Analysis of Flow and Heat Transfer in a Flat Solar Collector with Rectangular and Cylindrical Geometry Using CFD
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(2) Documento descargado de http://www.elsevier.es el 25/06/2016. Copia para uso personal, se prohíbe la transmisión de este documento por cualquier medio o formato.. Analysis of Flow and Heat Transfer in a Flat Solar Collector with Rectangular and Cylindrical Geometry Using CFD. Resumen La presente investigación describe la construcción y la experimentación de dos abȱȱÇȱȱȱ£ȱȱȱĚȱȱȱ¢ȱȱàȱ ȱ ¤ȱ ȱ Ěȱ ȱ ǻǼǯȱ ȱ ȱ ȱ ȱ ȱ àȱ transversal rectangular y el absorbedor B con sección transversal circular, la temperatura del agua se calculó utilizando la radiación solar y las mediciones de temperaȱȱȱȱȱȱŜŘǯśǚȱȱȱǯȱȱ àȱȱĚȱàȱ¤¡ȱȱȱȱȱȱȱŝŖȦȱ¢ȱȱȱȱȱȱŝşȦǯȱȱȱǰȱȱ·ȱȱȱęȱ¢ȱȱȱ£ȱ ȱ£ȱȱȱȱȱĚǰȱȱŚśǰȱśŖǰȱśśǰȱŜŖǰȱŜśȱ¢ȱŝŖȦȱȱ ȱȱàǯȱȱȱȱȱȱàȱȱȱȱøȱ ȱ ¢ǰȱ ¤ȱ ȱ ȱ ȱ ¤¡ȱ ǻŝŖȦǼȱ ȱ ȱ ¢ȱ àȱȱøȱȱ¢DZȱŘśȱǂȱȱǂȱŗŗśȱȱȱȱȱ¢ȱŗşşȱǂȱȱǂȱ ŘřśȱȱȱȱǯȱȱȱàȱȱȱȱȱǰȱȱĚȱȱ ȱȱȱȱȱ¤ȱǰȱȱȱȱ¤ȱȱęȱȱȱĚȱȱǯ. Introduction Solar energy collection as a topic of renewable energy has been the primary interest of many researchers for the past two centuries, because it can reduce the cost of ȱ ȱȱȱȱŝŖƖǯȱȱĴȱ ȱ ȱȱȱȱȱȱ¢ȱŝŖȱȱȱȱȱȱ ȱȱŗşŝřȱǻȱet alǯǰȱŘŖŖŞǼǰȱȱȱȱȱ Ĵȱ ȱ Ȭȱ ȱ ȱ ǯȱ ȱ ȱ ȱ ȱ ęȱ ȱ ȱ ȱ ¢tems, Naewngerndee et alǯȱ ǻŘŖŗŗǼȱ ȱ ȱ ȱ ȱȱĚ ȱ ȱ¢ȱ¢ǰȱȱ ȱȱ ȱȱĚ ȱȱȱȱǰȱ ȱȱ ȱ¢ȱǰȱȱȱȱ£ȱȱȱĚ ȱȱŗȱȦȱȱřȱȦȱ ȱȬ array modules are used. Design and validation were ȱȱȱęȱȱȱ ȱ ȱȱ ȱ ǯȱ ȱ ȱ et alǯȱ ǻŘŖŗŗǼȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱ Ěȱ velocity varies, validating the simulation results by ǯȱ ȱ ȱ ȱ ǻŘŖŖŞǼȱ ȱ ȱ ȱ ȱ ȱ ȱȱȱȱȱȱȱȱěȱȱȱ bow-shaped geometry working with the Reynolds ȱȱȱȬΉȱȱȱȱȱǯ ȱȱȱǻŗşŝŝǼȱȱ¡ȱ in a parallel-plate absorber which would be very similar to one single channel of Absorber A in this study. Evaluating the separation between the plates to deterȱȱĜ¢ǰȱ ȱȱȱȱ ȱ ȱ ȱ ȱ Ĝ¢ǯȱ ǰȱ reducing the separation between the plates also deȱȱĚ ȱǯȱȱ¢ȱȱ¢ȱȱ. 554. Descriptores: . IOXMRHVWUXFWXUDO FROHFWRUVRODUSODQR VLPXODFLyQHQ&)' WUDQVIHUHQFLDGHFDORU UDGLDFLyQVRODU. ȱ ȱ ȱ ȱ ȱ Ěȱ ȱ ȱ ȱ surface exposed to solar radiation. The main objective of this research is to evaluate the performance of two types of absorbers: One with pipes and the other with rectangular ducts, through the construction, experimentation, theoretical