Thermal Conductivity - Lab Report Example

Thermal conductivity: The materials ability to conduct heat through conduction as mode of heat transfer is referred to as thermal conductivity, given watts per meter kelvin (W/m.K). When any given material has a high thermal conductivity or low thermal conductivity, it either high or low rate of heat transfer respectively. In addition, thermal conductivity can be referred at as heat flux to temperature ratio. When this ratio is checked, it is used in determining the heat flow uniformity for any given material, thickness from the outer section of the any other given material. Conduction is the process by which heat is transferred from one material body to another through contact between the two bodies. Thermal conductivity can be defined as the ratio of heat flux to the temperature gradient. The ratio would be used to indicate the uniform flow of heat for a given sample thickness from one side to another. As the definition states, thermal conductivity, k, gives the property of any given material to conduct heat from an external source. Body conducting heat from another quantifies the process of heat transfer, and it is given by the Fourier’s Law equation. = Therefore, rearranging the Fourier’s Law equation we get thermal Conductivity equation. K= -QA Where: = thermal conductivity [W/ (m*C◦)]. = heat flux (Watts) - The temperature difference (temperature change), Where: – hot plate temperature and – cold plate temperature – sample thickness – sample cross-sectional area The temperature is negative since the heat transfer is from the hot plate to a cold place, which means the temperature transfer is in decreasing direction [1] Two principal methods are used for measuring thermal conductivity. These two methods include transient methods and steady-state methods. Transient methods are applied record measurements in the cooling down or heating up process for liquid or solid material. Steady state conditions pertain to temperature, which is constant at every point of the given sample, that is, not involving a function of time. Transient methods provide quicker measurements compared to steady state method giving it more advantage in application [3]. Transient methods Currently, there are modern data analysis tools and computers, which have made transient methods more accessible for measuring thermal conductivity. To measure response as a signal that has been sent to develop heat in the given test specimen, transient methods are used. At the start, the sample is supposed to be in thermal equilibrium with the atmospheric conditions. Then heating pulse, which is in short signal, is released to the specimen. During the measurement period, the temperature variance is recorded and used later to determine the test specimen thermal conductivity [7]. Transient techniques have a number of advantages in that less knowledge is required for stability, dimensioning and precise alignment, but duration required to conduct the experiment is the most recognized advantage. Compared to steady state measurement method, which can take one hour, transient analysis will take few minutes to complete a typical measurement. When measuring temperature in two opposite direction on the surfaces of a specimen that is required for steady state analysis is substituted by a measurement of temperature as a function of time at only single point for the transient methods [6]. The design of the transient measurement equipment is aboveboard, and they allow for betterment for accuracy of results. Nevertheless, transient conductivity measurements necessitate for data tools that are relatively elaborate, as well as using advanced tools. Steady- State methods In steady state, internal heat supplied by an electrical heat source helps to maintain the temperature in the system. This heat is measured to determine the temperature difference two given points in specimen that are separated by distance x [2]. Cell geometry is used to classify steady state methods to achieve heat transfer where radial and axial systems are the most used commonly. One of the methods that have proved to provide results that have the highest accuracy and most consistent is axial flow methods. The method that is usually used for axial system is the use of the parallel plate apparatus (also known as guarded hot plate apparatus). On the other hand, the concentric cylinder is frequently used for systems that are radial. One of the main disadvantages of using the steady state measuring method is that they are time consuming, although they give reliable and accurate results. Heat flow meter method Ideally, heat flow meter method measures the temperature difference through thermal resistor at steady state conditions to determine the heat flux. Heat flow meter method design is more like to the single specimen guarded hot plate apparatus, but it has a difference in that instead of having primary heat it has a heat flux sensor. Heat flux sensors, these are resistors for thermal changes and they have thermocouples installed in them. For some cases, to determine radial losses a heat flux sensor is placed on a plate that is cold and lower the measurement time required. Where thermal conductivity is lower than 0.3 W/(mK) especially for insulation materials and polymers, this is a method is used, and an uncertainty of 3% is achieved [4]. Nevertheless, in case of losses in the radial direction then there is chance for rapid increase in risk. Moreover, conventional heat flow meter method when measuring heat transfer it adopts conduction in one-dimension, i.e. there is no radiation or convection in the system. Therefore, it is sensible to have this assumption if the specimen tested is thin in the direction towards which the heat flow is, and its cross-section area is large. For radiation and convection, the surface area becomes less compared to the heat transfer by conduction through the specimen, and this is well set for materials that have low conductivity. However, a thicker test specimen is required for materials with high thermal conductivity; this is to enable the easy way to determine the difference in temperature. This leads to change in doubt regarding the measurement accuracy of