Use of fin analysis for determination of thermal conductivity of material

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1 RESEARCH ARTICLE OPEN ACCESS Use of fin analysis for determination of termal conductivity of material Nea Sanjay Babar 1, Saloni Suas Desmuk 2,Sarayu Dattatray Gogare 3, Snea Barat Bansude 4,Pradyumna Damangaonkar 5 1 Karad, Maarastra, India 2 Nanded, Maarastra, India, 3 Cincwad, Pune, Maarastra, India, 4 Katraj, Pune, Maarastra, India, 5 Pune,Maarastra, India Abstract: Te experiment demonstrates te use of fin analysis as one of te possible ways for determination of termal conductivity of material by using fins. In te experiment te termal conductivity of unknown material is determined by referring to te standard material of known termal conductivity. In te experimental set-up, a suitably designed eater coil is used as a eat source. An Aluminium rod is used as reference material and te provision is made in te setup to attac a test rod of wic termal conductivity is to be determined. A Multipole Digital Temperature indicator wit seven PT-100 termocouples are used to measure te temperatures. Te geometries of te test and reference rods are mandatory to be exactly same for analysis Keywords Termal Conductivity, Fin Analysis, Experimental Setup, Infinitely Long Fins Introduction: Termal conductivity is te ability of material to conduct te eat. It provides te base to differentiate te materials as conductors insulators etc. Tis differentiation forms one of te bases to select te material for particular application. Hence determination of termal conductivity is very essential. Various metods ave been developed in te recent past for tis. Tese conventional metods are bulky, expensive and require more time to acieve steady state. In te proposed experimental set-up, Fin Analysis is used as te basis to determine te termal conductivity of material wic overcomes te above mentioned drawbacks. Termal Conductivity of material is determined relatively by using te material of known termal conductivity. 1. Different metods to determine termal conductivity of metals: Following are te general metods available for determination of termal conductivity 1.1 Steady-state metod : In tis metod a sample of unknown conductivity is placed between two samples of known conductivity (usually brass plates). Te setup is usually vertical wit te ot brass plate at te top, te sample in between ten te cold brass plate at te bottom. Heat is supplied at te top and made to move downwards to stop any convection witin te sample. Measurements are taken after te sample as attained equilibrium (same eat over entire sample), tis usually takes about 30 minutes. 1.2 Transient metods Te transient tecniques perform a measurement during te process of eating up and ISSN: ttp:// Page 759

2 are quick processes. Transient metods are usually carried out by needle probes. Non steady-state metods to measure te termal conductivity do not require te signal to obtain a constant value. Instead, te C signal is studied as a function of time. AS Te advantages of tese metods are E tat tey can in general be performed more quickly, since tere is no need to A wait for a steady state situation. Te disadvantage is tat te matematical analysis of te data is in general more difficult. 1.3 Termo-reflectance is a metod by B wic te termal properties of a material can be measured, most importantly termal conductivity. Tis metod can be applied most notably to C tin film materials (up to undreds of nanometers tick), wic ave properties tat vary greatly wen compared to te same materials in bulk. Te idea beind tis tecnique is tat once a material is eated up, te cange in te reflectance of te surface can be utilized to derive te termal properties. Te reflectivity is measured wit respect to time, and te data received can be matced to a model wic contains coefficients tat correspond to termal properties. 2. Fin Analysis: Fins are te extended surfaces generally used to enance te eat transfer rate. Fins are used in many engineering applications to enance te convective eat transfer rate. Fins are used to enance convective eat transfer in a wide range of engineering applications, and offer a practical means for acieving a large total eat transfer surface area witout te use of an excessive amount of primary surface area. For accurate design all real time requirements and constraints are needed. Tis can be possible by exact assumptions and boundary conditions. Based on suc assumptions and boundary conditions following tree types can be considered. (For 1-D steady state eat transfer analysis). Table 1:Temperature distribution & eat transfer rate for 1-D steady state Heat Transfer in fins CONDI TION Infinite ly Long Fin. Fin wit Insulat ed Tip. Sort Fin. TEMPERATURE DISTRIBUTION ( ) HEAT TRANFER RATE [J/s] ISSN: ttp:// Page 760 ( )+ + + Using Infinitely Long Fin condition, calculations are quite simplified. In te condition: Fins wit Insulated Tips, certain amount of eat losses can be expected tereby getting error in te results. All te drawbacks of first and second conditions are overcome in te tird condition. Te condition: Sort Fin, gives exact results wit infinitesimally small error. But te calculations for sort fin analysis are very complicated. Hence, to simplify te calculations infinitely long fin analysis is considered. 3. Assumptions: Material used is isotropic in nature. Uniform eat transfer coefficient is considered. Fins are assumed as infinitely long. Steady state analysis is considered. 4. Experimental Set-up: Using te Fin Analysis, Termal Conductivity is determined in te proposed set-up. Te Set-up is a very concise, portable and ligt weigt. Termal conductivity of +