formulation and ȱȱȱĚ ȱȱȱǯ. Experimental &RQVWUXFWLRQRISURWRW\SH ȱ ȱ ȱ ȱ ǻȱ ŗǼȱ ȱ ȱ ŖǯŖşśȱ ȱ ǰȱ ŗǯŖŖȱ ȱ ȱ ȱ ŗǯŜŖȱ ȱ ȱ ȱ ȱ ȱ ȬŗśŖȱ ȱ ęȱ ǻǼȱ ȱ ŘŘȱ ȱ nized steel sheet. The joints were sealed with silicone to prevent air leakage and the inner part was covered with ȱŖǯŖŘȱȬȱ¢¢ȱǯȱȱȱ ȱȱ ȱȱȃȄȱȬȱȱȱǻŖǯŖŗȱȱǰȱ ŖǯŞşȱȱ ȱȱŗǯŚŝȱȱǼȱ ȱȱȱĚȱŘŘȱȱ £ȱ ȱ ǰȱ ȱ ŗŖȱ ȱ ȱ ȱȱǻŖǯŖŗȱȱǰȱŖǯŖŞȱȱ ȱȱŗǯŚŝȱȱ Ǽȱ ȱ ŖǯŖŗȱ ȱ ȱ ȱ ǯȱ ȱ ȱ channels were welded to two heads of galvanized pipe ǻŖǯŖřŞŗȱȱȱȱŗǯŗŖȱȱǼȱȱȱȱsorber painted with fast dry black paint. Absorber B ȱ ȱ ȱ ȱ ȱ ȱ ǻŖǯŖŗŘŝȱ ȱ ȱ ȱŗǯŚŝȱȱǼȱȱŖǯŖşȱȱȱȱȱȱ ȱȱ ȱȱȱȱȱǻŖǯŖřŞŗȱȱȱ ȱŗǯŗŖȱȱǼǯȱȱȱǰȱȱ ȱȱ ȱȱ ȱȱ¢ȱȱǯȱȱȱȱȱĚȱ ȱ Ȭȱ ŖǯŖŖŚȱ ȱ ǰȱ ŗǯŖŖȱ ȱ ȱ. Ingeniería Investigación y Tecnología, volumen XIV (número 4), octubre-diciembre 2013: 553-561 ISSN 1405-7743 FI-UNAM.
(3) Documento descargado de http://www.elsevier.es el 25/06/2016. Copia para uso personal, se prohíbe la transmisión de este documento por cualquier medio o formato.. Marroquín-De Jesús Ángel, Olivares-Ramírez Juan Manuel, Jiménez-Sandoval Omar, Zamora-Antuñano Marco Antonio, Encinas-Oropesa Armando. )LJXUH6RODUKHDWHUFRPSRQHQWV +RXVLQJ3RO\VW\UHQH3ODWH $EVRUEHU$$EVRUEHU%*ODVV. )LJXUH0HVKLQJRIDEVRUEHUV $ OHIW
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(5). ȱŗǯŜŖȱȱǯȱȱ ȱȱȱȱ¢ȱ ȱȱ¢ǯȱȱȱȱŖǯśŘȱȱȱȱȱ ¢ȱȱŖǯŝŘȱȱȱȱȱȱȱȱȱ ŖǯŝŘȱȱȱŖǯşŘȱǰȱ¢ǯȱȱȱ ȱȱ ȱ¢ȱ ȱęȱ ȱ¢ȱǯ. 0RGHOLQJ´$QV\V:RUNEHQFKµ²WKHSUHSURFHVV ȱȱ¢ȱȱȱĚȱ ȱȱȱ ȃȱ Ȅǯȱ ¢ȱ ǰȱ ǰȱ ȱ ȱȱȬȱ ȱȱȱȱǯȱ ȱ ȱ ȱ Ĵȱ ȱȱȱ ȱ ȱ DZȱȱȱ ȱŖǯŖŖŚȱȱȱŖǯŖŞȱDzȱȱ ȱȱȱȱȱȱĴȱȱ ȱ ȱȱřŖǚDzȱȱȱȱȱȱȱȱ ȱȱȱ ȱȱȱŗŞǚDzȱȱȱȱȱȱȱ ȱ ȱȱȱŖǯŖŖśȱȱ ȱȱ¡ȱȱĚȱȱŖǯŖŞȱǯȱȱȱȱĴȱȱȱ ȱ ȱȱ DZȱȱȱŖǯŖŗŘŝȱȱȱǰȱȱ ȱȱ ȱȱ ȱŖǯŖŖśȱȱȱŖǯŖŘśȱǰȱ ȱ řŖǚȱȱȱȱDzȱȱȱȱȱȱȱ ȱ ȱ ȱ ȱ ŖǯŖŖśȱ ȱ ȱ ŖǯŖŖŞȱ ȱ ȱ ȱ ¡ȱȱĚȱ ȱȱȱŖǯŖŘśȱǰȱating the mesh shown in Figure 2.. $. . . . %. System equations +HDWWUDQVIHU ȱ ȱȱȱřȱȱȱȱȱȱsorption of solar energy in the glass, the radiosity for the absorber is: Jŗ = Eŗ and the energy supplied to surȱŗȱ qº »¼ ŗ. ke qº (TŘ Tŗ ) » ȱ '¡ » ¼. ǻŗǼ. Considering the radiant exchange Ebŗ FŗŘ J Ř i. ke qº T Tŗ
(6) » '¡ Ř ¼. (2). The global energy balance of surface 2 is H2 2 Eb Ř JŘi JŘ e
(7) ŗ H2. ke T T
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(9) ȱ 'x Ř ŗ. Ingeniería Investigación y Tecnología, volumen XIV (número 4), octubre-diciembre 2013: 553-561 ISSN 1405-7743 FI-UNAM. ǻřǼ. 555.
