I am running a simulation on COMSOL Multiphysics in order to validate some existing results on natural convection of power law fluids inside a cylindrical can. The initial and boundary conditions are:
1) Initial temp of the fluid at t=0 : 313 K (40 C)
2) Temp of all the walls (constant throughout): 394 K (121 C)
3) No slip at the walls.
4) Power law fluid with n=0.57
5) Viscosity relationship 0.002232*exp((30.74*(10^3)*0.57)/(8.314*T))* (Shear rate)^(n-1)
It is a time dependent analysis from 0 to 2500 seconds. Boussinesq Approximation was used for the body force term. The author defines two averages to account for the average temperature of the system in order to calculate heat transfer coefficient and other parameters.
a) Volume Average Temperature (Same as the cup mixing temp of the whole system)
b) Average of absolute mass flow average temperature
My simulation results show good agreement with the existing results in terms of temperature profiles (both volume and mass average), heat transfer coefficient based on Vol. and mass avg temp, Heat flux from the surfaces etc. But there is substantial difference in volume avg. viscosity between my simulation results and the existing results both qualitatively and quantitatively.
1) My viscosity range varies from 8 Pa.s to 110 Pa.s while in the paper it is in between 4 to 13 Pa.S.
2) In the paper the viscosity plot looks like exponentially decreasing eventually reaching a constant value. In my results there is a steep exponential (appears to be) decrease then towards the end the viscosity increases from a value around 4 eventually ending at around 8.
3) The two plots coincide only in a very small part.
I can think of an explanation for my results. But since everything else is matching with the existing result, I feel the viscosity behaviour should be similar too. I have tried using finer mesh, smaller time step, manual calculation of viscosity from the formula etc. But in all the cases I have found the trend to be the same.
My questions are:
i) Have I possibly made any mistake while running the simulation?
ii) If yes, why is this single parameter not agreeing while everything else is (Because everything is coupled with one another)?
iii) Is there any other way (May be more accurate) to calculate viscosity that I might have missed (I calculated using COMSOL surface average selecting volume integral and MS Excel substituting the parameter values in the equation)?
Thank you for your responses!
I think I have figured out the problem. Power law for shear thinning fluids has this inherent demerit that it cannot cover the entire domain of shear rate as it is not based on factors in molecular level. The power law index is obtain by fitting experimental data to the model. So it is valid only in the range of experimentally obtained values of viscosity. Mathematically when n
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