Various causes for mantle melting (decompression, heating or release of water) combined with current estimates of upper mantle temperatures and the state of stress in the lithosphere suggest that in many regions the asthenosphere might be partially molten, but melts may not always be able to rise to the surface. The governing equations describing melting, melt segregation, compaction and deplet...

A series of analytical solutions are presented for viscous compacting flow past a rigid impermeable sphere. The sphere is surrounded by a two-phase medium consisting of a viscously deformable solid matrix skeleton through which a low viscosity liquid melt can percolate. The flow of the two-phase medium is described by McKenzie’s compaction equations which combine Darcy flow of the liquid melt w...

The work in this paper concerns a mathematical model of the contact melting process of a rectangular material in contact with a hot plate. The problem is described by a coupled system of heat equations in the solid and melt layer, fluid flow in the melt, a Stefan condition at the melt interface, and a force balance between the weight of the solid and the fluid pressure. Since the melt layer rem...

The upper Indus River basin has large masses of glaciers that supply meltwater in the summer. Water resources from are crucial for human activities and ecosystems Pakistan, but they vulnerable to climate change. This study focuses on impacts change, particularly effects receding water a catchment river basin. predicts flow using hydrologic model coupled with temperature-index snow glacier melt ...