as1-sol

# as1-sol - ME 608 Numerical Methods in Heat Mass and...

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Unformatted text preview: ME 608 Numerical Methods in Heat, Mass, and Momentum Transfer Solution to Assignment No: 1 Due Date: January 24, 2011 Instructor: J. Murthy 1. The governing equation for unsteady flow of a Newtonian fluid is: ∂ ∂ t ( ρ u )+ ∂ ∂ x ( ρ uu )+ ∂ ∂ y ( ρ vu )+ ∂ ∂ z ( ρ wu ) = − ∂ P ∂ x + b x + ∂ ∂ x parenleftbigg μ parenleftbigg 2 ∂ u ∂ x parenrightbigg − 2 3 ∇ · V parenrightbigg + ∂ ∂ y parenleftbigg μ parenleftbigg ∂ u ∂ y + ∂ v ∂ x parenrightbiggparenrightbigg + ∂ ∂ z parenleftbigg μ parenleftbigg ∂ u ∂ z + ∂ w ∂ x parenrightbiggparenrightbigg (a) Comparing with general scalar transport equation, φ =u, Γ = μ and S = − ∂ P ∂ x + b x + ∂ ∂ x parenleftbigg μ ∂ u ∂ x parenrightbigg + ∂ ∂ y parenleftbigg μ ∂ v ∂ x parenrightbigg + ∂ ∂ z parenleftbigg μ ∂ w ∂ x parenrightbigg − 2 3 ∂ ∂ x ( μ ∇ · V ) (b) When μ = constant and ρ = constant, φ = u, Γ = μ . Since ∇ · V =0, we can show that S = − ∂ P ∂ x + b x (c) When μ negationslash = constant and ρ = constant, φ =u, Γ = μ and S = − ∂ P ∂ x + b x + ∂ ∂ x parenleftbigg μ ∂ u ∂ x parenrightbigg + ∂ ∂ y parenleftbigg μ ∂ v ∂ x parenrightbigg + ∂ ∂ z parenleftbigg μ ∂ w ∂ x parenrightbigg (d) When μ = constant and ρ negationslash = constant, φ =u, Γ = μ and S = − ∂ P ∂ x + b x − 2 3 μ ∂ ∂ x ( ∇ · V )+ μ ∂ ∂ x ( ∇ · V ) = − ∂ P ∂ x + b x 2. (a) Source integration:2....
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as1-sol - ME 608 Numerical Methods in Heat Mass and...

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