Thermodynamic and Mechanical Analysis of a Thermomagnetic Rotary Engine

Transcription

1 Journal of hysics: onference Series AER OEN AESS Thermoynamic an Mechanical Analysis of a Thermomagnetic Rotary Engine To cite this article: D M Fajar et al 2016 J. hys.: onf. Ser View the article online for upates an enhancements. Relate content - allet Optimization of the Heavy Rotary Table Loa arrying System V G Atapin an A A Bataev - Observation of Oil Flow haracteristics in Rolling iston Rotary ompressor for Reucing Oil irculation Rate S j Song, K Y Noh, B Min et al. - arametric Design an Mechanical Analysis of Beams base on SINOVATION Z G Xu, W D Shen, D Y Yang et al. This content was ownloae from I aress on 09/02/2018 at 01:02

2 6th Asian hysics Symposium Journal of hysics: onference Series 739 (2016) IO ublishing oi: / /739/1/ Thermoynamic an Mechanical Analysis of a Thermomagnetic Rotary Engine D M Fajar 1,3,a, S N Khotimah 2,b, an Khairurrijal 2,c 1 Master rogram in hysics Teaching, Faculty of Mathematics an Natural Sciences, Institut Teknologi Banung, Jalan Ganesa 10, Banung 40132, Inonesia 2 Department of hysics, Faculty of Mathematics an Natural Sciences, Institut Teknologi Banung, Jalan Ganesa 10, Banung 40132, Inonesia 3 Natural Science Eucation rogram, Faculty of Tarbiyah an Teacher Training, Institut Agama Islam Negeri Jember, Jalan Mataram 1, Mangli Jember 68136, Inonesia a inarmaftukh@stuents.itb.ac.i; b nurul@fi.itb.ac.i; c krijal@fi.itb.ac.i Abstract. A heat engine in magnetic system ha three thermoynamic coorinates: magnetic intensity, total magnetization, an temperature T, where the first two of them are respectively analogous to that of gaseous system: pressure an volume V. onsequently, arnot cycle that constitutes the principle of a heat engine in gaseous system is also vali on that in magnetic system. A thermomagnetic rotary engine is one moel of it that was esigne in the form of a ferromagnetic wheel that can rotates because of magnetization change at urie temperature. The stuy is aime to escribe the thermoynamic an mechanical analysis of a thermomagnetic rotary engine an calculate the efficiencies. In thermoynamic view, the ieal processes are isothermal emagnetization, aiabatic emagnetization, isothermal magnetization, an aiabatic magnetization. The values of thermoynamic efficiency epen on temperature ifference between hot an col reservoir. In mechanical view, a rotational work is etermine through calculation of moment of inertia an average angular spee. The value of mechanical efficiency is calculate from ratio between rotational work an heat receive by system. The stuy also obtains exergetic efficiency that states the performance quality of the engine. 1. Introuction A thermomagnetic rotary engine constitutes one form of heat engines in magnetic system. The moel is thermoynamically analogous to heat engines in gaseous system. In general a heat engine in gaseous system is create in the form of a movable piston containing gas that coul expan an compress continuously with repeate isothermal an aiabatic processes. One common theory use to analyze the engine is arnot principle by assuming the system in an iealize conition. Thermoynamic coorinates that characterize the engine are pressure ( ), volume (V ), an temperature (T ). For a heat engine in magnetic system these quantities are respectively analogous to magnetic intensity ( ), total magnetization ( ), an temperature (T ) [1]. By employing influence of temperature on changing in the two coorinates, both heat engines are create. A thermomagnetic rotary engine is compose of a ferromagnetic wheel, a permanent magnet, an a heat source. It works base on a typical property of ferromagnetic materials, that is the total ontent from this work may be use uner the terms of the reative ommons Attribution 3.0 licence. Any further istribution of this work must maintain attribution to the author(s) an the title of the work, journal citation an DOI. ublishe uner licence by IO ublishing Lt 1

3 6th Asian hysics Symposium Journal of hysics: onference Series 739 (2016) IO ublishing oi: / /739/1/ magnetization rops with temperature increase, an experiences phase transition into paramagnetic when being heate until urie temperature ( T ). A thermomagnetic rotary engine presents a suitable moel to emonstrate a arnot engine besies gaseous system [2]. It also shows one moel of energy conversion from heat energy to magnetic work thermoynamically an rotational work mechanically. The stuy is aime to iscuss thermoynamic analysis of a thermomagnetic rotary engine as arnot cycle in gaseous system; an mechanical analysis regaring to rotational work prouce by the engine. Efficiency was calculate by ratio between work an heat receive by system associate with the engine performance. 2. Theory For a heat engine in magnetic system, as explaine above, the total magnetization rops with temperature increase as equations below [3]. c T Tc (1) c T (2) Equation (1) expresses mathematical formulation of urie-weiss Law that explains equilibrium state of paramagnetic phase for ferromagnetic material above urie temperature, with T > T an is urie constant. Equation (1) is erive from urie Law that explains equilibrium state of paramagnetic material. Equation (2) expresses mathematical formulation of urie Law. The latter is more relevant to explain arnot cycle for magnetic system as gaseous system than equation (1). Furthermore, it covers value of temperature of hot an col reservoir below urie temperature. The first law of thermoynamics that connects heat, internal energy, an magnetic work is written as follows đq U o (3) where μ o expresses a work in magnetic system. Substituting equation (2) to (3), it gets two funamental equations as follows [1,3]. đq T o (4) or đq T o (5) Where Q/T an Q/T expresses heat capacity at constant total magnetization an magnetic intensity respectively. Equation (4) an (5) formulate thermoynamic processes in the heat engine, such as isothermal an aiabatic process. The arnot principle of a thermomagnetic rotary engine employs both processes. In mechanical view, the mechanism of a thermomagnetic rotary engine is explaine by figure 1 below. 2

