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Zbl 0947.74040
Andrews, Kevin T.; Shillor, Meir; Wright, Steve
A model for heat transfer in grinding. (English)
[J] Nonlinear Anal., Theory Methods Appl. 35, No.2, A, 233-246 (1999). ISSN 0362-546X

From the introduction: We present a mathematical model which deals with the thermal aspects of a grinding process. In this model we are concerned only with thermal effects, leaving the mechanical effects for other studies. In effect, then, the part or workpiece and the grinding wheel are assumed to be perfectly rigid. The mathematical problem is formulated in abstract terms, so that the existence of a weak solution can be established. The proof is based on a theorem for degenerate evolution systems. Under additional assumptions on the data, we establish uniqueness and existence of a weak solution to the steady-state thermal problem. Interest in this problem is heightened by experimental evidence that an almost steady state is reached very quickly after grinding is initiated.

MSC 2000:: *74M15 Contact
74F05 Thermal effects
74H20 Existence of solutions
74H25 Uniqueness of solutions
74G20 Local existence of solutions (near a given solution)

Keywords: nonlinear heat exchange; coupled system of parabolic equations; grinding fluid flow; existence of weak solution; grinding process; thermal effects; degenerate evolution systems; uniqueness; steady-state thermal problem

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Zentralblatt MATH Berlin [Germany]