Consider an infinitely long two$-$dimensional rectangular fin of thickness $2H,$ width $W,$ and thermal

conductivity $k.$ The base temperature of the fin is $T_0,$ the ambient temperature is $T_{},$ and the heat

transfer coefficient between the fin surfaces and

the surrounding is $h.$

a$)$ Derive the differential equation for the

steady$-$state two$-$dimensional temperature

distribution of the fin. State all your

assumptions clearly.

b$)$ Write the appropriate boundary conditions

for the $0x$ and $0yH$ domain.

Do not change the position of the

origin!

c$)$ Find the two$-$dimensional temperature profile

in the fin assuming that the differential

equation modelling the heat transfer in the

rod is given by:

$\frac{de{l}^2}{del{x}^2}+\frac{de{l}^2}{del{y}^2}=0,$ where $=T-T_{}$