Synchronizing time-varying discrete heating elements in forced convection for minimal thermal resistance

In this paper, we numerically optimize the triggering time of several discrete heaters attached to a channel in forced convection. The flow is assumed laminar and fully developed and the strength of each dissipating heat source is determined by a sinusoidal function of time having a phase lag (image) and a frequency (ω). The objective of this work summarizes to numerically determine an optimal set of activation phase lag and position for each heater, such that minimal thermal resistance is achieved for the system. The calculations were performed using a finite volume numerical code. The temperature history in any point of the channel was decomposed as a combination of steady-state and two harmonic components leading to a linear system of differential equations. The optimization procedure relied on a genetic algorithm, which was coupled to the numerical code implemented. The optimized results show that the activation phase lag and position of each heater can significantly decrease the overall thermal resistance. The designs optimized with respect to phase lags are relatively insensitive to frequency. The numerical results were found to qualitatively agree with the scale analysis proposed.