(10) Documento descargado de http://www.elsevier.es el 25/06/2016. Copia para uso personal, se prohíbe la transmisión de este documento por cualquier medio o formato.. Analysis of Flow and Heat Transfer in a Flat Solar Collector with Rectangular and Cylindrical Geometry Using CFD. For the global system, the absorbed solar energy must in the end be transferred to the exterior of the glass by convection and radiation qº »¼ . h TŘ Tř
(11) H Ř Eb Ř Eb ř
(12) ȱ. ǻŚǼ. The lost radiation through the outer surface of the glass is qº »¼ rad. H Ř Eb Ř Eb ř
(13). H. Eb Ř JŘ e
(14) ŗ 2H. (5) 2. The heat exchange from the absorber to the working Ě qº qº » » ¼ s ¼ rad. ª º « » « Tŗ TŖ
(15) » « § 'xa ,b ŗ · » « ¸» ¨¨ hw ¸¹ »¼ «¬ © ka ,b. (6). Finally obtaining TŖȱ , which is the temperature of the ȱĚȱǻ ǰȱŘŖŖŗǼ. ȱ Ěȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱȱȱȱ ȱȱȱ thousands of calculations. In these complex situations it is almost impossible to manually do the calculations. ȱȱȱȱĚȱȱȱ ¢ȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱ Ěȱ relations are often solved numerically with a computer. ȱ¢ȱȱȱ¢ȱĚȱĚ ȱȱȱ¢ȱ ȱȱDZȱȱ¢ȱDZ w wt. ³³ ³ Udv
(16) ³³ UVds v. Ŗȱ. ǻşǼ. Ȃȱȱ ȱȱDZ § w wWxy wW yz wWzx · ¡ ¨ ¸ ¡¢£ U x¡¢£ ȱ ǻŗŖǼ ¨ wx wx wy wz ¸¹ © and energy conservation. The CFD software tool can replace integrals and partial derivatives with discretized algebraic forms, ȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱ ęȱ ȱ ȱ ȱ Ě ȱ ȱ ȱ ǰȱ ȱ ȱ ȱǻ ȱȱǰȱŘŖŗŖǼǯ. )OXLGPHFKDQLFV The independent parameters included are the Reynolds number and the geometry of each Absorber. The Reynolds number is based on the hydraulic diameter: Re. vUDh ȱȱ P. ǻŝǼ. For the geometry of Absorber A. Dh. ŚWH ȱȱ 2 W H
(17). ǻŞǼ. For the geometry of Absorber B, Dh is the diameter of ȱŖǯŖŗŘŝȱȱȱȱǻȱet alǯǰȱŘŖŗŖǼǯ. Test conditions 3URWRW\SHGDWD ȱ¡ȱ ȱȱȱ¢ȱŘŖŗŖǰȱ ȱȱ¢ȱȱȱ
(18) ȱȱÇǰȱȱȱ·ǰȱ·¡DzȱȱȱȱŘŖǚȱŘřȂǰȱşşǚȱśşȂȱǰȱ ȱȱȱdiation levels during the year. The collectors were side ¢ȱȱ ȱȱȱȱȱȱȱȱtude for both collectors. Between the thermo tank and ȱȱȱȱ ȱȱȱȱȱŖǯŘśȱ m to prevent the return of water overnight according to Rudnick et alǯȱǻŗşŞŜǼǯ Solar radiation was measured with an Eppleypyrheliȱȱ ǰȱȱȱȱȱȱȱȱ. )LJXUH&RQWUROYROXPHIRUPHGE\WKUHH VXUIDFHV. 556. Ingeniería Investigación y Tecnología, volumen XIV (número 4), octubre-diciembre 2013: 553-561 ISSN 1405-7743 FI-UNAM.
