$2.$ A large plate is with $4$ in thickness subjected to convection $($T$=90\backslash$deg F$),$ radiation $($Tsky$=50\backslash$deg F$),$

and specified temperature on the top surface and no conditions on the bottom surface. The top

plate temperature is constant at $75\backslash$deg F$.$ The thermal conductivity of the plate and its emissivity are

given to be k $=7\mathrm{.}2$ Btu$/$h$$ft$\backslash$deg F and $=0\mathrm{.}6.$ Convection heat transfer coefficient h $=12$ Btu$/$h$$ft$2$

$\backslash$deg F$.$

Determine $($a$)$ the temperature distribution equation in the plate, and $($b$)$ the bottom surface

temperature for steady one$-$dimensional heat transfer.