A bonding operation utilizes a laser to provide a constant heat flux, q"0, across the top surface of a thin adhesive-backed, plastic film to be affixed to a metal strip as shown in the sketch. The metal strip has a thickness d = 1.25 mm and its width is large relative to that of the film. The thermo physical properties of the strip are p = 7850 kg/m3, c p = 435J/kg. K, and k = 60 W/m*K. The thermal resistance of the plastic film of width W1 = 40 mm is negligible. The upper and lower surfaces of the strip (including the plastic film) experience convection with air at 25C and a convection coefficient of 10 W/m^2*K. The strip and film are very long in the direction normal to the page. Assume the edges of the metal strip are at the air temperature (To)
(a) Derive an expression for the temperature distribution in the portion of the steel strip with the plastic film (-w1/2 < x < +w1/2).