ME 105 Mechanical Engineering Laboratory Spring Quarter Experiment #2: Temperature Measurements and Transient Conduction and Convection

Size: px

Start display at page:

Download "ME 105 Mechanical Engineering Laboratory Spring Quarter Experiment #2: Temperature Measurements and Transient Conduction and Convection"

Penelope Watts
5 years ago
Views:

1 ME 105 Mechanical Engineering Lab Page 1 ME 105 Mechanical Engineering Laboratory Spring Quarter 2010 Experiment #2: Temperature Measurements and Transient Conduction and Convection Objectives a) To calibrate three types of temperature measurement devices, b) to characterize their sensitivity and response times, c) to use them in an experiment in transient heating or cooling, and d) to measure heat transfer coefficients under different conditions. Pre Lab Reading The fundamental concepts behind this lab are the three mechanisms of energy transfer: conduction, free convection, and forced convection. Most of the analysis for this lab and the data reduction relies on lumped capacitance modeling of heat transfer. Whether or not you have studied these topics before, review them in any of the standard textbooks on convective heat transfer (for example: Incropera and Dewitt is a reasonable reference). An overview is presented below, but this lab handout is not a substitute for more extensive background reading. This lab also deals with heat transfer to flowing fluids. Review relevant material from your undergraduate fluid mechanics courses, including the flow field around a sphere as a function of Reynolds number. Read Section 9.2 in Introduction to Engineering Experimentation. Pre Lab Exercises 1. This lab uses three devices to measure temperature thermocouples, thermistors, and resistive thermal devices (RTDs). Briefly explain the physical basis of operation of each. 2. In using a thermocouple, why is it necessary to measure the output voltage relative to that produced by a reference junction placed in an ice bath? 3. Why do RTDs sometimes have three leads? 4. What are the basic assumptions behind the lumped capacitance model for transient heat transfer? Is such a model always valid? 5. Define conduction, forced convection and free convection. How do they differ? Prepare and submit an outline that includes: Calibrations to perform Data sets to collect Possible sources of experimental uncertainty and a plan for quantifying these errors Brief description of the work plan Any equations or physical parameters that may be needed during the laboratory session (See general lab guidelines & print out grading sheet from website).

2 ME 105 Mechanical Engineering Lab Page 2 Equipment and Overview Thermocouples (chromel-alumel, so-called type K ) Thermistor Platinum RTD (3-lead) Ohmmeter Millivoltmeter Computer/LabView Thermometer Digital Thermometer Ice Gas stove Aluminum cooking pot with thermocouple well in lid Insulated containers Aluminum sphere with an embedded thermocouple In week one of the lab, you will develop a procedure for calibrating three measurement devices in order to establish a relationship between their output (voltage or resistance) and the temperature. You will also need to establish techniques for measuring or estimating the thermal response time for the three devices. In week two, you will need to use procedures you developed in week one to measure the transient response of the aluminum sphere when subjected to a step change in temperature under different environmental conditions. Theoretical Background 1) Transient energy transfer The key analysis underpinning this laboratory is that of lumped capacitance modeling of transient energy transfer. Consider an object of volume V, density, and surface area A that is initially at a uniform temperature T i and is suddenly exposed to an instantaneous step change in the external temperature to a final value of T. Under suitable assumptions (which you will examine in the prelab exercises), the temperature of the object T(t) is governed by the following differential equation expressing the balance law for energy: (1) with initial condition T(0) = T i. Here c P is the specific heat capacity and h is the heat transfer coefficient. Assuming all the parameters and properties are constant, Equation (1) can be integrated to yield:. (2)

3 ME 105 Mechanical Engineering Lab Page 3 Equation (2) may be written equivalently in terms of a dimensionless temperature difference Θ and a relaxation time,, as Θ, (3) which is a very standard result for a process exhibiting first order response. By comparing Equations (3) and (4), one finds that the thermal relaxation time is: 2) The heat transfer coefficient. (4) The heat transfer coefficient depends on the nature and strength of the fluid flow and the geometry of the object. For flow around a sphere, h is often expressed as a dimensionless Nusselt number, Nu: (5) where D the diameter of the sphere, and k is the thermal conductivity of the fluid. Simple relationships exist between the Nusselt number and the flow Reynolds number,, where U is the fluid speed, and the kinematic viscosity. For this experiment: / / (6) where Pr = /k is the Prandtl number of the fluid, which can be found in tables of thermophysical properties. Equation (6) establishes the dependence of the heat transfer coefficient on the fluid that is flowing around a sphere and the speed of the flow. (Note that there are analogous relationships for free convection, but they are more complicated and need not concern us here.) Experimental Procedure WARNING: Please be careful of the boiling water and steam it produces. Severe burns and/or scalding can result from carelessness. Be careful in lighting the stove burners - be sure to have the lighter flame ignited before turning on the gas. Note: This lab involves measuring transient energy transfer, by either heating or cooling of objects following a step change in temperature. Think through whether you are going to heat or cool in terms of which is the safer and easier to do. In any case, do not move the glass thermometer directly from boiling water into the ice bath (or vice versa). Doing so thermally shocks the glass, leading to cracks and eventual breakage of the device.

