Turbulent Forced Convection Inside a Parallel-Plate Channel With Periodic Variation of Inlet Temperature

The analysis of heat transfer in turbulent forced convection subject to a periodically varying inlet temperature leads to a nonclassical Sturm–Liouville type eigenvalue problem for which no known solution is available. In this work a new methodology is developed to alleviate the need for the solution of a complex eigenvalue problem in the analysis of turbulent forced convection inside a parallel-plate channel with a periodicially varying inlet temperature and a uniform constant wall temperature. In this approach, the problem is transformed to the solution of a system of coupled ordinary differential equations in the complex domain, which could readily be solved. For the cases considered it is demonstrated that the solutions obtained from the decoupled system, referred to as the lowest-order solution, produce sufficiently accurate results. The variation of the amplitudes and phase lag of both fluid bulk temperature and the wall heat flux along the channel is investigated and a simple approximate analytic formula is developed for determining the variation of the phase lag for the bulk temperature along the channel.