(19) Documento descargado de http://www.elsevier.es el 25/06/2016. Copia para uso personal, se prohíbe la transmisión de este documento por cualquier medio o formato.. Marroquín-De Jesús Ángel, Olivares-Ramírez Juan Manuel, Jiménez-Sandoval Omar, Zamora-Antuñano Marco Antonio, Encinas-Oropesa Armando. )LJXUH¸6RODUUDGLDWLRQ żDPELHQWWHPSHUDWXUH ƑFDOFXODWHGZDWHUWHPSHUDWXUH LQDEVRUEHU$ +FDOFXODWHGZDWHUWHPSHUDWXUH LQDEVRUEHU%. ŖȱȱŗŚŖŖȱ–2ǰȱȱȱȱȱȱȬŗǯȱȱȱȱ ȱȱ ȱȱȬśřśȱȱtor. With the radiation and ambient temperature data, the heat transfer model was solved to determine the working Ěȱǯȱȱȱȱ ȱȱȱŚǯ Water temperature was measured at the zenith time, ȱȱȱȱȬśřśȱȱ ȱȱȬŘřŘȱ communication port, programmable sampling rate and ȱ Ȭȱ ȱ ¢ǯȱ ȱ ȱ ȱȱȱǰȱ ȱȱŗȱ ȱȱ ȱȱȱȱȱȱŝȱȱȱȱǰȱȱ rest of the points were distributed evenly throughout each channel or pipe (depending on the absorber). Figure 5 shows the typical temperatures reached on chanȱŗǰȱŜǰȱȱŗŖȱȱȱȱȱȱŗǰȱŜǰȱȱşȱȱ Absorber B.. A Blue-White®ȱĚ ȱǰȱ ȱȱȱ ȱŖǯŚȱȱŚǯŖȱȦǰȱ ȱȱȱȱ ȱ the collector and the thermo tank. The temperature of the water contained in the thermo tank was measured ȱȱȱȱȬśřśǯȱȱȱȱ ȱȱ Figure 6.. $QDO\VLVLQ&)' Flow analysis was developed in CFD considering: The general domain as water, a Thermal Energy process, ȱȬΉȱǰȱȱŞŖŖȱȦ2ȱȱĚ ȱȱȱ ǰȱȱŗŘǯŗŝȱ ¡ȱŗŖȬřȱȦȱ¢ȱĚ ȱ¢ǰȱȱŘşřȱ ȱȱȱ ȱŖǯŖŖȱȱȱȱǯȱȱȱȱ ȱ ȱȱŝǯ. )LJXUH0HDVXUHGWHPSHUDWXUHYHUVXVORFDWLRQD
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(22) Documento descargado de http://www.elsevier.es el 25/06/2016. Copia para uso personal, se prohíbe la transmisión de este documento por cualquier medio o formato.. Analysis of Flow and Heat Transfer in a Flat Solar Collector with Rectangular and Cylindrical Geometry Using CFD. )LJXUHD
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(24) +IORZRXWOHWLQ$EVRUEHU%ż WHPSHUDWXUHPHDQLQWKHUPRWDQNZLWK$EVRUEHU%. )LJXUH9HORFLW\ SURILOHLQWKH DEVRUEHUV. Results and discussion 7KHUPDOSURILOH With the solar radiation and ambient temperature data applied to the theoretical heat transfer model the water temperature is obtained. The results are shown in Figure Śǯȱȱȱȱȱȱ ȱȱ¡mental data shown in Figure 5. The water temperature is similar in both absorbers according to the theoretical ǻȱ ŚǼȱ ȱ ¡ȱ ǻȱ śǼȱ ǯȱȱ Şȱ ȱ variation is noticed in the experimental results when measuring the temperature between the inlet and outlet. 558. water for both absorbers. The maximum variation be ȱȱȱřǯŚȱ ȱȱȱǯȱȱȱ low temperature increases according to the thermal testȱȱȱȱȱȱȱěȱȱȱ ǯȱ ǰȱȱĚ ȱȱȱǻȱŜǼȱ ȱěȱDZȱȱȱȱȱȱȱȱ Ě ȱȱȱȱǰȱĴȱȱȱȱ the water contained in the thermo tank, which repreȱȱȱĚ ȱȱȱȱǯȱǰȱ if the temperature variation between ducts for both absorbers is similar, this could mean that the amount of Ě ȱȱȱěȱ¢ȱȱĚȱȱȱȱ¢ȱ¢ȱ¢ȱȱěǯ. Ingeniería Investigación y Tecnología, volumen XIV (número 4), octubre-diciembre 2013: 553-561 ISSN 1405-7743 FI-UNAM.
