# Unification of Finite Element Methods (Mathematics Studies) by H. Kardestuncer By H. Kardestuncer

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7 Fluid motion coupled with thermal phenomena In this subsection we consider fluid motion coupled to thermal phenomena. 72) where denotes the position vector. 10), ( 2 . 12), respectively. 74) The time rate of the temperature i s associated with a mte of heat stored i n the fluid material. 75) where C denotes the specific heat capacity of the fluid. 73) the rate of heat stored i n the material may be composed in the Eulerian approach of two parts. 76) and i s associated with the tempemture rate obiained a t a fixed location.

Engrg. 17/18 (1979) 277-313. V. , Domain decomposition methods for nonlinear problems in fluid dynamics, Fenomech ‘81, Comput. Meths. Appl. Mech . , to appear. , Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Stand. 49 (1952) 409-436. Jennings, A . , The solution o f sparse linear equations by the conjugate gradient method, Int. J. Num. Meths. Engrg. 12 (1978) 141-158. E. , Quasi-Newton methods - Motivation and theory, SlAM Review 19 (1977) 46-89. Matthies, H. , The solution o f nonlinear finite element equations, Int.

Doltsinis 16 operator yielding the surfoce tractions. 1) i n natural or in Cartesian terms are possible as outlined i n section 2. 8) for the scalar product of two vectors. 26). 6. 61) and write i n na tura I terms where represents the virtual pressure field. We next turn our attention to the heat flow as occurring concurrently with the fluid motion. The heat balance of the volume in question may be expressed i n natural terms as Y I/ r/ where ? denotes a virtual temperature field. 75). 77). 84) by heat conduction.

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