Problem $3$: $(20$ pts$)$

Consider a pot with the lid handle design described below.

Find the length $)=(CD$ such that the temperature at $B($or $C)$ does not exceed $Tc=50C($the limit after

which a human skin begins to suffer$).$ What is the difference in length between making the handle out

stainless steels vs copper?

$[$Hint$1$: find length $AB($or $CD)$ for steel and copper and compare$/$discuss$]$

$[$Hint$2$: the handle can be modeled as a thin fin given it's high aspect ratio$]$

Given:

$T_a=20C$;$T_b=100C$;$,T_c=50C$

kcu$=400\frac{w^m}{mk}$;$,k_{\text{s}\text{t}\text{e}\text{e}\text{l}}=15\frac{w}{mk}$;$,h=7\frac{W}{m^2}k$

$=1\frac{m}{,}h=5cm$;$,R=1cm$

Section $z-Z$ :