You are to design a rooftop solar absorber made of black chrome. The purpose is to heat up $0\mathrm{.}01kg{s}^{-1}$ of tank water from $300$ to $360K.$ Every $1m^2$ surface of solar absorber can accommodate $1m$ length of thin$-$walled copper tube of diameter $0\mathrm{.}02m$ beneath its surface.

At noon, the intensity of direct solar irradiation $($normal to horizon$)$ was measured to be $1,154W{m}^{-2}.$ The ambient temperature is $305K,$ while the sky temperature is $270K.$ The convective heat transfer coefficient on the surface was measured to be $5W{m}^{-2}{K}^{-1}.$

a$)$ Write the steady$-$state energy balance equation when no water is flowing through the tube. What is the surface temperature of the solar absorber$?(15$ marks$)$

b$)$ How much heat load is required to heat up the water? $(10$ marks$)$

c$)$ Write the steady$-$state energy balance equation taking into account of the heat flux, $q_{\text{w}\text{a}\text{t}\text{e}\text{r}}^{\text{'}\text{'}},$ to be transferred to the water. $(10$ marks$)$

d$)$ Calculate the convective heat transfer coefficient within the tube, and subsequently estimate the tube length required. $(30$ marks$)$

e$)$ What is the total surface area of absorber$,A_{\text{s}\text{o}\text{l}\text{a}\text{r}\text{,}},$ required? $(5$ marks$)$

f$)$ Calculate the surface temperature of the solar absorber with water flowing through the tube. $(20$ marks$)$

g$)$ Your Supervisor suggests to increase the tube length per surface area of absorber to increase the overall solar efficiency. What is your take on this? Briefly elaborate your reasoning. $(10$ marks$)$

Provide final answer for every question $,$thank you.

Flow Rate is $0\mathrm{.}01$ kg$/$s $.$