Effect of delay in thermal systems with long ducts

We analyze simple, one-dimensional models of thermal systems with long ducts in which there is a delay due to the time it takes the fluid to travel along the duct. A general solution of the dynamic problem of a single duct with time-dependent inlet and ambient temperatures is obtained, and several special cases are described in detail. Of particular interest is the periodic case in which the inlet and ambient temperatures are sinusoidal in time. Also presented is a model that includes the effect of thermal inertia of a heater located at the entrance to a duct for which the time-dependent temperature fields for periodic heating are calculated. Periodic behavior in closed loops and open loops with branching are also discussed.