entropy_producti

entropy_producti - ENTROPY PRODUCTION AND NONLINEARITY. Is...

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ENTROPY PRODUCTION AND NONLINEARITY. Is entropy production an exclusively nonlinear phenomenon? Must it always vanish in a linearized model? Consider simple heat transfer modeled by Fourier's law: ˙ Q = (kA/l)(T 1 - T 2 ) where ˙ Q is heat flow rate, k is thermal conductivity, A is a surface area, l is length and T 1 and T 2 are absolute temperatures. Entropy flow and heat flow are related by temperature. ˙ Q = T 1 ˙ S 1 = T 2 ˙ S 2 ˙ S 1 = (kA/l) (T 1 - T 2 ) T 1 ˙ S 2 = (kA/l) (T 1 - T 2 ) T 2 Mod. Sim. Dyn. Sys. Entropy production page 1
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Net entropy production is: ˙ S net = ˙ S out ˙ S in = ˙ S 2 ˙ S 1 = (kA/l)(T 1 - T 2 ) 1 T 2 - 1 T 1 = (kA/l) (T 1 - T 2 ) 2 T 1 T 2 Hence, as dictated by the second law, net entropy production is never negative. Mod. Sim. Dyn. Sys. Entropy production page 2
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L INEARIZE Now linearize the two entropy flow equations. Subscript o denotes operating point. ˙ S
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.141 taught by Professor Nevillehogan during the Fall '06 term at MIT.

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entropy_producti - ENTROPY PRODUCTION AND NONLINEARITY. Is...

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