Conceptual Design of Forced-Free-Mixed Convection Experiment

This assessment is to be completed individually.

1. Learning Outcomes:

- Develop a basic ability to conceptually design an experimental apparatus
- Use theory in order to guide the design of an experimental convective heat transfer system
- Enhance the theoretical treatment of convection by considering a "mixed-convection" regime

2. Background:

So far we have examined forced and free convection separately. In many practical scenarios these forms of convective heat transfer occur simultaneously, however only under certain conditions. If you were to design an experiment to test free or forced or "mixed" convection you need to first use theory in order to guide your experimental design. Figure 1 below shows you, in a horizontal tube, under which conditions (enclosed in the shaded boxes) forced convection, natural (free) convection, and mixed convection prevail for both laminar and turbulent horizontal tube flows based on previously acquired experimental data.

In Fig. 1 the "Graetz" number is Gz=RePr(d/l), μW is the fluid dynamic viscosity at the wall, μF is the film dynamic viscosity (based on the film temperature), Re, Pr, Gr and Nu are the Reynolds, Prandtl, Grashof and Nusselt numbers respectively and d and l are the diameters and length of the tube. The data in the figure is valid under these conditions:

10^-2 < Pr(d/L) < 1

In practice, many of the "regimes" shown on Fig. 1 are open to scrutiny, particularly as much of the data comes from old experiments. Your task is to design the conditions for an experiment that would be able to replicate some of the convective regimes shown in Fig. 1 for laminar and/or turbulent flows.

Figure 1: Regime Map for Forced, Free and Mixed Convection in a horizontal tube. Shaded boxes indicate where different regime spaces apply

3. Specifically your tasks are:
1) To determine physical conditions and geometry that would allow for you to take measurements in "mixed convection-turbulent flow", "mixed convection-laminar"
flow regimes, and in pure forced convection (laminar or turbulent). Your theoretical experiment must be able to generate those conditions in a horizontal tube with air flowing through the inside diameter.

Specific tasks related to point 1
a. If you used air; what temperatures, tube diameter, tube length, flow-rates and/or pressures would you use to operate your experiment in the various regimes?
b. If relevant, specify any other physical parameters needed for your experiment.
c. Design an experiment that allows you to swap from one regime to another with the least amount of variables having to change.

2) Undertake a theoretical "parametric analysis" for your experiment. For example, if you want to investigate a range of Reynolds numbers from 103 to 104, you could plot what the heat transfer rate from your inner pipe surface will be as a function of flow- rate over that range, according to say mixed-convection theory. In practice, were you then to take a measurement in that mixed-convection regime from your experiment, you would have some theory to compare too. You could also for instance, consider what your heat transfer coefficient should be as a function of the Reynolds number or another dimensionless number. These two examples are only suggestions to what you could plot or analyse, however you must have at least 4 graphs in your results (including at least 1 item of analysis which excludes the two examples given above).
Specific tasks related to point 2
d. You must generate at least 4 graphs plotting one relevant quantity vs. another, comparing/contrasting theoretical results of mixed convection to pure forced convection, discussing differences in trends in your plots.
e. You must discuss, in practice, what specific measurements you would take in order to test the validity of your theoretical results. Consider where/how you would take the measurements from your horizontal pipe. You may also consider what sort of equipment you would use here (of course you may draw on the experience gained from the prac sessions).

What is the point of this?

The purpose of this analysis is to show how one variable will affect another "in- theory", therefore giving you something to expect were you to run an experiment. If in practice you then did not acquire the expected result in your experiment (within experimental error), and you are certain your experiment is well-designed, it means the theory does not hold up and requires revision.

4. Written Report
The written reports should follow the normal guidelines for technical report writing (some suggestions are given below). In particular, there must be an Executive Summary which concisely reports the objectives and conclusions reached, as well as a reference list.
- Responses to the questions raised in the section "3. Specify your tasks".
- Presentation and discussion of the results of analyses.
- Describe what parameters/equations were used to specify the problem.
- Describe how (and why) the calculations were carried out.
- Present a summary of the results obtained (figures if needed).
- Discuss the results obtained.

We appreciate that some of you may have limited experience in writing technical reports. This is an important engineering skill. Here are some tips:
- Technical writing is not essay writing. There is no need for flowery words or grand

sentences - simple clear language is best.
- Skills needed for technical writing are exactly those needed to be a successful engineer
- logic & precision.
- Present the information in the order in which readers can best follow it.
- Write from the reader's perspective.

5. Assessment
This assignment contributes towards the assessment of MECH302. You will work for this project and hand in a report. The report will be marked out of 30.
- Report due on Sunday 11th November 2018. For assignments handed in late the following penalties apply: 0-24 hrs - 25 %, 24-48 hrs -50%, more than 48 hrs -100%.
- Report must not be longer than 8 pages plus appendices, executive summary (max 1 page) and references.
- All relevant supporting material calculations must be incorporated into an Appendix.
- Must reference sources of information and include a complete reference list.
- The report must be well written, concise and clear.
- Report must address key aspects outlined in 3. Specify your tasks.