Question $1(6$ marks$)$

A plane wall separates two fluids at temperatures $T_1$

and $T_2.$ In addition to convection heat transfer, the left

surface is exposed to solar flux $q_{\text{s}\text{o}\text{l}}^{\text{'}\text{'}}$ with absorptivity $,$

while the right surface is subjected to net radiation

cooling flux with surroundings $q_{\text{r}\text{a}\text{d}}^{\text{'}\text{'}}.$

$(1\mathrm{.}1)$ Develop an expression for $q_{\text{r}\text{a}\text{d}}^{\text{'}\text{'}}$ in terms of:

$T_{s1},T_{s2},T_1,T_2,h_{c1},h_{c2},q_{\text{s}\text{o}\text{l}}^{\text{'}\text{'}},$ and $.$ Note:

temperature distribution is not required.

$(1\mathrm{.}2)$ Calculate $q_{\text{r}\text{a}\text{d}}^{\text{'}\text{'}}$ if: $T_{s1}=50C,T_{s2}=26C,T_1=40C,T_2=24C,h_{c1}=20\frac{W}{m^2}*K,$

$h_{c2}=10\frac{W}{m^2}.K,q_{\text{s}\text{o}\text{l}}^{\text{'}\text{'}}=500\frac{W}{m^2},$ and $=0\mathrm{.}6.$

$(1\mathrm{.}3)$ For wall thickness $L=0\mathrm{.}3m,$ calculate the thermal conductivity $k.$

$(1\mathrm{.}4)$ Calculate the emissivity of the right surface $()$ if the surroundings temperature is $10C.$

Also, determine the value of the radiation coefficient at the right surface $(h_r).$