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Problem 5.96 - Problem 5.96[Difficulty 2 Given...

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Problem 5.96 [Difficulty: 2] Given: Temperature-dependent fluid density and the Navier-Stokes equations Find: Explanation for the buoyancy-driven flow; effect of angle on fluid velocity Solution: Governing Equations: 0 z w y v x u (Continuity Equation) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 z w y w x w z P g z w w y w v x w u t w z v y v x v y P g z v w y v v x v u t v z u y u x u x P g z u w y u v x u u t u z y x (Navier-Stokes Equations) Assumption: Incompressible fluid (1) The first term in the right-hand-side of the momentum equations (5.27a)-(5.27c) represents the gravitational body force, which is proportional to the local fluid density. The fluid density in the region
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