l8 - Lecture 8: A First Look at the Diffusion Equation...

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1 Lecture 8: A First Look at the Diffusion Equation (cont’d)
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2 Last Time… We looked at the 2D diffusion equation on Cartesian structured meshes. We Discussed properties of discrete equation set including » Boundedness » Scarborough criterion Looked at boundary conditions
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3 This Time… Start looking at conjugate heat transfer » Spatially variable , particularly when there are material discontinuities » Source term linearization » Under-relaxation
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4 Interpolation of Recall we need at faces Stored at cell centroids Possible to interpolate linearly as: Instead we consider an alternative treatment
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5 Harmonic Mean Interpolation Consider 1D conjugate heat transfer Two blocks E and P with different thermal conductivities, say Heat transfer rate found by drawing thermal circuit P E 0.5 E E x 0.5 P P x
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6 Harmonic Mean Interpolation (cont’d) Equivalently, define e   e E P e e J x   
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7 Discussion
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This note was uploaded on 12/29/2011 for the course ME 608 taught by Professor Na during the Fall '10 term at Purdue University-West Lafayette.

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l8 - Lecture 8: A First Look at the Diffusion Equation...

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