In this module we model the boundary layer equations for forced convection over a flat plate in their primitive form. That is, we relax the similarity restrictions of the Blasius solution. The result can be considered a “virtual” laboratory. The user can take the data produced in this simulation just as in a real physical laboratory. But in this virtual laboratory they don’t need to worry about toxicity, burning themselves, etc. Furthermore they can work with a range of fluids that no one physical laboratory could ever hope to study.
Module Description
InsightsInputs
The user inputs the plate Reynolds and fluid Prandtl numbers, along with the freestream turbulence level (as a percent). On a separate input form they may specify up to five independent zones where either the surface temperature or surface temperature gradient will be specified. We use an algebraic model to estimate the transition point as a function of the freestream turbulence level. A simple mixing length model extends the calculation into the transition and turbulent region. (A frequently used transition criterion is Re = 500,000, which corresponds to 1% freestream turbulence.)
Display
The on-screen output includes a line indicating the edge of the velocity boundary layer as a function of position on the plate. The main feature is a color contour plot of the calculated temperature field. In the results for Reynolds numbers of 1,000,000 and 3,000,000 above, you will note a change in slope part way down the plate (corresponding to local Reynolds number Rex of 500,000) indicating the beginning of the transition to turbulence. In the cases included in this animated gif display above, we use a fixed temperature for the entire plate. Since the Prandtl number used in the above demonstration is slightly less than unity (0.7, corresponding to air), the thermal boundary layer does, as expected, grow faster than the velocity layer. With the equations being parabolic, a single calculation takes only an instant on any modern personal computer.
Measurements
For any reasonable value of Reynolds number, both the velocity and thermal boundary layers are very thin. For that reason, the user has the option of expanding the vertical scale of these plots in order to see more detail. (The figure above uses a vertical magnifier of 10.0.) The “experimenter” can measure the local plate surface temperature and the local surface temperature gradient directly from the screen using the scrollbar seen in the lower left.
The user can use these results to develop local and overall convection correlations. These “experimental-numerical” results compare very favorably with those from the standard correlations based on similarity and integral methods for laminar boundary layer flows and favorably with experimentally derived correlations for turbulent flows. The user can “measure” horizontal velocity at any point in the flow using the mouse, and the boundary layer velocity profile at any point along the plate may be displayed using the same scrollbar. (In the figure above, we fixed the probe three quarters of the way down the plate.)
Thermal Boundary Conditions
To add increased capability to this numerical model, a pop-up form allows the user to specify different thermal boundary conditions in up to five (5) zones along the length of the plate. These thermal conditions include fixed temperatures and fixed heat fluxes (q”) as either constants or linear functions of x position.
Insights
The numerical procedures used in this forced convection module are certainly well beyond the undergraduate level. However, with this very well equipped “virtual” laboratory, students can run a large number of parameters quickly and “see” what happens physically — even to the point of deriving their own correlation. For instance, at a Reynolds number of 1.5e6, the user can see the distinct change in the surface temperature gradient about a third of the way down the plate. Following a rise through the transition region, We observe a subsequent decay as the turbulent boundary layer thickens. Sure beats just reading about it in a textbook!
We follow up with an exercise involving a geometry (an infinite cylinder) which does not yield to a relatively simple numerical solution. At least by that point students have developed an appreciation for the physical basis of convection correlations.
Convection Correlations
Users can access an Excel workbook that implements conventional empirical correlations for forced convection over a flat plate here.
Virtual Laboratory Assignment:
Jorge Navalho has created a virtual laboratory assignment based on the HTTflatp module that may be downloaded here.
Video Introduction:
VIDEO INTRODUCTION TO HTTflatp MODULE (4:35 m)
Reference:
Ribando, R.J., Coyne, K.A., and O’Leary, G.W., “Teaching Module for Laminar and Turbulent Forced Convection on a Flat Plate.” Computer Applications in Engineering Education, Vol. 6, No.2, pp. 115-125,1998. The transition and turbulence models are from other sources.
Software Availability:
If you are up to date with your Windows updates, this executable should work directly without any installation needed. It will not work on Mac computers (unless installed in cloud environment). You are welcome to contact me with suspected errors and suggestions for improvements.
Notice to International Users where decimal points (periods) are used instead of commas to break up long numbers. If this module does not work properly, then change the language setting to English (US).