MIT2_094S11_lec16

# MIT2_094S11_lec16 - 2.094 Finite Element Analysis of Solids...

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± ± ± 2.094 Finite Element Analysis of Solids and Fluids Fall ‘08 Lecture 16 - F.E. analysis of Navier-Stokes ﬂuids Prof. K.J. Bathe MIT OpenCourseWare Incompressible ﬂow with heat transfer Reading: Sec. We recall heat transfer for a solid: 7.1-7.4, Table 7.3 Governing diﬀerential equations ( ,i ) ,i + q B = 0 in V (16.1) is prescribed, k = q S ∂θ (16.2) θ ∂n S θ S q S q S θ S q = S S θ S q = (16.3) Principle of virtual temperatures θ ,i ,i dV = θq B dV + θ S q S dS q (16.4) V V S q for arbitrary continuous θ ( x 1 ,x 2 ,x 3 ) zero on S θ For a ﬂuid, we use the Eulerian formulation. 65

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MIT 2.094 16. F.E. analysis of Navier-Stokes ﬂuids ρc p v θ | x ρc p v θ | x + ∂x ( ρc p ) dx ± + conduction + etc (16.5) In general 3D, we have an additional term for the left hand side of (16.1): · ( ρc p v θ ) = ρc p · ( v θ ) = ρc p ( · v ) θ ρc p ( v · ) θ ² ³´ µ term (A) (16.6) where · v = 0 in the incompressible case. · v
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## This note was uploaded on 12/29/2011 for the course ENGINEERIN 2.094 taught by Professor Prof.klaus-jürgenbathe during the Spring '11 term at MIT.

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MIT2_094S11_lec16 - 2.094 Finite Element Analysis of Solids...

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