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Unformatted text preview: 2.094 Finite Element Analysis of Solids and Fluids Fall 08 Lecture 17- Incompressible uid ow and heat transfer, contd Prof. K.J. Bathe MIT OpenCourseWare 17.1 Abstract body Reading: Sec. 7.4 Fluid Flow Heat transfer S v , S f S , S q S v S f S S q = S = S S v S f = 0 S S q = 0 17.2 Actual 2D problem (channel ow) 71 MIT 2.094 17. Incompressible uid ow and heat transfer, contd 17.3 Basic equations P.V. velocities v i v i,j v j dV + ij e ij dV = v i f i B dV + v i S f f i S f dS f (17.1) V V V S f Continuity pv i,i dV = (17.2) V P.V. temperature c p ,i v i dV + ,i k ,i dV = q B dV + S q S dS (17.3) V V V S q F.E. solution x i = h k x k i (17.4) v i = h k v i k (17.5) = h k k (17.6) p = h k p k (17.7) v F ( u ) = R u = p nodal variables (17.8) 17.4 Model problem 1D equation, d d 2 c p v = k (17.9) dx dx 2 ( v is given, unit cross section) Non-dimensional form (Section 7.4) d d...
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