Unsteady Laminar Forced Convection in Ducts With Periodic Variation of Inlet Temperature

A theoretical and experimental study of laminar forced convection in the thermal entrance region of a rectangular duct, subjected to a sinusoidally varying inlet temperature, is presented. A general boundary condition of the fifth kind that accounts for both external convection and wall thermal capacitance effects is considered, and an analytical solution is obtained through extending the generalized integral transform technique. The variations of amplitudes and phase lags of centerline and bulk temperatures are determined as functions of modified Biot number, fluid-to-wall thermal capacitance ratio, and dimensionless inlet frequency. An apparatus has been designed, built, and used for the experimental study to provide validation of the mathematical modeling employed. Good agreement is obtained when the nonuniform sinusoidally varying inlet temperature profile obtained by experiments is incorporated into the theoretical model.