$1.$ AISI $316($ $=3\mathrm{.}48$ x $10-6$ m$2/$s$)$ stainless steel plate of $4$ cm thickness is maintained at room temperature $(25)$ initially. This plate is then placed in a furnace, maintained at $850.$ Considering the convection heat transfer coefficient to be h$=120$ W$/$m$2$K$.$ Answer the following using one$-$term approximations. $[$Refer to Appendix or literature for determining properties of AISI $316]$ a$.$ Using one$-$term approximation, determine the temperature at the center of the plate after $3$ min. Show details of the calculations. $[$Ans:$415$ C$][10$pt$]$ b$.$ Using one$-$term approximation, determine the surface temperature of the plate after $10$ min. Show details of the calculations. $[$Ans:$777$ C$][10$pt$]$