In the *Project Schematic* double click * Results* to open the post-processor. When the

In the Post-Processing window, click the Vector icon to create a vector result. When prompted, name the result `Velocity Vector`

. In the *Details of Velocity Vector* window, begin on the * Geometry* tab. Under

`0.1`

. Finally, move to the In Ansys version 14.5 and later, only one half of the pipe cross-section is displayed after using the mirroring option. You can work around this by applying the mirroring condition in the "Default transform" setting and not in the "View" Tab. To do this select "Default Transform" in the left-hand menu, uncheck "Instancing Info from Domain", check "Apply Reflection" and select to mirror about the ZX Plane.

In the Post-Processing window, click the Contour icon to create a Contour result. When prompted, name the result `Velocity Contour`

. In the *Details of Velocity Contour* window, begin on the ** Geometry** tab. Under

`1,10,1`

. When finished, press In the Post-Processing window, click the Contour icon to create another Contour result. When prompted, name the result `Temperature Contour`

. In the *Details of Temperature Contour* window, begin on the ** Geometry** tab. Under

Create another contour result, and name it `Pressure Contour`

. Use all of the same settings as the previous results, but this time choose ** Variable > Pressure** in the

To graph the temperature along the centerline, we first need to create the centerline as a path. To accomplish this, click on the Location icon , select ** Line**, and name the line

`Centerline`

. In the To create a chart, press the chart icon . When prompted, name the page `Temperature Along Centerline`

. In the *Details of Temperature Along Centerline* window, begin on the ** General** tab. In the

`Temperature Along Centerline`

. Next, click on the To graph the temperature along the outlet, we need to create the outlet as a path much like we did with the centerline. Click on the Location icon , select ** Line**, and name the line

`Outlet`

. In the Press ** Apply** once finished.

Next, press the chart icon . When prompted, name the page `Temperature Along Outlet`

. In the *Details of Temperature Along Outlet* window, begin on the ** General** tab. In the

`Temperature Along Outlet`

. Next, click on the The ** Nusselt number** is a non-dimensional parameter that provides a measure of the convection heat transfer at a surface. It is the ratio of convection to pure conduction heat transfer. We will now derive the Nusselt number as a function of the given parameters and temperature.

The convection heat transfer at the pipe wall is:

We can rearrange terms to find an expression for h, the ** convection coefficient**:

Substitute the ** convection coefficient** expression into the

where

h is the convection coefficient.

k is the thermal conductivity.

L is the length scale. Similar to the Reynold's Number, the length scale is the diameter of the pipe for an internal pipe flow.

q''_w is the heat flux at the heated surface, 37.5 W/m^2.

Tw is the pipe wall temperature at a given location along the pipe.

Tm is the mean temperature in the pipe at the location where Tw is defined.

To find the temperature at the wall, click on ** insert** >>

Click on Expression right below and right click in the window to create a new expression named *Tw*. Under ** Details of Tw** panel, enter

*Tw* now gives the temperature at the location (8.64, 0.06, 0), which is on the exit pipe wall.

To find the mean temperature at a given location in the pipe, click on ** insert** >>

Click on the ** Calculators** tab and double click on

Under ** Expressions**, right click in the window to create a new expression and name it Tm. In the Details of Tm window, enter the following:

lengthInt(Velocity u*Y*Temperature)@exit/lengthInt(Velocity u*Y)@exit

This expression will now give the mean temperature at the location which we called "exit." Recall the pipe radius r is defined in the Y direction in Fluent. Hence, we will use Y to define the radial position in the pipe, as shown in the expression above.

We are now ready to find the Nusselt Number. Create another expression and name it * Nu exp*. Under the Definition tab, enter the Nusselt Number expression shown in the equation above. The units are entered in square brackets; this is done to ensure that the expression for the Nusselt Number is dimensionless.

You may get a slightly higher or lower value for the Nusselt Number here.

We would like to compare the Nusselt Number along the heated section of the pipe. We can generate the Nusselt Number at a different location by simply changing the x-coordinate of * exit* and

We can expect a maximum and dominant convection heat transfer at the entrance of the heated section of the pipe. The convection heat transfer raises the temperature inside the pipe, as well as the mean temperature, along the downstream direction. The mean temperature near the exit is higher relative to the entrance and therefore a lower convection heat transfer is expected at the exit. Again, the Nusselt Number is a measure of convection heat transfer relative to conduction heat transfer. Thus, we should expect the Nusselt Number to decrease along the length of the pipe.

To export the data, click on the "export" button. Comma Seperated Value (.csv) is able to be read by matlab and Excel, so it should be fine.

We are now ready to validate and verify our results.