(25) Documento descargado de http://www.elsevier.es el 25/06/2016. Copia para uso personal, se prohíbe la transmisión de este documento por cualquier medio o formato.. Marroquín-De Jesús Ángel, Olivares-Ramírez Juan Manuel, Jiménez-Sandoval Omar, Zamora-Antuñano Marco Antonio, Encinas-Oropesa Armando. )ORZSURILOH One of the CFD software functions is measuring the velocity at any location of the designed geometry. A simuȱ ȱȱ¢ȱȱĚ ȱȱŚśȱȦȱȱŝŖȱȦǰȱ registering the velocity values for each simulation result. The Reynolds number for each registered value was calculated. The results for Absorber A are shown in ȱŞǯ. ȱȱȱȱęȱŝȱȱȱȱȱŞǰȱşȱȱŗŖǯȱǰȱȱȱȱȱȱ ȱěȱȱȱǰȱȱȱȱȱȱȱȱȱȱȱ¢ȱ¢ȱȱȱřȱ channels from left to right in Absorber A. For Absorber B, the Reynolds numbers are higher ǻȱ şǼȱ ǰȱ ȱ ȱ ȱ ȱ ǰȱ the velocity is higher compared to Absorber A. The ȱȱȱ¢ȱȱ ȱȱŗȱ ȱȱşȱȱȱĚ ȱȱŚśȱȦȱȱŘŘȱǰȱȱȱȱ ¡ȱ ȱ Ě ȱ ǻŝŖȱ ȦǼȱ ȱ ěȱ ȱ řŜȱ units. Therefore, it will have similar performances for all pipes, each of them transferring similar amounts of heat to the thermo tank. This isa possible reason why it ȱ Ĵȱ Ě ȱ ȱ ȱ ¢ǰȱ ȱ perature values at the thermo tank, due to the possibil¢ȱȱĴȱĚȱȱǯ. &RPSDULVRQVZLWKSUHYLRXVZRUN. )LJXUH5H\QROGVQXPEHUYHUVXVFKDQQHOIRUDEVRUEHU$ ¸OKOKƑOKżOK×OKǻOK. ȱ ȱ ȱ ȱ ǰȱ ȱ ȱ ȱ ěȱ ȱ ȱ ¢ȱǯȱȱȱ ȱȱěȱȱŚŘȱ ȱ ȱ ȱ ŗȱ ȱ ȱ ŗŖȱ ȱ ȱ Śśȱ Ȧȱ Ě ǰȱȱȱȱ¡ȱȱĚ ȱǻŝŖȱȦǼȱȱ ěȱȱşŖȱǯȱ ȱȱȱȱȱȱȱ. )LJXUH5H\QROGVQXPEHUYHUVXVSLSHIRUDEVRUEHU%¸OK +OKƑOKżOK×OKǻOK. Selmi et alǯȱǻŘŖŖŞǼȱȱȱȱȱȱǯȱȱŖǯŖŗŘŝȱȱȱ ȱȱȱȱ ȱ housing with a glass cover. The heat absorber was composed of the copper pipe and a sheet of aluminum with ȱ¢ȱȱȱȱĴǯȱȱȬȱȱ collector was exposed to sunlight radiation to heat up ȱ ȱȱȱĚ ȱȱśŚŖȱȦ2Dzȱȱ ȱȱȱ¡¢ȱ ȱřŘŜȱ ȱȱȱȱȱřŘŝȱ ǯȱȱȱȱȱȱĚ ȱȱ ȱȱȱȱǰȱȱȱ ȱřřŗȱ ǯȱ ȱȱȱŚȱ ȱȱȱ¢ȱȱȱȱěences between the materials used in the construction of the prototype and design considerations. For his analyǰȱȱȱȱęȱȱȱȱȱȱ CFD results. On this basis, CFD is considered a consistent solving method for this research work. Fan