THERMAL ANALYSIS ON VARIABLE THICKNESS ABSORBER PLATE FIN IN FLAT-PLATE SOLAR COLLECTORS USING DIFFERENTIAL TRANSFORM METHOD
Year 2020,
, 157 - 169, 06.01.2020
Balaram Kundu
Abstract
This article highlights a parametric investigation of the thermal analysis of variable thickness flat plate solar collector. Triangular profile of an absorber plate has been adopted from the point of view of saving in material. An approximate analytical model based on the Taylor series of expansion has been implemented for finding out the temperature distribution in the heat conduction direction of the absorber plate. Differential transform method (DTM) has been used to establish a new analytical formulation. The Modified Bessel’s function has been applied for the comparison of the results produced by DTM. The variation of several temperature dependent parameters is studied for knowing the dependency effect. The efficiency of absorber plate has been analysed as a function of Biot number and the impact of aspect ratio on the plate performance has been highlighted. The present analytical approach has ability to determine the thermal performance of an absorber plate under an actual design condition with a minor modification of the analysis. The formulation of the present work is also suitable for the analysis of any shape of an absorber plate in flat-plate solar collectors.
References
- [1] Duffie JA, Beckman WA. Solar Engineering of Thermal Processes. 2nd ed. New York: John Wiley & Sons; 1991.
- [2] Hollands KGT, Stedman BA. Optimization of an absorber plate fin having a step change in local thickness. Solar Energy 1992; 49: 493–495. https://doi.org/10.1016/0038-092X(92)90157-6.
- [3] Ong KS. Thermal performance of solar air heaters: mathematical model and solution procedure. Solar Energy 1995; 55(2): 93–109. https://doi.org/10.1016/0038-092X(95)00021-I.
- [4] Ong KS. Thermal performance of solar air heaters-experimental correlation. Solar Energy 1995; 55(3): 209–217. https://doi.org/10.1016/0038-092X(95)00027-O.
- [5] Kundu B. Performance analysis and optimization of absorber plates of different geometry for a flat-plate solar collector: a comparative study. Appl Therm Eng 2002; 22: 999–1012. https://doi.org/10.1016/S1359-4311(01)00127-2.
- [6] Dhariwal SR, Mirdha US. Analytical expressions for the response of flat-plate collector to various transient conditions. Energy Conv Manag 2005; 46 (11–12): 1809–1836. https://doi.org/10.1016/j.enconman.2004.08.008.
- [7] Badescu V. Optimum size and structure for solar energy collection systems. Energy 2006; 31: 1819–1835. https://doi.org/10.1016/j.energy.2005.09.008.
- [8] Gao W, Lin W, Liu T, Xia C. Analytical and experimental studies on the thermal performance of cross-corrugated and flat plate solar sir heaters. Appl Energy 2007; 84 (4): 425 – 441. https://doi.org/10.1016/j.apenergy.2006.02.005.
- [9] Kundu B. Performance and optimum design analysis of an absorber plate fin using recto-trapezoidal profile. Solar Energy 2008; 82: 22– 32. https://doi.org/10.1016/j.solener.2007.05.002.
- [10] Ho CD, Yeh HM, Cheng TW, Chen TC, Wang RC. The influences of recycle on performance of baffled double-pass flat-plate solar air heaters with internal fins attached. Appl Energy 2009; 86: 1470–14788. https://doi.org/10.1016/j.apenergy.2008.12.013.
- [11] Kundu B. Analytic method for thermal performance and optimization of an absorber plate fin having variable thermal conductivity and overall loss coefficient. Applied Energy 2010; 87: 2243–2255. https://doi.org/10.1016/j.apenergy.2010.01.008.
- [12] El-Sebaii AA, Aboul-Enein S, Ramadan MRI. Thermal performance investigation of double pass-finned plate solar air heater. Applied Energy 2011; 88: 1727–1739. https://doi.org/10.1016/j.apenergy.2010.11.017.
- [13] Kundu B, Lee K.-S. Fourier and non-Fourier heat conduction analysis in the absorber plates of a flat-plate solar collector. Solar Energy 2012; 86: 3030 – 3039. https://doi.org/10.1016/j.solener.2012.07.011.
- [14] Subiantoro A, Ooi KT. Analytical models for the computation and optimization of single and double glazing flat plate solar collectors with normal and small air gap spacing. Applied Energy 2013; 104: 392 – 399. https://doi.org/10.1016/j.apenergy.2012.11.009.
- [15] Bracamonte J, Baritto M. Optimal aspect ratios for non-isothermal flat plate solar collectors for air heating. Solar Energy 2013; 97: 605 – 613. https://doi.org/10.1016/j.solener.2013.09.007.
- [16] Eismann R. Accurate analytical modelling of flat plate solar collectors: Extended correlation for convective heat loss across the air gap between absorber and cover plate. Solar Energy 2015; 122: 1214 – 1224. https://doi.org/10.1016/j.solener.2015.10.037.
- [17] Sun C, Liu Y, Duan C, Zheng Y, Chang H, Shu S. A mathematical model to investigate on the thermal performance of a flat plate solar air collector and its experimental verification. Energy Conv Manag 2016; 115: 43 – 51. https://doi.org/10.1016/j.enconman.2016.02.048.
- [18] Diego-Ayala U, Carrillo JG. Evaluation of temperature and efficiency in relation to mass flow on a solar flat plate collector in Mexico. Renew Energy 2016; 96: 756 – 764. https://doi.org/10.1016/j.renene.2016.05.027.
- [19] Tiwari GN. Solar Energy Fundamentals, Design, Modeling and Applications. 247, Narosa Publishing House; 2002.
- [20] Zhou JK. Differential Transformation Method and its Application for Electrical Circuits. Hauzhang University Press, Wuhan (China); 1986.
- [21] Abbasov A, Bahadir AR. The investigation of the transient regimes in the nonlinear systems by the generalized classical method. Math Prob Eng 2005; 5: 503–519. http://dx.doi.org/10.1155/MPE.2005.503.
- [22] Rashidi MM, Laraqi N, Sadri SM. A novel analytical solution of mixed convection about an inclined flat plate embedded in a porous medium using the DTM-Padé. Int J Them Sci 2010; 49(12): 2405–2412. https://doi.org/10.1016/j.ijthermalsci.2010.07.005.
- [23] Ghafoori S, Motevalli M, Nejad MG, Shakeri F, Ganji DD, Jalaal M. Efficiency of differential transformation method for nonlinear oscillation: comparison with HPM and VIM. Current Appl Phys 2011; 1: 965–971. https://doi.org/10.1016/j.cap.2010.12.018.
- [24] Kundu B, Lee K.-S. A proper analytical analysis of annular step porous fins for determining maximum heat transfer. Energy Conv Manag 2016; 110: 469–480. https://doi.org/10.1016/j.enconman.2015.09.037.
- [25] Yaghoobi H, Torabi M. The application of differential transformation method to nonlinear equations arising in heat transfer. Int Commun Heat Mass Transf 2011; 38: 815–820. https://doi.org/10.1016/j.icheatmasstransfer.2011.03.025.
- [26] Dogonchi AS, Ganji DD. Convection–radiation heat transfer study of moving fin with temperature-dependent thermal conductivity, heat transfer coefficient and heat generation. Appl Them Eng 2016; 103: 705 – 712. https://doi.org/10.1016/j.applthermaleng.2016.04.121.
- [27] Bervillier C. Status of the differential transformation method. Appl Math Comp 2012; 218: 10158–10170. https://doi.org/10.1016/j.amc.2012.03.094.