Modeling and optimizing a road de-icing device by a nonlinear heating

Abstract

In order to design a road de-icing device by heating, we consider in the one dimensional setting the optimal control of a parabolic equation with a nonlinear boundary condition of the Stefan–Boltzmann type. Both the punctual control and the corresponding state are subjected to a unilateral constraint. This control problem models the heating of a road during a winter period to keep the road surface temperature above a given threshold. The one-dimensional modeling used in this work is a first step of the modeling of a road heating device through the circulation of a coolant in a porous layer of the road. We first prove, under realistic physical assumptions, the well-posedness of the direct problem and the optimal control problem. We then perform some numerical experiments using real data obtained from experimental measurements. This model and the corresponding numerical results allow to quantify the minimal energy to be provided to keep the road surface without frost or snow.

Thermal performance of a controllable pavement solar collector prototype with configuration flexibility

“…As discussed in Sections 3.2.1 and 3.3.1, supply temperature, flow rates, and pipe length are critical operating parameters for the heating loads of the HEAL prototype. Although an evident strategy to optimize the heat loading of the HEAL system is to maximize the energy harvesting capacity and minimize the energy consumption, advanced strategies to optimally control the road de-icing systems already exist in the literature [42,43].…”

Parameter study and experimental analysis of a scraping de-icing concept for thin ice using end-of-life wire ropes

“…The heating cable method uses a metal wire or carbon fiber bundle as the heating body, converts electrical energy into heat energy after electrification, and transfers the heat to the road surface utilizing heat conduction to melt ice and snow. Although the heating cable method has many advantages such as low pollution, low cost, good thermal stability, and convenient control, it consumes a large amount of power with soft energy efficiency [25].…”