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April 17, 2012, 09:32 
plzzz help::energy equation using power law method

#1 
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maryam
Join Date: Jan 2012
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hello every body
I am writing fortran code for 3D fluid flow in a rectangular duct. I have problem with descritising energy equation using pawer law method (finite volume). integrating viscous term is some how inpossible. one friend told me to take out that part out of integral like a constant number. is it right??????? and if it is right i have other problem descritising terms like d(u)/d(y). should i do it like what i do for momentom equation( i mean the formula used to find a(nb)) or the accsess is gained only through interpolation? thanks. sepideh 

April 17, 2012, 18:36 

#2  
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Arjun
Join Date: Mar 2009
Location: Nurenberg, Germany
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Quote:
The temperature equations has viscous heating term = viscosity * shear rate^2 . Thats all. The viscosity is calculated based on what is currently available as best guess for temperature. Typically power law with temperature dependence would be of this form: viscosity = m * EXP(tc * (T  t0)) * shear rate ^ (n1) Where T is temperature. PS: This is not an easy calculation to do. I did last week or two ago for our company and i can tell you it is very tricky business to put into practice. 

April 18, 2012, 01:09 

#3 
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maryam
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thanks arjun
but I have a problem understanding you. do you mean with integrating energy equation I will reach your last equation? what is tc and t0? i should mention that I am studying steady flow 

April 18, 2012, 03:32 

#4  
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Arjun
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Quote:
There are no terms related to time in it. Tc and T0 are constant so you can use it for steady case too. In fact i also did steady calculation. 

April 20, 2012, 05:36 

#5  
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Quote:
Energy equation is a transport equation with a convective term , a diffusive term and sometime a source term. The power law scheme is used to discritize the convective term of the equation (one could use UDS scheme, CDS scheme etc....) The diffusive term are generally discritized using central second order finite difference. To me the both are not linked (power law scheme and diffusive term) Check Patankar' book or Versteek and Malalasekera book. Everything is perfectly explained in it. 

April 20, 2012, 08:05 

#6  
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Arjun
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Quote:
O man, I completely mistook him. I thought he was asking about power law fluid with viscous heating in temperature equation. 

Tags 
energy equation, finite volume method, pawerlaw 
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