4 6th Asian hysics Symposium Journal of hysics: onference Series 739 (2016) IO ublishing oi: / /739/1/ Figure 1. Mechanism of a thermomagnetic rotary engine. F Figure 1 epicts arrangement of a ferromagnetic wheel, a permanent magnet, an a er as heat source positione below the wheel. Before the er is ignite up, the resultant of magnetic attractive forces equals zero ( F F F F ) so that the wheel oes not move. oint 1 locate in front of magnet is then heate. When the temperature is raise up, the magnetization of point 1 weakens so that ecreases. When it reaches urie temperature, point 1 has change into paramagnetic. Since F F F, point 2 will shift an replace position of point 1 cause by torque create by the nonzero resultant. When point 2 is heate likewise, point 3 will shift point 2, an so on. The heating an shift occur continuously so that the wheel can rotate counter clockwise. 3. Analysis A thermomagnetic rotary engine works by converting heat receive by system to change the magnetization thermoynamically an then prouce wheel rotation mechanically. It is illustrate by iagram below. Figure 2. The principle of energy conversion of a thermomagnetic rotary engine Base one iagram above, there are three efficiencies obtaine by the analysis: thermoynamic efficiency ( η term ), mechanical efficiency ( η mek ), an exergetic efficiency ( η ex ). Exergetic efficiency ( η ex ) states how much maximum work obtaine from an engine associate with environmental equilibrium 4. This term is commonly iscusse in engineering view to analyze performance of the engine commercially. The formulation of it is substantively complex since it engages some external quantities. However, the stuy refers to Karle (2001) stating that exergetic efficiency is simply calculate by ratio between mechanical an thermoynamic efficiency [5]. 3

5 6th Asian hysics Symposium Journal of hysics: onference Series 739 (2016) IO ublishing oi: / /739/1/ ex mek term. (6) 3.1 Thermoynamic Analysis This stuy is limite to focus on obtaining the first two efficiencies in thermoynamic view, a thermomagnetic rotary engine has three basic components: hot reservoir Q (with temperature T ), col reservoir Q (with temperature T ), an thermoynamic work W. The system also experiences term four processes consist of 2 isothermal an 2 aiabatic processes as arnot cycle in gaseous system. Suppose initially the system is in thermoynamic equilibrium in col reservoir with temperature of T. The four processes occur are liste below [3]. (1) Aiabatic magnetization, when the temperature is raise to T. (2) Isothermal emagnetization, when the constant temperature T is reache an the system absorbs heat from hot reservoir Q. (3) Aiabatic emagnetization in opposite irection to process no. 1, when the temperature rops to T. (4) Isothermal magnetization in opposite irection to process no. 2, when the constant temperature T is reache an the system emits heat to col reservoir Q. The arnot cycle graph is plotte by fining intersection between isothermal an aiabatic curves. For isothermal curve, by assuming T in equation (2) as a constant, then it obtains equation below. where a T/ it has two equations: = constant an 0 a (7) a. For aiabatic curve, by rewriting Eqs. 4 an 5 an using đ Q 0, T T o By iviing both equations, integrating in left sie an in right sie, it obtains where γ / an b is constant. o p b (8) Since γ > 1, the aiabatic curve forms steep arch, while the isothermal curve forms straight line. ompare to arnot cycle of gaseous system plotte tilt from upper left to lower right, the arnot cycle of magnetic system is plotte tilt from lower left to upper right. It is because the coorinate, which is parallel with V as generalize isplacement, is inversely proportional to T. While V in gaseous state is proportional to T. Figure 3 compares arnot cycle for gaseous system (figure 3.(a)) an magnetic system in a thermomagnetic rotary engine (figure 3.(b)). 4

