Problem $2$:

Your company has received complaints about condensation on the outside surface of their new model of refrigerator. The walls have fiberglass insulation with thickness $L_f$ in between two layers of $1mm$ thick sheet metal. For the insulation, $k_f=0\mathrm{.}035\frac{W}{m*K}$; for the sheet metal, $k_m=15\frac{W}{m*K}.$ The operating manual suggests that the refrigerator's internal temperature should be kept at $3C.$ The heat transfer coefficients at the inner and outer surfaces of the wall are $h_{in}=5\frac{W}{m^2*K}$ and $h_{\text{o}\text{u}\text{t}}=10\frac{W}{m^2*K},$ respectively. The kitchen temperature averages $23C.$

In initial testing, you find that condensation occurs when the temperature of the outer surface drops below $18C.$

A$)$ Calculate the maximum heat flux through the refrigerator wall that will prevent condensation.

B$)$ Calculate the minimum thickness $L_f$ of fiberglass insulation needed to prevent condensation.

C$)$ If this thickness is used, determine the temperatures on both sides of the fiberglass layer. $($Use $L_f=0\mathrm{.}5cm$ if you could not solve part B$.)$