Integral_Energy_Balance_web

# Integral_Energy_Balance_web - ENU 4133 Integral...

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ENU 4133 – Integral Conservation of Energy January 25, 2011

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Applying Reynolds Transport to Energy For energy, B = E , β = dE / dm = e . Most general case (in scope of class) for this equation, stationary CV: dE dt = d dt Z CV e ρ d V + Z CS e ρ ~ V · ~ n dA (1) dE dt = dQ dt - dW dt (2) e = e internal + e kinetic + e potential + e other (3) e other includes nuclear & chemical reactions that we’ll ignore in this equation.
Heat and Work Terms dQ / dt is the primary focus of heat transfer texts; in this course, we’ll take it as an input, sometimes written as ˙ Q . Work term: dW dt = ˙ W = ˙ W shaft + ˙ W pressure + ˙ W viscous stress (4) ˙ W = ˙ W s + ˙ W p + ˙ W v (5) Work from gravity forces is in the potential energy term, e potential . Electromagnetic (etc.) forces are ignored. Shaft work: work from some machine, usually given in the problem.

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Pressure and Viscous/Shear Work Terms Pressure work: d ˙ W p = - ( pdA ) V n , in = p ~ V · ~ ndA (6) ˙ W p = Z CS p ~ V · ~ ndA (7) Viscous work: d ˙ W v = - ~ ~ τ · ~ V · d ~ A (8) ˙ W v is usually negligible. At solid surfaces, taken as shaft work. At
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