there is integral and differential method to calculate thermal and frictional entropy generation in in annuli. but i am looking for algebraic formulas as integral and differential method shields different results for developing flow.
Dear Mehedi Hasan Tusar ,
According to your problem, generally speaking, there is no algebraic formula to calculate thermal and frictional entropy generation for turbulent flow of nano fluid in annuli. The problem can only be solved precisely by using experimental or numerical methods.
Have a nice research.
Regards,
Nazar
Nazar is correct, there are numerical methods that require that you obtain experimental data for modeling the process. Companies such as D'Assault will do this for you with finite element analysis, but this can be expensive. The problem belongs in the category of irreversible thermodynamics. I am publishing a state space for this analysis next year, but the state equations still require you to collect experimental data such as the force or pressure on input and output side, heat capacity and diffusivity of the pipe material, etc.
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