Numerical and experimental analysis of unsteady heat transfer with periodic variation of inlet temperature in circular ducts

Abstract

This work focusses on a numerical and experimental analysis of unsteady forced convection in hydrodynamically developed and thermally developing laminar air flow in a circular duct, subjected to a periodic variation of the inlet temperature. The experiments were conducted over a wide range of Reynolds number (281.2 ≤ Re ≤ 1024.3) and inlet frequency (0.01 ≤ β ≤ 0.20 Hz) of the periodic heat input. In the numerical study, the non-uniform inlet temperature amplitude profile derived from the experiments, was included in the numerical model. A fully explicit, second-order accurate finite difference scheme was developed and used for the solution of the unsteady energy equation. Numerical results are obtained with the fully developed parabolic velocity profile under the boundary condition of the first kind, which was verified by the experiments. Temperature variations along the centerline of the circular duct are observed to be thermal oscillations with the same frequency as the inlet periodic heat input and amplitudes that decayed exponentially with distance along the duct. Thermal response along the wall exhibits negligible amplitude variation with changes in Reynolds number and inlet frequency. The variation in the periods and amplitudes of the thermal oscillations are observed to be a function of spacial system variables only. Satisfactory agreement between the numerical and experimental results are obtained.