Melting Solid Plug Between Two Coaxial Pipes by a Moving Heat Source in the Inner Pipe

Melting of a solid plug in the gap between two coaxial pipes by inserting a moving heat source in the inner pipe is investigated. Using a scale analysis, closed-form solutions for temperatures of liquid in the inner pipe, solid plug and liquid in the annular gap, and the surrounding medium around the outer pipe are determined. It is shown that eight independent dimensionless parameters are required to specify the entire process. The effects of independent parameters on the shapes of the molten region in the gap are found. The analysis and results provided are useful for the design of oil pipes.