6. (30 pts.) A long brass bar of rectangular cross-section, whose width w is much greater than its thickness b, is maintained at a constant temperature To. Suddenly, an electric current is passed through the bar, and the bar is put in contact with air at temperature To (a) Obtain the differential equation, the initial conditions, and the boundary conditions that could be solved to determine the time-dependent temperature profile in the middle section of the bar as a function of position and time. (10 pts) (b) Obtain the differential equation and the boundary conditions that could be solved to determine the steady temperature profile in the middle of the bar as a function of position. (10 pts) (e) Obtain the differential equation and the boundary conditions that could be solved to determine the steady temperature profile at the bar edge as a function of position. (10 pts)