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Temperature dependent properties relation

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Old   July 11, 2018, 03:34
Default Temperature dependent properties relation
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A. Min
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Hi all

I want to simulate a forced convection that is report in paper:

Accounting for temperature-dependent properties in viscoelastic duct flows

by Nobrega.

Like the other papers, all of the results are reported in non-dimensioned form. I have calculated initial and boundary conditions based on these dimensionless numbers.
Dimensionless temperature is defined as:
where Ts and Ti are wall and inlet temp. Scince the real or physical values of Ts and Ti are not mentioned in the paper, I decided to select to arbitrary values like 1 and 0 respectively.
Viscosity is changing with

etta(T) = etta0 * aT

aT = exp [a(1/T-1/T0)]
where T0 = 463 K and a = 1720 K

Now I have a question:

My T* values that are come from BC, IC or from the energy Eqn are dimensionless, how can I put these dimensionless values in a relation with real physical To and a ?!!!

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dimensionless temperature, temperature dependence

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