C10_Shell_Energy_Balance

C10_Shell_Energy_Balance - Shell Energy Balance Energy...

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Shell Energy Balance Energy conservation for homogeneous media Heat source Energy influx (inward arrows) Energy outflux (outward arrows) by convection ˆ () Ki EU u ρ + by conduction ii i T qk x =− x 3 x 1 x 2 11 2 2 3 3 i i uu u p u ττ τ ++ + by works Energy influx Energy outflux Sources/ Sinks Energy accumulation Work by body force Energy influx Energy outflux Sources/ Sinks Work by body force Energy flux in the i-direction
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Shell Energy Balance Energy conservation for homogeneous media x 3 x 1 x 2 Total energy flux in the i-direction () 3 1 ˆ iK i ii i j j j eE U u q p u u ρτ = =+ + + + Heat source Energy influx (inward arrows) Energy outflux (outward arrows) 3 1 or ˆ i K i i ij j j H u q u = + + 3 1 g i Wu g ρ = = Work done by gravity per unit volume Energy sources/sinks S g : amount of energy generated per unit volume S d : amount of energy lost per unit volume
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Shell Energy Balance A methodology for solving energy transfer problems Statement of nonisothermal problems 1. Define the domain boundary 2. Choose a coordinate system such that there are more vanishing terms (i.e. components of velocity, velocity gradient, temperature gradient, and forces). 3. State assumptions to simplify the problem (i.e. set zero more terms) 4. List heat sources/sinks and non-zero components of velocity, velocity/temperature gradients, forces, and works. 5. For each phase, writing equations of continuity, equations of motion, and energy balances over an elementary volume. 6. Make use of the derivative definition to convert the balances into equations in which temperature is dependent variables. 7. Identify initial and boundary conditions, and then solve the velocity and temperature equations. 8. Determine other quantities related to velocity and temperature profiles Heat source Energy influx (inward arrows) Energy outflux (outward arrows )
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A methodology for solving energy transfer problems Common boundary conditions Momentum balance a. At solid-liquid interface: ‘no-slip’ condition is frequently assumed b. At liquid-liquid interface: ‘no-slip’ condition is frequently assumed and viscous stresses are continuous at the interface. c. At gas-liquid interface: viscous stress may be negligible for small gas velocity gradient of gas Energy Balance d. At interfaces the continuity of temperature and of the heat flux normal to the interface are required.
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This note was uploaded on 09/01/2011 for the course PGE 312 taught by Professor Peters during the Fall '08 term at University of Texas at Austin.

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C10_Shell_Energy_Balance - Shell Energy Balance Energy...

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