Question $3.$ Certain graphite reinforced polymer

composite material may be modelled as a layer of car$-$

bon fibers $0\mathrm{.}45$ mm thick sandwiched between two lay$-$

ers of polymer, each $1$ mm thick. The conductivity of

graphite is $5\mathrm{.}7W*m^{-1}*K^{-1}$ across the fibers while the

conductivity of polymer material is $0\mathrm{.}35W*m^{-1}*K^{-1}.$

$($a$)$ Estimate the R $-$value $(R^{\text{'}\text{'}})$ of the composite

material.

$($b$)$ Estimate the heat flux across this material

when the temperature difference of the air on its two

sides is $20C$ with convection coefficients of $10$ and

$20W*m^{-1}*K^{-1},$ respectively.