Nonlinear systems arising from nonisothermal, non-Newtonian Hele-Shaw flows in the presence of body forces and sources
✍ Scribed by R.P. Gilbert; M. Fang
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 785 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0895-7177
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✦ Synopsis
In this paper, we first give a formal derivation of several systems of equations for injection moulding. This is done starting from the basic equations for nonisothermal, non-Newtonian flows in a three-dimensional domain. We derive systems for both (T °, p0) and (T 1 , p l) in the presence of body forces and sources. We find that body forces and sources have a nonlinear effect on the systems. We also derive a nonlinear "Darcy law". Our formulation includes not only the pressure gradient, but also body forces and sources, which play the role of a nonlinearity. Later, we prove the existence of weak solutions to certain boundary value problems and initial-boundary value problems associated with the resulting equations for (T°,p °) but in a more general mathematical setting.