radiation and convection will remain. When the experiments are conducted under high vacuum conditions, it helps in reducing the convective heat losses [6]. The method is best suitable when testing specimens that are anisotropic and is reliable and very accurate when determining thermal conductivity in a single dimensional heat-flow. Figure 3: heat flow meter apparatus for typical heat flux transducer Thermal diffusivity As discussed earlier, thermal conductivity, controls heat flow through the material when it is at steady state. On the other hand, thermal diffusivity is the property of the material to heat flow control. (Units are m2/s). Thermal diffusivity and thermal conductivity are related by: Where: = Thermal diffusivity (m2/s) = Density (kg/m3) = Thermal conductivity (W/m.K) = Specific heat (J/m3K) It takes a component of thickness, w, to determine the time, t, required to attain equilibrium state when there is a sudden change in temperature and it is given by the equation below: Where is t = time (s) a = thermal diffusivity (m2/s) w = thickness (m) Thermal conductivity Experiment 5.1 Sample preparation procedure List of equipment and tools used for this experiment: Three large empty buckets Gypsum Flax dust Electric hand mixture Weight scale Volume Measuring Tube Metal bowl Two wooden moulds Screwdriver Gloves Since the mould is larger compared to the first experiment moulds, there is a need to have a vibration table. 5.1.1 Moulds preparation Wooden moulds have been given in the lab for the experiment. These moulds are of 30 × 30 cm and 5cm in thickness. To assemble the mould, there are 8, 5mm screws used. Screws are used to ensure that it is easy to un-screw when de-moulding. Methodology The preparation procedures used for sample material preparion (Gypsum, Water) included, measuring Gypsum in one bucket and the water was measured using a separate bucket, then gypsum and water mixed in a separate empty bucket. To start, we poured the Gypsum in the empty bucket and waited for two minutes to settle, then we pour water into the bucket with Gypsum and used an electrical blender to mix the two to acquire best results of the mixture. The use of electrical hand blender is continued for approximately two mininutes. Then slowly we pour the mixture inside the mould to the brim. For the Gypflax samples the same steps as for Gypsum are repeated but here there is 4% flax dust which is added when pouring Gypsum in the mixing bucket, then we mix using hand and leave the mixture for two –five minutes then we add specific quantity of water prepared in the dry Gypfax. Then we use electrical hand tool to mix, but in this case we mix for shorter time, since it solidifies faster than Gyspum only, then we pour the mixture into the wooden mould. To remove air bubbles from the mould we use vibrating table, since air bubbles can weaken and affect the sampel results. To remove the bubbles, we place the moulds on the vibrating table switch it on then hold the moulds using the hand for three times. However, if the sample is allowed to vibrate for a longer time, it may create a risk to go through aggregate breakup from fine materials. After the moulds have completed 48 hours, they have solidified well to do the de-moulding process by unscrewing the 8 screws from the moulds, and then we allow the mould 48 hours for fresh air and ensure that they solidify properly. 5.2 Thermal conductivity experiment procedure The property of a material to transfer heat through conduction is referred to as thermal conductivity given in Watts per meter Kelvin (W/ m·K). A rig with flow meter has been used in measuring thermal conductivity for determining heat flux q. To begin with, we open the door of the rig then press start button to raise the hot plate lowering the cold plate, then we put silicon sheet on the cold plate the place the sample on top of the silicon sheet. This is to make sure that it touches the hot plate after closing the rig. Then we switch on the rig while connecting it to the computer to get the measurement readings. To do this, we start the rig program and specify on the measuring points (6 points) selecting the number of steps for temperature measurement on the cold and hot plates at 120 seconds. Having set all the system, then we launch the test, which is carried out at the University of Brighton Laboratories. Experiment Calibration Heat flow meter was broken last year; therefore, another method was used in determining thermal conductivity. Nevertheless, heat flow meter has been fixed this year and it is operational. Thus, I used it in calculating thermal conductivity. Additionally, I used last year method results to compare if the test results were tallying. Method 1: using Nylon 66 sample This is done using two experimental samples where one sample is the test sample with unknown thermal conductivity and the second sample with known thermal conductivity. However, it is easy to determine thermal conductivity of the sample without reading from the flow meter through calculations if you have sample thickness, T1, T2 and T3, sample cross sectional area and thermal conductivity of one sample. This equation for the heat flux is as the following: Applying this equation to acquire heat flux for unknown sample, it can be similarly used to acquire heat flux for a known sample, thus, q1=q2. Since Nylon66 has a known thermal conductivity of λ = 0.243 (W/ (m·K). Then, applying the previous equation it is easy to determine the heat flux, q, using test results from the precious test results (see graph below): Graph (16): Temperature difference (ΔT) for Nylon66 Sample We used the heat flux equation: We use Nylon66 heat flux, q, to calculate thermal conductivity (λ) for the other samples using this equation: Method 2: using the Heat flow meter When using flow meter to determine thermal conductivity of a material, a number of stages must be used a number of equations applied to attain the final thermal conductivity for the given material. 