$(30)$ Consider a $11m$ flat, square horizontal plate embedded in an insulating material and exposed

to air at $10C$ as shown in the figure. The plate is electrically heated to maintain its exposed surface

at $100C.$ The bottom surface and the edges of the plate are insulated, while the upper surface is

also exposed to Solar irradiation of $500\frac{W}{m^2}.$ The "Reflectivity $"$ of this opaque plate is given in

the following figure. The radiation temperature of the environment is also $T_{\text{R}\text{a}\text{d}-\text{e}\text{n}\text{v}}=10C$

a$.$ What is the absorption rate of the solar radiation on the plate? $\frac{W}{m^2}$

b$.$ What is the net radiative heat exchange rate between the plate and the environment?

c$.$ For quiescent$/$still air conditions, find the $h_{\text{c}\text{o}\text{n}\text{v}}$ and estimate the power required $P_{\text{e}\text{l}\text{e}\text{c}}$ in

Watts to maintain the surface temperature at $100C.$

d$.$ Now, consider turbulent wind blowing over the surface with a free stream air velocity of

$10\mathrm{.}0\frac{m}{s}$ blowing "from one of the sides $($figure$).$ Find the $h_{\text{c}\text{o}\text{n}\text{v}}$ and calculate the "Power"

required to maintain the same temperature of $100C$ over the surface.

Hint: Look at your HW#$3$ Pr$.$#$5$

Note: ${}_{}={}_{}$

For air: $v_{\text{a}\text{i}\text{r}}=20\mathrm{.}0{10}^{-6}\frac{m^2}{s}$;${}_{\text{a}\text{i}\text{r}}=40\mathrm{.}0{10}^{-6}\frac{m^2}{s}$;$Pr=0\mathrm{.}7$;$k_{\text{a}\text{i}\text{r}}=0\mathrm{.}0263\frac{W}{m}K$;$=0\mathrm{.}0025K^{-1}$

Radiation: $=5\mathrm{.}67{10}^{-8}\frac{W}{m^2}{K}^4,R{a}_{\frac{?}{\text{b}\text{a}\text{r}}(L)}=\frac{g(T_s-T_{0s})L_c^3}{v}$;$R{e}_L=\frac{\text{V}\text{e}\text{l}\text{.}L}{v}$

Characteristic $L_c=$ Area$/$Perimeter ;