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-   -   energy equation in terms of entropy (http://www.cfd-online.com/Forums/main/15751-energy-equation-terms-entropy.html)

kiran September 18, 2008 05:37

energy equation in terms of entropy
 
Hi is it possible to have energy equation in in terms of entropy. thanx.

mettler September 18, 2008 09:09

Re: energy equation in terms of entropy
 
just as a quick thought: I know you can get it in terms of enthalpy and enthalpy has Q, which is in the entropy integral. I have never seen it or derived, so I am not sure if there would be any snares when trying to derive it.

Paolo Lampitella September 19, 2008 03:56

Re: energy equation in terms of entropy
 
Of course, it is. It should be (for a Newtonian - Fourier fluid):

rho * T * DS/Dt = div(Kh * grad(T)) + k * div(u)^2 + 2 * mu * (Sij - 1/3 * div(u) * dij) * (Sij - 1/3 * div(u) * dij) + rho * E

where:

rho = density

mu = dynamic viscosity

u = velocity vector

S = entropy

E = source term

DS/DT = dS/dt + div(uS) = material (or substantial) derivative

Kh * grad(T) = thermal flux (following fourier)

k = lambda + 2/3 * mu = bulk viscosity (usually set to zero following Stoke's Hypotesis)

dij = i,j component of the Kronecker's delta tensor

Sij = 1/2 * (dui/dxj + duj/dxi) = i,j component of the symmetric part of grad(u)

(Sij - 1/3 * div(u) * dij) * (Sij - 1/3 * div(u) * dij) = Aij * Aij = trace of the tensor A*A (A squared)

It is difficult to distinguish the different operators but should be clear

Ahmed September 20, 2008 04:49

Re: energy equation in terms of entropy
 
The Energy equation, is a statement of the first law of thermodynamics,i.e. the principle of conservation of energy, on the contrary, entropy, is a property of matter that is always increasing as long as there is a change of state. You can write a transport equation for the entropy (Check the book bt Vedat Arpaci Convection Heat Transfer)but not a conservation principle. I hope you get the picture and see the difference. Good luck

Paolo Lampitella September 20, 2008 05:11

Re: energy equation in terms of entropy
 
Of course, i was not clear about this. This is a second law of thermodynamics statement, nothing to do with first law.

In fact, the equation writed is not a conservation principle.

Kiran September 22, 2008 09:52

Re: energy equation in terms of entropy
 
Hi, Thanks a lot !!!


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