Solve Problem $3\mathrm{.}1($Thomson text book$).$ Note that plexiglass acts as an insulat Assume one$-$dimensional transport, by neglecting its transfer along its width e thickness. $($Points: $15)$

$3-1$

Describe how you would mathematically model the following physical problem; clearfy mating $($and justifying$)$ all of the assumptions you make:

A this aluminum strip, $3mm$ thick by $2cm$ wide by $25cm$ long, and encased in plexiglass is shown in the sketch$)$ has one end immersed in boiliag waser and the other end immersel is ist waier. Wo wish to know the Iemperature distribution within the alumieum at disuly elate

$6.$ Draw the physical system and show the direction of transport, and fluxes, along with the coordinate system.

b$.$ Identify your differential volume and the IN$,$ OUT, ACCUMALATION, SOURCE, SINK terms.

c$.$ Perform your molecular transport balance, assuming a one$-$dimensional flow direction.

d$.$ Derive the particular solution of the temperature distribution within the alyminum at steady$-$state. State the boundary conditions you used to obtain the particular solution $($hint$-$ boundary conditions are given in a subtle way in the problem Statenunt above$)$