Thermal ResistancebyDan SchwarzSchool of EngineeringGrand Valley State UniversityEGR 468 – Heat TransferSection 02Instructor: Dr. M. SozenFebruary 28, 20081OutlineI. Introduction/Purposea. Purpose Statement: Find the R-value of Plexiglas and Polystyreneb. Equation 1: One-dimensional heat transferc. Equation 2: R-valueII. Procedurea. Describe heat sourceb. Figure 1: Illustration of systemc. Describe measurement schemeIII. Lab-equipmentIV. Resultsa. Figure 2: Experimental temperature curve for Plexiglasb. Equation 3: R-value of Plexiglasc. Figure 3: Experimental temperature curve for Polystyrened. Equation 4: R-value of PolystyreneV. Discussion/Conclusiona. Possible sources of errorVI. Appendixa. Answer to Question 1b. Answer to Question 2c. Answer to Question 3d. Answer to Question 4e. Answer to Question 5f. Answer to Question 62Introduction/PurposeThermal resistance is a material property that describes a material’s ability to resist heattransfer. In this lab, samples of both Plexiglas and Polystyrene were tested to determine their R-value. A 25-watt heat source was used to create a measureable one dimensional temperaturegradient within the material. A one dimensional heat transfer condition was achieved bycontaining the heat source within an insulated box. The sample material was used to replace thetop surface of the insulated box so that most of the heat would flow through the sample only.The one-dimensional heat transfer rate was modeled using Equation 1.(1)The system was allowed time to approach steady state so that the temperature gradient wasconstant throughout the sample. Thus, . The R-value was found bysubstituting into Equation 1 and by solving for R to obtain Equation 2. (2)ProcedureThe heat source of this experiment was 25-watt light bulb contained inside an insulatedwooden box as shown in Figure 1. A piece of sample material was cut to 7x7¼” to serve as thetop surface of the container. One thermocouple was placed in the inside surface of the sampleand one thermocouple was placed on the outside surface. The sample was then placed in the topopening of the box and the light bulb was turned on just as the data acquisition system began tocollect data. The experiment was complete once the plotted temperature curves began to leveloff, indicating that the steady state condition had been reached.Figure 1: Insulated box with heat source. (One-dimensional heat transfer system)3Lab Equipment- National Instruments DAQ (CA-1000)- National Instruments Voltage Meter (NI-4350)- Labview Data Acquisition Software- K-type Thermocouples- Insulated Wooden Box- Square Plexiglas Sample (0.0055m Thick)- Square Polystyrene Sample (0.0095m Thick)- 25-watt Light BulbResultsFigure 2 shows plotted temperature data that was collected from thermocouples on boththe inside and outside surfaces of the Plexiglas. The temperature curves were level enough thatthe system was considered to be at steady-state.Figure 2: Plotted temperature of the plexiglas sample.Using the temperature data of the system at steady state, the R-value of plexiglas was calculatedin Equation 3.(3)Figure 3 shows plotted temperature data that was collected from thermocouples on boththe inside and outside surfaces of the Polystyrene. The temperature curves were level enoughthat the system was considered to be at steady-state.4Figure 3: Plotted temperature of the Polystyrene sample.Using the temperature data of the system at steady state, the R-value of polystyrene wascalculated in Equation 4.(4)Discussion/ConclusionThe results of this experiment are logical in that the Polystyrene, which is designed to bean insulator, has a high R-value than the Plexiglas. Thus, for any given thickness, thePolystyrene will provide more thermal resistance than the Plexiglas.The most likely source of error in this experiment was the insulated box. The sampleswith higher R-values, such as the Polystyrene, insulate the top of the box well. This would causemore heat to be transferred through the other walls of the box. Since the governing equation isone-dimensional, there would be heat transfer that is unaccounted for. The result would be a lowestimate for the R-value of the sample material.Another likely source of error is in our assumption of steady-state. If steady state had notyet been achieved, the temperature gradient using in Equations 3 and 4 would be incorrect. Theresult would be a low estimate for the R-value.Appendix A: Answers to Lab QuestionsQuestion 1: Under what conditions does the general energy equation results in Equation 2?If the heat transfer conditions were multi-dimensional we could notuse Equation 2. Equation 1 would also be inappropriate if thesystem was not at steady state.5Question 2: Consider the apparatus that we used in lab. What steps were taken to assure one-dimensional heat flow? Could a thick sample of a good insulator be accurately tested?One dimensional heat flow was assumed because the walls of thebox were designed to insulate the heat source better than thematerial sample. A thicker sample material would not yield goodresults because thicker material would insulate the box better. Thiswould cause more heat to flow through the walls of the insulatedbox which is multi-dimensional flow.Question 3: What steps did you take to assure that steady state was achieved? How would thegoverning equations change if the problem was unsteady?We plotted the temperature with respect to time in order to assurethat the temperature was approaching steady state. We continuedto take heat measurements until the temperature curves leveled off.If the system was not at steady state then the governing equationwould need to account for the change in the temperature gradientwith respect to time.Question 4: Suppose that it takes a long time for your sample to reach steady state. Are there anypractical benefits or drawbacks for a material that reaches steady state slowly? If the material requires a long time to reach steady state, it is likelyto be a good insulator. This means that more heat will flowthrough the walls of the insulated box instead of the sample. Thiscreates a multi-dimensional heat transfer condition which is harderto model.Question 5: How would you estimate the experimental uncertainty for this experiment?Question 6: From the ASTM standard