4 ME 105 Mechanical Engineering Lab Page 4 Laboratory: Week One 1) Accuracy of the thermometer The thermometer will be used to calibrate the devices. The calibration will only be as accurate as the thermometer itself, so the purpose here is to establish the degree of uncertainty in the temperature readings of the thermometer. Use the ice bath and boiling water to accomplish this and report thermometer accuracy in terms of +/- o C. 2) Calibration Using water baths of varying temperature, establish a calibration between the outputs of the thermocouple, thermistor, and RTD and temperature (as measured by the thermometer). The thermistor and RTD will be supplied, but you should make your own thermocouple by twisting Cr and Al wires together and crimping with pliers. In commercial thermocouples, the two metals are welded into a small bead, but since we are calibrating our home made thermocouple, that isn t necessary (although we will later make an assumption that our calibration also holds for the thermocouple embedded in the aluminum sphere.) Connect the ends of these two wires to the volt/ohmmeter and interface with the computer using Labview. Be sure to place the cold junction appropriately in the circuit (see prelab question #2.) 3) Sensor response time An important characteristic of a temperature measuring device is its response time. Often the need to have a rapid response (thus a small response time) dictates the type of device chosen for a given application. Estimate the response time of the three devices by subjecting them to a step change in external temperature. 4) Transient heating or cooling of a sphere You are supplied with a large aluminum sphere with an embedded Cr-Al thermocouple. Using Labview, take data on the transient heating (or cooling) of the sphere by subjecting it to a step change in the external temperature and measuring the temperature of the sphere as a function of time. Be sure to record the initial and external temperatures and save T(t) as a data file for later analysis. 5) A simple test of conservation of energy Fill one of the insulated containers with a known volume of water at a known temperature and immerse one of your devices in the water in order to monitor its change in temperature. Heat or cool the large aluminum sphere to a given (different) temperature and then place it in the bath. Using Labview and/or manual data logging, measure the temperature of both the water bath and the sphere as a function of time. Analysis: Between Weeks One and Two Please complete the following tasks, and include these results in your rough draft report/summary. 1) Calibrations, linearity, and sensitivity Analyze your data to obtain calibration curves for the three devices. For each device, plot T vs. measured voltage or resistance. By observing the data, and using a least squares regression

5 ME 105 Mechanical Engineering Lab Page 5 analysis, determine the degree to which any of these devices are linear over the range of temperatures studied. Another important property of temperature measuring devices is the sensitivity. This is defined either in terms of the output (voltage or resistance) per unit degree Kelvin or in terms of the percentage change in voltage or resistance per degree Kelvin. Using both definitions, calculate the sensitivity of all three devices. Which is the most sensitive? 2) Response times Estimate the response time for the three devices. Which is the fastest and which is the slowest? Discuss possible reasons for these differences. Using your data on the transient heating (cooling) of the large sphere, determine the degree to which the data are approximated by the exponential form of equation (3). Estimate the thermal response time of the aluminum sphere. (Hint: Use a semi-log plot to simplify the curve fitting). 3) A test of conservation of energy Using the initial and final temperatures of the aluminum sphere and the water in the insulated container, compute the total energy gain (loss) in Joules from the sphere and compare it with the energy loss (gain) to the water in the insulated container. Discuss the degree to which your data support the principle of conservation of energy. Discuss possible reasons for a discrepancy. Laboratory: Week Two 1) Repeat any of the measurements from week one that were not satisfactory. 2) Convective heat transfer Equation (4) expresses the thermal response time as a function of physical properties, the size of the object in question, and the heat transfer coefficient. Measurement of the thermal response time allows the heat transfer coefficient to be determined if all other quantities are known. Measure the temperature response of the large aluminum sphere to a step change in temperature for the following four situations: Sphere in still air Sphere in moving air Sphere in still water Sphere in flowing water (you may have to either stir the water or move the sphere around in a bath in order to accomplish this last one.) Data Analysis: Week Two 1. Use the transient heating (cooling) data from week two to calculate the heat transfer coefficient for the four cases studied. Below is a table of ranges of heat transfer coefficients in air and in water. Compare your data with these ranges. Do they fall within these ranges? If not, can you think of reasons why they might not?

6 ME 105 Mechanical Engineering Lab Page 6 Air Water Free convection Forced convection ,000 Table 1. Range of experimental values of the heat transfer coefficient, in W/(m 2 K) 2. The heat transfer coefficient varies with the properties and the speed of the flowing fluid responsible for the convective energy transfer. If this relationship is known, then measurement of the heat transfer coefficient allows one to infer the velocity of the fluid. This is the basis of hot film and hot wire anemometers. In this lab, we built a simple (and relatively crude) anemometer, but we can use the data to illustrate the principle. Using your measured values of h and Equations (5) and (6), estimate the speed of the water and air used in your forced convection experiments. Report Your report should cover the main points of the laboratory work and discusses all the questions raised above. In particular, be sure to: Describe the three devices and how they work Report the properties of the devices including linearity, sensitivity, and response time Test of the predictions of exponential decay of dimensionless temperature and measurement of response times for the large Al sphere. Test of conservation of energy Report the heat transfer coefficients for both free and forced convection in both air and water. Report estimate of air and water velocity in forced convection experiments. As always, your report should clearly state the objectives, give the background theory, and show all the data and results of analysis and curve-fitting using professionally drawn figures and tables. For a detailed description of expectations and requirements, see the general lab guidelines & print out grading sheet from website.

ME 105 Mechanical Engineering Laboratory Spring Quarter INTRODUCTION TO TRANSIENT CONDUCTION AND CONVECTION

ME 105 Mechanical Engineering Lab Page 1 ME 105 Mechanical Engineering Laboratory Spring Quarter 2003 2. INTRODUCTION TO TRANSIENT CONDUCTION AND CONVECTION This set of experiments is designed to provide