1. Air-Water Heat Exchanger Lab In this lab, YOU will design, conduct, and analyze your experiment. The lab handout will not tell you exactly what to measure or calculate! You will use an air-water heat exchanger testing unit to verify the energy balance and determine important heat exchanger parameters for a variety of CFM.

2. Lab Schedule Week 1: discuss design of experiments and uncertainty, sketch and become familiar with apparatus, design experiment, and sign up for a time to take data Week 2: take data and begin analysis Week 3: analyze data and write report; take additional data if needed

3. Design of Experiments “Design of experiments (DEX or DOE) is a systematic, rigorous approach to engineering problem-solving that applies principles and techniques at the data collection stage so as to ensure the generation of valid, defensible, and supportable engineering conclusions. In addition, all of this is carried out under the constraint of a minimal expenditure of engineering runs, time, and money. “ http://www.itl.nist.gov/div898/handbook/pmd/section3/pmd31.htm

4. Types of DOE “There are 4 general engineering problem areas in which DOE may be applied:  Comparative  Screening/Characterizing  Modeling  Optimizing Comparative: The engineer is interested in assessing whether a change in a single factor has in fact resulted in a change/improvement to the process as a whole. “ This is what we’ll be doing. http://www.itl.nist.gov/div898/handbook/pmd/section3/pmd31.htm

5. DOE for this lab DOE is a complex engineering field. We’ll use only a few of the most basic ideas here. If multiple input parameters are varying at the same time, it’s very difficult to know what’s causing a change in an output.  In this lab, we’ll vary the air CFM but keep all other parameters constant. Two data points do not prove a linear/parabolic/exponential relationship. We typically cannot extrapolate results beyond the range for which we took data with any level of certainty.

6. Significance of Results In our old HX setup (used several years ago), the temperature of the water changed only about 2 or 3ºC from inlet to exit. With a temperature uncertainty of >2ºC, was there a significant temperature change? 95% confidence interval: 95% of data will fall within +/- 1.96  of the mean for a Gaussian distribution We typically say differences are significant if they are outside of the 95% confidence interval

7. Simplified Uncertainty Analysis Random (precision) error  For temperature measurements, this typically includes fluctuations in the electronics of the data acquisition units as well as fluctuations in the quantities measured Bias (fixed) error  For temperature measurements, this typically includes the finite resolution of the A/D card (if one is used), the use of a curve fit for the thermocouples, reading of calibration thermometers, and conduction and radiation errors. Total uncertainty is found using the root mean square (RMS) of these two errors

8. Random Error 95% confidence interval – 95% of temperature readings will fall in this range  =+/- 2 (or 1.96) standard deviations  For your lab, you could estimate this error by taking more than 30 data points (N=30+) for one temperature, mass flow rate, and CFM for one of your CFM. Then the average and standard deviation could be calculated using the equations below.  Excel can be used instead.  Unfortunately, you will have limited time available to take data for this lab, so you may ignore random error.

9. Bias Error For our lab, we will do a simplified analysis using manufacturers’ provided uncertainties. Mass flow meter uncertainty: +/- 1% of reading CFM uncertainty: +/- 5% of reading > 185 CFM. Below 185 CFM, the uncertainty may be greater. Thermocouples: +/- 1.8ºF each (varies with type of thermocouple) Thermocouple reader: 1ºC + 0.1% of reading You may assume that the uncertainty of properties such as specific heat and density are negligible.

10. Temperature Uncertainty To find the error of one temperature reading, use the RMS of the thermocouple and thermocouple reader errors To find the bias error in your temperature difference, use the RMS: Divide by the  T to find the percent uncertainty in  T  You can pick an average  T – don’t do this for every different  T that you measure  Since the air and water  T’s are different, they have different percent uncertainties in  T as well.

11. Propagating Errors To find the percent uncertainty in Q, you must propagate the errors. In ME 120, you will study uncertainty analysis in detail. For this class, all you need to know is this:  If A=B*C*D, then Where U is a percentage uncertainty in each component For this lab, find the percent uncertainty in Qair and Qwater. Do this at an average CFM reading – you don’t need to do it for each CFM.