Performing a local heating electrically in a glass furnace is a common industrial practice. A difference of electrical potential will be applied at given locations in the glass furnace, and an electrical current will heat the glass by Joule effect, which acts as a source term in the energy equation.

The numerical treatment of electrical heating does not present great difficulties. Under classical assumptions, the electrical potential field is governed by a Laplace equation:

(25–1)

where is the electrical conductivity of the material, and can be a function of temperature .

Equation 25–1 is associated to boundary conditions of the Dirichlet type (potential imposed) or of the Neumann type (electrical current imposed). In all practical cases, either the electrical potential is imposed as a constant, or the electrical current is zero. Each type of boundary condition can be prescribed in Ansys Polydata along each part of the boundary.

The Joule contribution to the energy equation is written as

(25–2)

where stands for the heat source per unit volume in the energy equation.

When considering Equation 25–1 and Equation 25–2, it is important to note that the assumption is made of an electric current of the AC type, single phase. This is reflected through the factor in Equation 25–2, which results from an averaged integration over unit of time. Therefore, peak values should be provided when entering data on potential.