C13_Nonisothermal_Turbulent__Flow

C13_Nonisothermal_Turbulent__Flow - Temperature Temperature...

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1 Nonisothermal Turbulent Flow Temp erature
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2 Nonisothermal Turbulent Flow Time Smoothed equations of change for incompressible nonisothermal flow Time-smoothed equation of energy for incompressible fluids without sources 0 0 /2 0 where 1 ( ) tt TTT T T s d s t + =+ = () 2 ˆ : v p DT Ck T Dt µ ρ = ∇− ∇ τ u ±²³²´ 0 0 0 where 1 ( ) xxx x x uuu u u s d s t + =
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3 Nonisothermal Turbulent Flow Time Smoothed equations of change for incompressible nonisothermal flow Time-smoothed equation of energy for incompressible fluids without sources () 2 2 2 ˆˆ . ˆˆˆ + 2 2 ... 2 pp px py pz y xx x CT k T t CuT xyz u uu u xy y x ρρ ρ µ =−∇ + ∇ ⎡⎤ ∂∂∂ ′′ ++ ⎢⎥ ⎣⎦ ⎛⎞ ⎛⎞ ⎛⎞ ∂∂ ∂ + + ⎜⎟ ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ ⎝⎠ ∂∂ + u 2. . . y x u u yy yx ⎛⎞⎛⎞ ⎜⎟⎜⎟ ⎝⎠⎝⎠ ˆ ; t ip i qC u T = 33 11 j t ii i v ij u u jj ji == Φ= + ∑∑ ; v i i T qk x =−
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4 Nonisothermal Turbulent Flow Time Smoothed equations of change for incompressible nonisothermal flow Time-smoothed equation of energy for incompressible fluids without sources [] () ( ) normally negligible ˆˆ .. vt v t pp v v T CC T t ρρ µ ⎡⎤ =− − ∇ + + Φ ⎣⎦ uq q ±²³²´ ˆ ; t ip i qC u T ρ ′′ = ; v i i T qk x 33 11 j t ii i v ij u uu u jj ji == ⎛⎞ ∂∂ Φ= + ⎢⎥ ⎜⎟ ⎝⎠ ∑∑
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5 Nonisothermal Turbulent Flow Time Smoothed equations of change for incompressible nonisothermal flow Time-smoothed equations of change for incompressible fluids without sources Continuity ( ) ( ) .. 0
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C13_Nonisothermal_Turbulent__Flow - Temperature Temperature...

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