6 6th Asian hysics Symposium Journal of hysics: onference Series 739 (2016) IO ublishing oi: / /739/1/ (a) Figure 3. arnot cycle for: (a) gaseous system, an (b) magnetic system. (b) Figure 4. Thermoynamic processes in a thermomagnetic rotary engine. Figure 4 epicts thermoynamic process occurs in the engine. The alphabets in figure 4 are place from interpretation of arnot cycle plot in figure 3.(b). The placement cannot be specifically etermine since the process takes place fast an continuous. The work each process in figure 3.(b) is erive from equation (2), (3), (4) an (5). rocess A-B (aiabatic magnetization) W T T AB c rocess B- (isothermal emagnetization in temperaturet ) otc 2 2 WB B 2 rocess -D (aiabatic emagnetization) W T T c D c rocess D-A (isothermal magnetization in temperaturet ) ot W DA A D c. (12) W expresses total work in all thermoynamic process. Since two works in aiabatic process term cancel each other, it only uses two works in isothermal process. The effective works in a cycle obtains (9) (10) (11) 5

7 6th Asian hysics Symposium Journal of hysics: onference Series 739 (2016) IO ublishing oi: / /739/1/ Wterm WB WDA Qp Q (13) The heat receive by system ( Q ) is from isothermal magnetization process. Since đq = - đw then it obtains Q T o c 2 2 p B 2c The efficiency is obtaine from ration between work W an heat absorbe from hot reservoir term (14) Q. Wterm term Q. p (15) from other calculations, not erive herein, then equation (15) is It also gets - A D formulate as common arnot efficiency as follows [5]. B term 1 T T c (16) Base on equation (16), the thermoynamic efficiency only epens on the value an the ifference between hot an col reservoir temperature. The larger the ifference, the larger the arnot efficiency. 3.2 Mechanical Analysis In mechanical view, the work that can be observe in the thermomagnetic rotary engine is a rotational work of wheel as consequence of attractive magnetic force. The components necessary to fin are rotational work an heat from er, then fin mechanical efficiency. The rotational work is etermine through Work-Energy rinciple by fining rotational kinetic energy ( E ). krot 1 2 Wmek Ekrot I 2 (17) Moment of inertia ( I ) is obtaine from summing moment of inertia of all wheel components, such as axis, trellis, an circular ferromagnetic wire. It can also be irectly etermine from experiment. The angular spee ( ω ) is obtaine from average number of rotation uring a time interval. It is also influence by the power of er use until certain limit that epens on urie temperature of material. Above the limit, the power of er oes not affect significantly [6]. So, it is more effective to use the largest power. ompare to other metho, Karle (2001) fin mechanical efficiency by calculating power ( ) mek generate immeiately when the er ignite up. The metho is conucte when the time neee for wheel starts to move since the er signe up is relatively long. Moreover, the rotation is preicte not smooth [5]. mek F v (18) The initial force ( F ) is etermine by a finite ifference metho by reference of starting time an temperature ifference between initial an urie temperature of material. The initial spee ( v ) is obtaine from measurement. The heat from er cannot be irectly etermine but it nees aitional experiments. One is by calorimetric metho that is aime to etermine power of er ( ). It is one by heating a vessel contains water an noting the change of heat with time in a time interval, then it fins the power of er. T maca mbcb t (19) 6

8 6th Asian hysics Symposium Journal of hysics: onference Series 739 (2016) IO ublishing oi: / /739/1/ where m c an m c express mass times specific heat of water an the vessel respectively. Then a a b b times perio of rotation fins heat of er ( Q ). The heat from er can also be etermine by using enthalpy of stanar combustion ata of er material by measuring ifference of final an initial mass of er in a perio. The number of mole emitte expresses the value of Q by assuming all emission is completely e [7]. After all, the mechanical efficiency is formulate as follows. Wmek mek Q or similarly [5], mek 4. onclusion A thermomagnetic rotary engine is a suitable moel to emonstrate a arnot engine in other systems besie gaseous system. It also presents a moel of energy conversion from heat to change of magnetization thermoynamically an prouce rotational work mechanically. The analysis fins three kins of efficiency: thermoynamic efficiency ( η term ), mechanical efficiency ( η mek ), an exergetic efficiency ( η ex ). The thermoynamic efficiency only epens on temperature ifference between hot an col reservoir. While mechanical efficiency epens on urie temperature of material, components of wheel, an power of ers. It was calculate from ratio between rotational work an heat of er. From thermoynamic an mechanical efficiency, it also obtaine exergetic efficiency that state the performance quality of the engine. It was obtaine from ratio between mechanical an thermoynamic efficiency. The stuy promotes some father experiments to fin practical aspects that affect the engine s performance. It is also intene to fin various applications of heat energy conversion to broa aspects. mek (20) (21) References [1] George B 1989 Am. J. of hys [2] Hans T 1987 Am. J. of hys. 55, 48 [3] Mark W Z an Richar H D 1997 Heat an Thermoynamics (Singapore: McGraw-Hill) p 368, 81-86, [4] Michael J M an Howar N S 2006 Funamentals of Engineering Thermoynamics (hichester : John Wiley & Sons Lt) p 273 [5] Anton K 2001 Int. J. Therm. Sci. 40, [6] George B 1986 hys. Teach. 24, 204 [7] Raymon 2011 General hemistry: The Essential oncepts, Sixth Eition (New-York: McGraw-Hill) p 187 7