Nearly_incompressible_laminar_flow

Nearly_incompressible_laminar_flow - Nearly Incompressible...

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Nearly Incompressible Laminar Flow – Equations and Solution Technique Author: John M. Cimbala, Penn State University Latest revision: 31 October 2007 Assumptions and Approximations The fluid is Newtonian with constant properties ( μ , ν , k , α , κ , C P ). The flow is laminar rather than transitional or turbulent. The fluid is nearly incompressible – either an incompressible liquid or an ideal gas at very low Mach numbers . Differential Equations of Motion for Nearly Incompressible Flow (general review) Conservation of mass : 0 i i u x = . Momentum equation : 2 ii i ji i j ij Du u u u p ρρ u ρ g μ Dt t x x x x ⎛⎞ ∂∂ =+ = + + ⎜⎟ ⎝⎠ j . Conservation of energy (first law) : For incompressible liquid : 2 p DT T ρ Ck Dt x x φ = + , where 2 ij ij ee = . For ideal gas at very low Ma : 2 p DT T ρ Dt x x = ∂ ∂ , or 2 DT T κ Dt x x = ∂ ∂ ( p k κ ρ C = thermal diffusivity).
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