=T_{}-(T_{}-T_s)exp(-\frac{v}{{}_{\text{f}\text{u}\text{i}\text{d}}}y)$

The airflow at $1$ atm has a free stream velocity and temperature of $0\mathrm{.}08\frac{m}{s}$ and $20C,$ respectively.

Additionally, the local convective heat transfer coefficient along the $x-$axis is given by another equation as below:

$h_x(x)=b{x}^{-0\mathrm{.}1}$

Where $x(m)$ is the distance from the leading edge of the plate.

You have to determine the heat flux on the plate surface, the convection heat transfer coefficient, and the thermal conductivity of the air.

Formulate an equation to calculate the average heat transfer coefficient $\frac{?}{\text{b}\text{a}\text{r}}(h(L))$ from a plate of length $L.[2$ pts$]$ Show all your steps to get full points.

If unit of $x$ is meter, and $h_x(x)$ is $\frac{W}{m^2*(K)},$ what is the unit of constant $b$ in equation $(2)?[1$ pts$]$

In order to calculate heat transfer, you will need air properties such as thermal conductivity and thermal $[1$ pts$]$ diffusivity. Select, what temperature you will use to find air properties.

b$.20C$

c$.120C$

a$.220C$

If $b=2$ units, and ${}_{\text{f}\text{l}\text{u}\text{i}\text{d}}=3\mathrm{.}565{10}^{-5}\frac{m^2}{s},$ what is the total heat transfer from a plate of $1$ meter $[3$ pts$]$ width and $2$ meter length?

By applying the principles of no$-$slip and no$-$temperature jump conditions, estimate the average thermal conductivity of the air.

$[3$ pts$]$