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 sepidehkavousi April 17, 2012 09:32

plzzz help::energy equation using power law method

hello every body
I am writing fortran code for 3-D 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:):D

 arjun April 17, 2012 18:36

Quote:
 Originally Posted by sepidehkavousi (Post 355157) hello every body I am writing fortran code for 3-D 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:):D

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 ^ (n-1)

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.

 sepidehkavousi April 18, 2012 01:09

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

 arjun April 18, 2012 03:32

Quote:
 Originally Posted by sepidehkavousi (Post 355285) 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

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.

 leflix April 20, 2012 05:36

Quote:
 Originally Posted by sepidehkavousi (Post 355157) hello every body I have problem with descritising energy equation using pawer law method (finite volume). integrating viscous term is some how inpossible. i have other problem descritising terms like d(u)/d(y). sepideh:):D
Hi,

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.

 arjun April 20, 2012 08:05

Quote:
 Originally Posted by leflix (Post 355782) Hi, 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.

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

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