Leak free current collector assemblage for metallurgical vessel and methods of manufacture

A method of manufacturing a current collector assembly, the method comprising:

• receiving as an input for a model an initial number and arrangement of conductive elements for a hypothetical current collector assembly;
• iteratively solving the model on a computer to determine as an output a heat distribution within a hypothetical current collector assembly;
• identifying as a solution to the model a number and arrangement of conductive elements associated with a current collector;
• and
• manufacturing the current collector assembly, wherein the current collector assembly comprises a defined plurality of apertures within a refractory base of the current collector assembly in a pattern configured to receive the number and arrangement of conductive elements identified as the solution to the model.

A method of manufacturing a current collector assembly, the method comprising:

• iteratively solving the model on a computer to determine as an output a heat distribution within a hypothetical current collector assembly, wherein the heat distribution within the hypothetical current collector assembly is based on the solution to at least the following equation:
• ρ
• ⁢
• C
• p
• ⁢
• d
• ⁢
• T
• d
• ⁢
• t
• -
• ∇
• →
• ·
• (
• k
• ⁢
• ∇
• →
• T
• )
• =
• Q
• ˙
• v
• wherein ρCp is density times specific heat, T is temperature, t is time, k is thermal conductivity, and {dot over (Q)}v is volumetric generation rate of heat;
• identifying as a solution to the model a number and arrangement of conductive elements associated with a current collector;
• and
• manufacturing the current collector assembly, wherein the current collector assembly comprises a defined plurality of apertures within a refractory base of the current collector assembly in a pattern configured to receive the number and arrangement of conductive elements identified as the solution to the model.