1- Determine (q̇) by using this equation q̇ = heat flow rate = final heat flow meter reading Calibration constant 2- Calculate drop in temperature across the silicon sheets ( (thickness of the silicon combined sheets = 6mm). Where: q̇ = heat flow rate w = silicon sheet thickness A= sample Area The sample area and sheet thicknesses where constants figures so 3- Calculate drop in temperature across the sample ( Where: = Average Temperature of Hot plate = Average Temperature of Cold plate = temperature drop across the silicon sheets 4- Calculating the sample thermal conductivity (λ) Where: q̇ = heat flow rate l = sample thickness ∆TS = Temperature drop across the sample Standard Derivation Calculations: We used excel to calculate most of the standard derivation used for the thermal conductivity, where the following equation was used; Gypsum Sample: Graph (17): Temperature difference (ΔT) for Gypsum Sample From the graph above, it is observe that steady state started after 42 minutes of the experiment indicated by black vertical line in the graph. Then the temperature starts rising until it stops rising maintain separating with an accuracy of ±1.8 C◦. On attaining the maximum temperature graph cannot rise any further and then stops indicating that the gypsum has reached maximum temperature that it can conduct heat. GypFlux Sample: Graph (18): Temperature difference (ΔT) for GypFlax Sample From the graph above, steady state started after 42 minutes of the experiment, which is indicated by a black vertical line. Then the temperature difference was rising then stopped rising and kept separating with an accuracy of ±2.2 C◦. This separation continued up to 500 minutes of the experiment. Beyond this point, any change in temperature has no effect on the Gypflax sample behavior when exposed to heat. It is therefore, we can conclude that, Gypflax will respond to changes in temperature to a certain point where temperature changes has no effect on the sample. To get the time taken for steady state period we calculated the thermal diffusivity Results Analyses Graph19: Thermal Conductivity difference between Gypsum and Gypflax samples The above graph is a plot of the differences between thermal conductivity of Gypflax and Gypsum samples, where Gypsum has a higher thermal conductivity than Gypflax, which is attributed to the fact that, Gypflax has higher insulation by 10% more than Gypsum samples. The additional flax dust accounts for this insulation in Gypflax. Although Gypsum and Gypflax takes an equivalent amount of time to reach the steady state, Gypsum has a higher thermal conductivity than Gypflax sample. Gypsum has molecules of the type, which makes it good material in thermal conductivity compared to Gypflax that has flax dust, which lowers its ability to conduct heat easily. Table (6) below is a summary of thermal conductivity experiment results and it indicates the thermal conductivity comparison between Gypsum and Gypflax samples only. Thermal Conductivity Comparison Table Sample Gypflax Gypsum 1 0.6 0.6 2 0.4 0.6 3 0.4 0.4 Average 0.48 0.53 ST.DV 0.1 0.1 10 % Table (6): Comparison Table for Thermal Conductivity Comparing thermal conductivity between, Gypsum and Gypflax samples from the experiment, thermal conductivity for Gypflax sample is 10% lower than Gypsum samples. This indicates that flax dust contributed favors to the Gypsum complex pertaining thermal properties, this made Gypflax sample to have satisfactory thermal properties. Additionally, for both samples, steady state is at exactly after 42 minutes, which means the two samples takes equal time to reach steady state and at the same point. This means that particulate behavior of the two samples is the same up to the steady state temperature, however, gypflax changes due to increased insulation, which is attributed to the addition of flax dust in the gypsum composite. On the other hand, Gypsum has similar particles that have similar behavior and they have no intermolecular particle insulation. Therefore, at the beginning of the test, the particulate behavior in the two samples is contributed to fact that Gypflax has Gypsum composite, which will act as pure Gypsum until the particles attain a separation temperature at which flax dust insulates the Gypsum composite particles. Flow Meter Reading Graph (20): Flow meter readings for three samples for the last hour Comparing the three samples, the readings from the flow meter indicate that Gypsum had the highest readings after testing for thermal conductivity rig where their readings are made after every two minutes for one hour. For gypsum, it started 15.30 and its increase until it reaches up to 15.63 for one hour, which means gypsum conducts heat better than the others do. On the other hand, Gypflax samples have 10% insulation capabilities than the gypsum samples. On average, there is a difference of 0.77 ± 0.05 between Gyspsum and Gypflax samples, where Gypsum samples are higher than Gypflax samples by 5%. Nylon66 indicate the lowest increase in temperature change starting at 14.18 to 14.23 within 1 hour. Since heat flow meter method is used in measuring temperature difference via a thermal resistor, it is clear heat flux for Gypsum is higher compared to Gypflax and Nylon66 since they both have thermal conductivity lower than 0.3 W/(mK). This is because Gypflax has insulation material and Nylon66 is a polymer. References [1] Alessandro, F., (2007). An apparatus for the routine measurement of thermal conductivity of materials for building application based on a [transient hot- wire method. Applied Thermal Engineering. 27(14–15): p. 2495-2504 [2] Ashby, M (2005). Materials selection in Mechanical design. Oxford: ELSEVIER Butterworth-Heinemann. [3] Buck, W. and S. Rudtsch, (2006). "Thermal Properties" Springer Handbook of Materials Measurement Methods. Ed. New York: Springer. p. 399-429. [4] Incropera, F.P., et al., (2011) Fundamentals of heat and mass transfer 2011. New York: Wiley. [5] Mahanta, N.K. and Abramson, A.R. (2010). The dual-mode heat flow meter technique: A versatile method for characterizing thermal conductivity. International Journal of Heat and Mass Transfer. 53(23–24): p. 5581-5586. [6] Subhash, L. S. and Jitendra, G., (2006) High Thermal Conductivity Materials. New York: Springer Science & Business Media. 22 [7] Ventura, G. and Perfetti, M., (2014). Thermal Properties of Solids at Room and Cryogenic Temperatures. New York: Springer. 13 Read More

