entropy_producti

# entropy_producti - ENTROPY PRODUCTION AND NONLINEARITY. Is...

This preview shows pages 1–4. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
L INEARIZE Now linearize the two entropy flow equations. Subscript o denotes operating point. ˙ S

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 5

entropy_producti - ENTROPY PRODUCTION AND NONLINEARITY. Is...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online