Problem #$1$:

A gas $)$ is heated up by a radiator of square shape that runs hot fluid $($at $T_{,i}=98C)$ inside. Consider one side of this radiator as shown below with six rectangular fins. The width and thickness of the squared steel plate are $W=250mm$ and $L_1=15mm.$ The thermal conductivity of the steel plate is $k_s=19\frac{W}{m}-K.$ Fins and their base plate are made of aluminum alloy with $k_{Al}=202\frac{W}{m}-K.$ The thickness of the aluminum base plate is $L_2=10mm.$ The thickness and length of rectangular aluminum fins are $t=3mm$ and $L_t=40mm,$ respectively. The corresponding convective heat transfer coefficients of two fluids are $h_i=120\frac{W}{m^2}-K$ for hot fluid and $h_c=24$ W$/\frac{?}{m^2}-K$ for gas. There is a thermal contact resistance of $R_{,x}^{\text{'}\text{'}}=1\mathrm{.}2{10}^{-1}{m}^2\frac{K}{W}$ between the steel plate and aluminum base plate. With a steady$-$state operation and one$-$dimensional heat transfer, you are asked to do the following:

a$)$ Treat the entire fin array as a thermal resistor, construct a thermal circuit to represent the heat transfer from hot fluid to gas.

b$)$ Determine the fin efficiency $({}_t)$ and the fin effectiveness $($st$)$ of a single rectangular fin.

c$)$ Determine the thermal resistance of the thermal resistor made of the $6-$fin array, R$$arnuy$.$

d$)$ Estimate all other thermal resistances in your circuit.

e$)$ Determine the total heat transfer rate from hot fluid to gas of the given setting.

f$)$ Determine surface temperature of the aluminum base plate, $T_b.$