An analytical model for time-varying surface heat flux, consisting of two integrals, is used to solve for the wall temperature and fluid bulk mean temperature distributions as a function of axial position and time. This is done for a parallel plate duct with generation occurring in the duct walls. A solution is found using the Laplace transform for the case of generation rate varying linearly with axial position, a situation for which the flux model is exact at small time. A solution, using the flux model, is also found for a wall generation rate that is linear axially and exponential in time. Results from the two integral flux model used are compared to results with a finite difference solution of the governing partial differential equation