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Make sure that Position on X Axis is set under Options, that 1 is the value next to X, and 0 is the value next to Y under Plot Direction. Recall that this tells FLUENT to plot the x-coordinate value on the abscissa of the graph. Select Turbulence... under Y Axis Function and select Wall Yplus from the drop down list under that. Since we want the y+ value for cells adjacent to the wall of the pipe, choose plate under Surfaces.

Click Plot.

(Click picture for larger image)

https://confluence.cornell.edu/download/attachments/90745540/06_yplus2.jpg?version=1

As we can see, the wall y+ value is between 1.0 and 1.4 (ignoring the anamolous at the inflow). Because these values are less than 5, the near-wall mesh resolution is in the laminar sublayer, which is the most accurate region to which we can resolve the boundary layer.

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Uncheck Write to File. Click Plot.

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https://confluence.cornell.edu/download/attachments/90745540/06_outflow2.jpg?version=1

We notice here that the x velocity reaches 1 m/s at approximately y = 0.02 m. This shows the relative thinness of the boundary layer compared to the length scale of the plate. We also notice that the velocity profile is slightly greater than 1 m/s above the boundary layer. We know this would not happen in real flow, rather it is a result of the boundary condition we have chosen for our model. We chose the Symmetry boundary condition at the top of our flow field, which is essentially a wall without the no-slip condition. Thus, no flow is permitted to escape through this boundary.

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Recall that the Nusselt Number is a non-dimensional heat transfer coefficient that relates convective and conductive heat transfer.

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In order to obtain the Nusselt Number from FLUENT, we will begin by plotting Total Surface Heat Flux.

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In the Options box, change back to Position on X Axis. In the Plot Direction box, enter the default values of 1 in the X box and 0 in the Y box. Under Y-Axis Function choose Wall Fluxes. In the box below, chose Total Surface Heat Flux. Select Plate under Surfaces. Before plotting, be sure to turn on Auto Range for the Y axis under Axes....

Click Plot.

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https://confluence.cornell.edu/download/attachments/90745540/06_heatflux4.jpg?version=1

Now Select Write to File. Save the data for this plot as heatflux.xy. Click Write....

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Reynolds Number can be defined at each x location by

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Now plot Re vs. Nu in Excel. Your plot should look like this:

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https://confluence.cornell.edu/download/attachments/90745540/06_fluent_results2.jpg?version=1

Compare Results with Correlation & Experiment

Validate your results form FLUENT by comparing to a correlation and experimental results. The correlation we will use is derived by Reynolds \[1\]:

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All properties in this correlation are evaluated at the free-stream static temperature of 300K.This correlation assumes the following:

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6. Friction factor calculated from the following relation (implicit in Nu equation above, does not need to be calculated in your analysis):

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Add the Reynolds correlation for Nusselt Number to your Excel spreadsheet.

Seban & Doughty \[2\] performed a heated flat plate experiment for which they derived the following expression for Nusselt Number:

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The Seban & Doughty experiment was performed with air as the fluid (Pr = 0.7) and at various Reynolds Numbers in the range 1e5 < Re < 4e6. Add the this experimental relation for Nusselt Number to your Excel spreadsheet.

Now plot and compare Re vs. Nu from FLUENT, the Reynolds Correlation, and Seban's experiment.

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https://confluence.cornell.edu/download/attachments/90745540/06_fluentr11.jpg?version=1

As we can see, there is very little variation between these 3 results. The largest % error between the FLUENT results and the Reynolds correlation is only 7.5%. In turbulent flow as we have here, similar results between FLUENT and correlation are more difficult to come by than in laminar flow because a turbulent model must be used in FLUENT, which does not solve the Navier-Stokes Equations exactly. Experimental error (in experiments from which correlations are derived) also accounts for some of this 7.5% error. Each of the turbulence models that FLUENT offers produces results similar to these, although the k-epsilon model is the most appropriate model to use in this case.

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