Consider a fin of rectangular cross section for heat rejection in an electronic system. The heat dissipation within the fin corresponds to a uniform heat generation of 10^5W/m^3 and assume uniform properties equivalent to plain carbon-steel. Given that the convection heat transfer coefficient is 25W/m^2K, ambient temperature is 20 C, and the base of the fin is at 400 K. Determine the temperature distribution along the fin and the total heat transfer rate from the fin to the surroundings. State any assumptions you make clearly.