Problem 5.90

# Problem 5.90 - Problem 5.90 Given temperature profile and...

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Problem 5.90 [Difficulty: 3] Given: temperature profile and temperature-dependent viscosity expression Find: Velocity Profile 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) Assumptions: Incompressible fluid Similar to the Example 5.9, the x-component momentum equation can be simplified to sin g dy d yx (1) Integrating once, one has 1 sin C gy yx (2) Using the boundary condition: 0 ) ( h y yx sin 1 gh c (3) Substituting c 1 into eq. (2), sin ) ( y h g dy du yx (4) Here, the fluid viscosity depends on the temperature,

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Problem 5.90 - Problem 5.90 Given temperature profile and...

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