# How to solve Non-Dimensional model equations in Fluent!!

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The non-dimensional (ND) equations (continuity, r-momentum, z-momentum and energy equations) are to be solved with fluent. Now, how can one implement this in Fluent?

Approach 1: The comparison of coefficients from ND model equations and Fluent's governing equation could be used to modify the thermophysical properties (temperature-dependent) of solids/fluids. Is it the correct methodology?

Approach 2: Is there a way to approach the problem using UDS or UDF? If so, for which equations one should write UDS/UDF. The thermophysical properties are temperature-dependent.

## Answers

11,730Forum CoordinatorWe usually alter the material properties to suit. Maybe if you explain why you want to do this someone can offer advice.

30Member@Rob Thanks for the quick response!

I am simulating the behaviour of the porous medium under various conditions. As the material properties are highly temperature-dependent (for solid as well as fluid), I wish to know if UDS/UDF are a better choice or altering material properties, for solving the model equations (in ND form). Moreover, I want to implement specific correlations for wall heat transfer coefficient (HTC) and effective thermal conductivity, which in turn will be updated as per the temperature.

I hope it helps to gain clarity now.

11,730Forum CoordinatorI'd model everything with the correct properties: the whole point of simulation is that we can avoid a lot of the assumptions made when we mess with non-dimensional terms.

If you want a specific wall HTC on the inside you'll need to rewrite the wall functions, that will require UDF.

30Member@Rob Thanks for the update!!

Wall HTC is surely user dependent in case of a porous media, i. e. Constant or udf etc. How about effective thermal conductivity (or Peclet number in N-D form) for LTE approach. In that case, if one wants to implement the effective thermal conductivity then, do altering the material properties is a good choice or some UDF?

30Member@Rob Kindly see to the following query also, which I faced now.

The second question in this regard is about the dimensionless temperature which ranges from 0 to 1. The (hot) fluid is coming to the bed and the non-dimensional temperature (theta) is 1, and the porous bed (LTE model) is at theta=0. But while Initialization, I am getting the following message in the console.

"temperature limited to 1.000000e+00 in 60400 cells on zone 2".

And an initial condition of theta=0 is not displayed in the contours.

11,730Forum CoordinatorWhich I answered here. https://forum.ansys.com/discussion/33812/issue-in-initialization-of-temperature-field-in-porous-medium#latest Friendly reminder, do NOT multi post.

7,890Forum Coordinator:)

30Member@Rob Thanks for the reply, and apologies for the 2 similar posts. I was not able to see the post from my account, so had to post it separately. Continued at https://forum.ansys.com/discussion/33812/issue-in-initialization-of-temperature-field-in-porous-medium#latest

30Member@Rob

Thanks for the update.

I would like to share an observation here, and kindly let me know your opinion.

The model is developed in non-dimensional form, so the inputs to Fluent are made in that manner. Now, what I observed was that, the limits of (static) temperature were set from 1 K - 5000 K by default. Upon reducing it to 0 K- 1 K, the simulation ran fine. So the solution remains the same, provided the model inputs are consistent with the mathematical model developed.

11,730Forum CoordinatorGood workaround. Except that if you use any temperature dependent properties and get a temperature of 0K you may get a divide by zero issue. The whole point of CFD is that we don't need to non-dimensionalise or scale to be able to model something.

30Member@Rob All the help is greatly appreciated!!

I agree with your view; however, the packed bed case which I am tackling involves a lot of parameters, therefore non-dimensionalization was deemed necessary. Further, in my case, I have thermophysical properties that are temperature-dependent only (100 K-- 300 K) and I have made the input accordingly in form of UDF/polynomials which depend upon theta (ND temperature). So far, I have not encountered any issues.