Compared to steady state measurement method, which can take one hour, transient analysis will take few minutes to complete a typical measurement. When measuring temperature in two opposite direction on the surfaces of a specimen that is required for steady state analysis is substituted by a measurement of temperature as a function of time at only single point for the transient methods [6]. The design of the transient measurement equipment is aboveboard, and they allow for betterment for accuracy of results.

Nevertheless, transient conductivity measurements necessitate for data tools that are relatively elaborate, as well as using advanced tools. Steady- State methods In steady state, internal heat supplied by an electrical heat source helps to maintain the temperature in the system. This heat is measured to determine the temperature difference two given points in specimen that are separated by distance x [2]. Cell geometry is used to classify steady state methods to achieve heat transfer where radial and axial systems are the most used commonly.

One of the methods that have proved to provide results that have the highest accuracy and most consistent is axial flow methods. The method that is usually used for axial system is the use of the parallel plate apparatus (also known as guarded hot plate apparatus). On the other hand, the concentric cylinder is frequently used for systems that are radial. One of the main disadvantages of using the steady state measuring method is that they are time consuming, although they give reliable and accurate results.

Heat flow meter method Ideally, heat flow meter method measures the temperature difference through thermal resistor at steady state conditions to determine the heat flux. Heat flow meter method design is more like to the single specimen guarded hot plate apparatus, but it has a difference in that instead of having primary heat it has a heat flux sensor. Heat flux sensors, these are resistors for thermal changes and they have thermocouples installed in them. For some cases, to determine radial losses a heat flux sensor is placed on a plate that is cold and lower the measurement time required.

Where thermal conductivity is lower than 0.3 W/(mK) especially for insulation materials and polymers, this is a method is used, and an uncertainty of 3% is achieved [4]. Nevertheless, in case of losses in the radial direction then there is chance for rapid increase in risk. Moreover, conventional heat flow meter method when measuring heat transfer it adopts conduction in one-dimension, i.e. there is no radiation or convection in the system. Therefore, it is sensible to have this assumption if the specimen tested is thin in the direction towards which the heat flow is, and its cross-section area is large.

For radiation and convection, the surface area becomes less compared to the heat transfer by conduction through the specimen, and this is well set for materials that have low conductivity. However, a thicker test specimen is required for materials with high thermal conductivity; this is to enable the easy way to determine the difference in temperature. This leads to change in doubt regarding the measurement accuracy of radiation and convection will remain. When the experiments are conducted under high vacuum conditions, it helps in reducing the convective heat losses [6].

The method is best suitable when testing specimens that are anisotropic and is reliable and very accurate when determining thermal conductivity in a single dimensional heat-flow. Figure 3: heat flow meter apparatus for typical heat flux transducer Thermal diffusivity As discussed earlier, thermal conductivity, controls heat flow through the material when it is at steady state. On the other hand, thermal diffusivity is the property of the material to heat flow control. (Units are m2/s).

Thermal diffusivity and thermal conductivity are related by: Where: = Thermal diffusivity (m2/s) = Density (kg/m3) = Thermal conductivity (W/m.

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