A semi$-$infinite solid bar, x $0,$ is initially at a uniform temperature Ti$.$ Obtain an expression for the unsteady$-$state temperature T$($xt$)$ in the bar, if at time t$=0$ the left end of the bar is brought in contact with a heat reservoir and follows a temperature at x$=0$ is given as:T$($O$,$ t$)=$ To $+($AT$)$osinct for times t $0.$Assume constant thermophysical properties for the solid.Given: Tr $=100\backslash$deg C; To $=200\backslash$deg C $=2$m s$-1$; t $=$ time in seconds;thermal diffusivity, a$2,$ of the bar $=10-4$ m$2/$s