$2.$A temperature field is described by T$($x$,$y$)=$c $($x$/$L$)2($xy$)/$L$2+($y$/$L$)2+300$K where c is $50$K and L is $2$m$,$and the material is pure copper$($find k in Table A$\mathrm{.}1).$Use this temperature field to $($a$)$Evaluate the heat flux vector,~ q$00=$ krT$,$at the location x$=1\mathrm{.}5,$y$=0\mathrm{.}5($answer: $12\mathrm{.}5$ i$+2\mathrm{.}51$ j kW$/$m$2).$ For the remainder of this problem assume that the value of k is constant at the value you used for this answer.