Transient conjugate convection heat transfer in duct with wall generation

An approximate 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 in the first time domain with generation occurring in the duct walls. An exact solution is found using the Laplace transform for the case of generation rate varying linearly with axial position, a situation for which the two integral flux model is exact. An approximate solution, using the flux model, is also found for a wall generation rate which is linear axially, and exponential in time. Validation of the two integral flux model used is accomplished by comparing results with a finite difference solution of the governing partial differential equation. Comparisons are also made to a much simpler quasi-steady analysis