$-$ E$\_($gen $)^()=$q$^()$A$*$L

$-$ E$\_($in $)^()=$a$\_($in $)$

$-$ E$\_($out $)^()=$q$\_($out $)$

$()/($bar$)($I$)\_($ge $)^()=(2)(10)=20^(60$t$)$

Consider two blocks A and B of different materials that are in contact with each

other as shown in the Fig. $1.$ The left block has a length of L$\_($A$)=2$m$,$ thermal

conductivity k$\_($A$)=8($W$)/($m$)*$K$,$ and a volumetric heat source of q$\_($A$)^()=10($W$)/($m$^(3)).$

k$\_($B$)=4($W$)/($m$)*$K$,$ and q$\_($B$)^()=20$

For block B$,$ these quantities are L$\_($B$)=5$m$,$k$\_($B$)=4$

$2($a$)$ and Fig. $2($b$).$

Apply an energy balance at the junction of the two blocks to select a plausible $,$Egen$\_($A$)=10(2)=20($w$)/($m$^(2))$

temperature profile shown in Fig $2.$ Show all the steps.

E$\_($gen $()/($anit$))$ arca: E$\_($in $)-$E$\_($rif $)+\backslash$Delta E$\_($gen $)=$F$\_($st $),$ Egen $\_(()()10)=(20)($s$)=100($w$)/($m$^(2))$

Fig. $1$

$-$ Egen$^()=$q$^()$A$*$L

$-$ E$\_($in $)^()=$a$\_($in$)$

L$\_($A$)=2$m

L$\_($B$)=5$m

k$\_($A$)=8($W$)/($m$)*$K

k$\_($B$)=4($W$)/($m$)*$K

q$\_($A$)^()=10($W$)/($m$^(3))$

q$\_($B$)^()=20($W$)/($m$^(3))$

q$=$q$^(\text{'}\text{'})$A

Consider two blocks A and B of different materials that are in contact with each

other as shown in the Fig. $1.$ The left block has a length of L$\_($A$)=2$m$,$ thermal

conductivity k$\_($A$)=8($W$)/($m$)*$K$,$ and a volumetric heat source of q$\_($A$)^()=10($W$)/($m$^(3)).$

For block B$,$ these quantities are L$\_($B$)=5$m$,$k$\_($B$)=4($W$)/($m$)*$K$,$ and q$\_($B$)^()=20$

$($W$)/($m$^(3)).$ Two possible temperature profiles for the two blocks are shown in Fig.

$2($a$)$ and Fig. $2($b$).$

Apply an energy balance at the junction of the two blocks to select a plausible

temperature profile shown in Fig $2.$ Show all the steps.