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Unformatted text preview: ME 608 Numerical Methods in Heat, Mass, and Momentum Transfer Assignment No: 1 Due Date: January 24, 2011 Instructor: J. Murthy 1. Write the u-momentum equation for the unsteady flow of a Newtonian fluid with variable density and viscosity . Expand the Newtonian stress tensor in terms of the spatial derivatives of velocity. The objective of this problem is to derive the special forms , and S take for various scenarios described below. (a) By comparing the equation to the general scalar transport equation, derive expressions for , and S . (b) If both and are constant, what are , and S ? (Hint: use the continuity equation). (c) If is constant, but is not, what are , and S ? (d) If is constant and is not, show it is possible to define an effective pressure P = p- 1 3 V so that the source term in the u-momentum equation can be written in terms of- P / x . Hence derive expres- sions for , and S ....
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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.
- Fall '10