Problem #$6$

A composite rod consists of two different materials, A and

B $,$ each of length $0\mathrm{.}5$ L $.$ The thermal conductivity of

Material A is half that of Material B$,$ that is$,\frac{k_A}{k_B}=0\mathrm{.}5.$

Sketch the steady$-$state temperature and heat flux

distributions, $T(x)$ and $q_x^{\text{'}\text{'}},$ respectively. Assume constant

properties and no internal heat generation in either

material. Please comment on the features of the steady$-$

state temperature profile $T(x)$ and heat flux distributions

$q_x^{\text{'}\text{'}},$ and state why they should have those features.