$($Mathematical Modelling Problem$)$ A copper slab $(k=401\frac{W}{m}*K,a=117{10}^{-6}\frac{m^2}{s})$ of thickness $2cm$ is initially at a temperature of $25C.$ At $t=0,$ one side of the slab starts receiving a net heat flux of $5000\frac{W}{m^2},$ while the other side dissipates heat to the surrounding fluid at a temperature of $25$@$C$ with an average heat transfer coefficient of $70\frac{W}{m}2*K.$ How long does it take for the slab temperature to reach $60*C?$

a$.356s$

b$.1091s$

c$.2563s$

d$.12\mathrm{.}5$min

e$.659s$