Question $1)-$ A rod with rectangular cross$-$sectional area as shown below is exposed to convection on its top and

bottom surfaces, while receiving constant surface heat flux from bottom surface. At the steady state condition, the rod

is producing volumetric energy $q_g^{}[\frac{W}{m^3}],$ while its two ends are kept at constant surface temperature $T_1.$

a$)$ Using slicing method $($Method of extended surfaces$)$ find the temperature profile inside the rod.

b$)$ Locate the location and value of maximum temperature in the rod.

Note: $T=T(x).$

$T_{}=25[C],h=50[\frac{(W)}{(K)*m^2}],q_s^{\text{'}\text{'}}=100[\frac{(W)}{m^2}],q_g^{}=5{10}^5[\frac{(W)}{m^3}],T_1=20[C]$

$k=400[\frac{(W)}{(m)*(K)}],W=8[mm],h=3[mm],L=100[mm]$

Section A view

Iso view