Following continuous casting, a steel slab whose surface temperature is $T_{s}K$ is left to cool

in air. The dimensions of the steel slab are as follows: length $=900mm,$ width $=800mm,$

and thickness $=100mm.$ The convective heat flux from the surface of the slab to the

ambient is $4050\frac{W}{m^2}$ and the ambient temperature $(T_{})$ is $298K.$ Under the given

conditions, an average value of the heat transfer co$-$efficient $(\frac{?}{\text{b}\text{a}\text{r}}(h)),$ for heat$-$transfer from the

surface of the slab to the ambient, is given as

$\frac{?}{\text{b}\text{a}\text{r}}(h)(\frac{W}{m^2}*K)=1\mathrm{.}476(\frac{T}{L}{)}^{0\mathrm{.}25}$

where,

and $T_{}$ are both expressed in $\{$:$K)$ and $L$ is the length of the slab in metres.

Calculate $T_S.$