Mathematical Model of an Electric Glass Furnace: Effects of Glass Color and Resistivity

A quantitative mathematical analysis of coupled electrical power dissipation, heat transfer, and natural convection in a hypothetical all-electric glass tank furnace was conducted using a two-dimensional computer model. The model simulated numerically the complex interactions which occur among charge, mass, energy, and momentum transport in a vertical plane section through the melter. Computer generated contour plots of the power density, isotherms, and stream-lines in the rectangular enclosure are presented for both a flint glass and an amber glass, each with and without the variation of electrical resistivity with temperature taken into account. The total electrical power consumption was held constant in all cases investigated in order to establish a common basis for comparison of the results. It is shown that although the variation in melt resistivity, associated with the range of temperatures encountered in the interior of the hypothetical glass furnace, approaches 10 percent of the mean isothermal value, it has subsequently very little effect on the calculated temperature and velocity distribution within the enclosure over a wide range of effective thermal conductivities. Hence the electrical resistivity can be assumed consistent for all practical purposes when these are the results of primary interest. It is also shown that the electric melting behavior of colored glasses may be quite different from that of a flint glass under the same basic furnace operating conditions.