$($a$)$ An insulated $1-$D bar is $1$ m in length. A heat transfer rate of $10$ W results in a temperature difference of $10C$ across the length bar. If the thermal conductivity of the bar is doubled $($all other factors unchanged$),$ what is the resulting temperature difference?

$($b$)$ Laminar flow forced convection occurs across the entire span of a $1$ m long plate. The resulting average heat transfer coefficient was $20\frac{W}{m^2}-K.$ What was the local heat transfer coefficient at the trailing edge of the $1$ m long plate?

$($c$)$ Convection over a flat plate produces a heat transfer coefficient of $40\frac{W}{m^2}-K$ when using fluid A $.$ If the same Reynolds number is achieved for fluid B $,$ but the thermal conductivity fluid B is double that of fluid B$,$ what is the resulting heat transfer coefficient?

$($d$)$ A copper fin is MORE EFFICIENT than a similar fin made of stainless steel if all other parameters are identical $($True$/$False$)?$

$($e$)$ The transient temperature response of a $10$ mm diameter stainless steel sphere subjected to forced convection of $50\frac{W}{m^2}-K$ may be computed using lumped capacitance.