Finite Control Volume –
Conservation of Energy
In a Nutshell: For
conservation of energy, the time rate of increase of total stored energy in a
system
(constant mass) must equal the net time rate of energy addition by heat
transfer to the system plus
the net time rate of energy addition by work transfer into the system. D/Dt ∫ e ρ dV = {
Σ dQ/dt in
– Σ dQ/dtout
}sys + { Σ dW/dtin - dW/dtout }sys sys The
Reynolds Transport Theorem provides an expression for conservation of energy using
a finite control
volume. The result is that the energy
stored in the control volume plus the net energy flux
across the control surface sums to the net heat transfer rate in plus the net
work rate on the contents
of the control volume. Energy transfer
in integral form is: ∂/∂t ∫ e ρ dV +
∫ e ρ V . n dS = dQ/dt net in + dW/dtshaft net
in cv cs where ∂/∂t ∫ e ρ dV represents the rate of change of energy in
the control volume cv ∫ e ρ V . n dS represents the energy flux across the
control surface cs dQ/dt net in
represents the net heat transfer into the control volume dW/dtshaft net
in represents the net shaft
work into the control volume Click here to continue this discussion. |
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