3 unknown material is determined using te known termal conductivity of known material. Te setup is composed of two base plates, tree fins, eater coil, a Fe-k temperature sensor, a voltmeter, an ammeter, and a dimmer stat to vary te voltage. Heater coil is sandwiced between two Aluminum base plates of 150[mm] X 100[mm] as Aluminum as constant termal conductivity over te working temperature range of te experiment. Tree fins of Aluminum of 12[mm] diameter and 160[mm] in lengt are treaded into te upper base plate centrally. Te first and tird fin is made of reference material (Aluminum) of known termal conductivity and te middle one is made of material wose termal conductivity is to be determined. Termal sensors are fixed at te fin base and at 100[mm] from te base plate, on eac of te tree fins to determine fin base temperature and temperature at a distance x on fin. Tis assembly is enclosed in an acrylic casing to get constant eat transfer coefficient wile experimentation as sown in figure 1.a. By knowing te termal conductivity of reference material and te temperatures at fin base and fin tip and atmosperic temperature te termal conductivity of te unknown material can be determined. Figure 1.b Figure1.a 5. Procedure: Set constant current and voltage. From tat eat supplied (Q) V x I Wait till te steady state is acieved i.e. base plate is at constant temperature. Note down te temperature readings at respective termocouples. So now we ave te base plate temperature, fin base and fin temperature at distance x. Calculate termal conductivity k using formula given below. 6. Formulae: Temperature distribution for infinitely long fin is given as -! "# $ %& ( '( ) )..(1) ISSN: ttp:// Page 761

4 Simplifying eq (1) for reference material i.e. Al and for specimen material respectively *[ ]! "# % (2) $ - $ %) & $ -./ ( ( 0 ( 1 ( 2 ( 3 ) 4 0! "# 0 *[ 0 ]! "# ) (3) $ )& $ %5 Here : (4) Rewriting eq (4) as % : & ) : 0 (5) Subscripts 1 and 2 are used for reference and specimen respectively. Here 12, p1p2, A1A2 can be assumed. From eq (5) (6) Dividing eq (3) by (2) and putting te value of m1/m2 from eq (6), we get?0@? > (? ) 1[! ) > )]) By putting te value of k 1 i.e. termal conductivity of reference material and oter values from observation, we can calculate te value of k 2 i.e. termal conductivity of specimen. Were, 1. k1 & k2: Termal conductivities of known and unknown material respectively. 2. Tbase: Temperature of fin base 3. T 1x: Temperature of reference at a x distance. 4. T2x: Temperature of specimen at a x distance 7. Limitations: Heat transfer coefficient is assumed to be constant for surrounding air. Te value of termal conductivity for reference material is taken as constant value. In fact termal conductivity of material varies wit working temperature. 8. Result and Conclusion Comparative analysis under identical surrounding and geometrical constraints provides minimum error. Te setup offers flexibility to test different metals on same setup. Experimental setup is designed to minimize te contact resistance. No insulation is required and specimen size is small wic makes te setup compact and portable. Specimens required are easy to manufacture. Power source and temperature sensors are te only instrumentation required. Te setup can be used in tecnical institutes for experimental purpose for te determination of termal conductivity. 9. Future Scope: To develop a program to calculate te termal conductivity of material by accepting te temperature readings and termal conductivity of reference material as input values to make te setup more user friendly. Te purpose of tis project is also to develop a test set up to cater to academic need. Tis will also ISSN: ttp:// Page 762

5 make available an opportunity to go for start-up. Tese set ups can be made available to oter Engineering colleges as academic setups. 10. References: [1] Y.A. Cengel, Heat and Mass Transfer, Tata McGraw Hills publications, Fift Edition [2] ttps:// [3] Termal conductivity- Different metod to find termal conductivity of material. URL: ttp:// ID5615 [4] Heat transfer from fin e-learn URL: ttp://web.mit.edu/16.unified/www/fall /termodynamics/notes/node128.tml [5] Rames S. Goankar, Microprocessor Arcitecture, Programming and Applications wit t Edition. ISSN: ttp:// Page 763