ИСТИНА

During winters and ice storms, ice forms on high voltage electrical transmission lines. This ice formation often results in downed lines and has been responsible for considerable damage to life and property. The model concerns melting of ice due to a higher current applied to the transmission line. We consider a two dimensional cross-section which contains four material layers: (i) transmission line, where the Joulean heat is generated, (ii) water due to melting of ice, (iii) ice, and (iv) atmosphere. Heat propagation and ice melting are put as a Stefan like problem. The model takes into account gravity. This leads to downward motion of ice and to forced convection in the water layer, in addition to natural buoyancy driven convection. The convection is described by the Navier-Stokes equation. The most intensive melting occurs in a region near the top of the electrical wire. A very thin layer of water carries weight of the ice shell due to big pressure gradients. Big temperature gradients are also present there. In order to make the model computationally tractable, we single out simplified submodels and demonstrate estimations of melting time using values obtained for those submodels treated quasi-statically. The main submodels are: (i) heat transfer and melting, assuming known velocity field in the liquid, and (ii) boundary layer equations assuming known melting rate and a geometry of ice/water frontier. We also discuss the validity of physical assumptions, sensitivity to external boundary conditions, and present numerical results. Support by a grant from Manitoba Hydro is acknowledged.