et alǯȱ ǻŘŖŖŝǼȱ ȱ ȱ ȱ ǻ¡perimentation and CFD simulation) of a U-type solar ǰȱ ȱ ȱ Ě ȱ ȱ ȱ ȱ Ȭ ȱ ȱ ȱ ȱ ȱ ŗŜȬȱ ¢ȱ ȱ ȱ ¢ǯȱ¢ȱȱĚ ȱȱŗśŖȱȦȱȱŗśŖŖȱȦǰȱȱ velocity characteristic curves show similar performancȱȱȱ ȱȱȱŞǰȱȱ ȱȱȱȱ ȱȱȱȱĚȱǰȱȱȱȱĚ ȱ¢ȱ ȱȱȱȱȱǻȱȱęȱȱȱȱȱ amount of ducts). For the other half, a mirror view of such curves can be considered because Fan used a U¢ȱǰȱ ȱȱ¢ȱȱȱȬ¢ȱǯ In the experimental work for Absorber A, the water ȱ ȱ ȱ ȱ ȱ ȱ Ĵȱ ȱ ȱȱŗřȱ ȱȱȱ£ȱǰȱ ȱĵȱet al. ǻŘŖŖřǼȱȱȱȱȱȱŗŚȱ ǯ. Ingeniería Investigación y Tecnología, volumen XIV (número 4), octubre-diciembre 2013: 553-561 ISSN 1405-7743 FI-UNAM. 559.
(26) Documento descargado de http://www.elsevier.es el 25/06/2016. Copia para uso personal, se prohíbe la transmisión de este documento por cualquier medio o formato.. Analysis of Flow and Heat Transfer in a Flat Solar Collector with Rectangular and Cylindrical Geometry Using CFD. Conclusions ȱ¢ȱ ȱȱȱȱȱĚȱȱ performance of two absorbers from experimental data. The calculated and simulated values show consistency ȱ ȱ ȱ ȱ ȱ ȱ ȱ ¢ȱ ěȱ authors as well. The calculated values of water temperature for a typical day are similar for both absorbers. In the experimental data for Absorber A the highest ȱȱȱȱȱȱȱȱĚȱȱ ȱ ȱȱřŚŝȱ ǰȱřŚŜȱ ȱȱřŚśȱ ȱȱȱŗǰȱŜȱȱ ŗŖǰȱ¢ǯȱȱȱȱȱȱȱ ȱȱ ȱřŚśǯśȱ ǰȱřŚŚǯśȱ ȱȱřŚŚǯśȱ ȱȱȱŗǰȱ Ŝȱȱşǰȱ¢ǯȱȱȱȱȱ for each absorber were calculated from the experimenȱȱȱDzȱȱȱȱȱ average variation from one absorber to the other is only ŗȱ ǯȱ ȱȱȱȱȱȱȱěǰȱȱ ȱȱȱȱśŖȱȦȱĚ ȱ ȱȱȱ¡ȱ¢ȱȱȱȱ ȱŗǯřŞȱƼȱŗŖ–2ȱȦȱ¢ȱ ȱȱŞǰȱşȱȱŗŖǰȱ ȱȱȱȱȱ¢ȱȱȱȱȱȱŗǯŝȱƼȱŗŖ–2ȱȦȱȱȱşȱǰȱ ȱȱȱȱȱȱȱȱĚ ȱȱsorber B similarly the Reynolds is a function of velocity ȱ ȱ ȱ ȱ ¢ȱ ȱ Ě ȱ ȱ ŝŖȱ Ȧȱ ȱȱǰȱ¢ȱȱȱȱŘśȱȱŗŗśȱȱ ȱ ŗȱ ȱ ȱ ŗŖȱ ¢ǰȱ ȱ ȱ variations in velocity, however for Absorber B under ȱ ȱ Ě ȱ ȱ ȱ ŘŖŖȱ ȱ ŘŘśȱ ȱ ȱ ȱ ¢ȱ ȱşȱȱȱȱȱ ȱȱ ȱȱǰȱȱȱȱȱȱĜȱing system.. Acknowledgements ȱȱȱ¢ȱȱȱǯȱ
(27) ȱ ·£ȱ Villarreal for his guidance, useful suggestions, and for ȱȱȱȱȱǯȱŗŚŗŞŞşȱȱȱ study.. Nomenclature A Dh Ebȱ. ȱ hȱ hwȱ Jȱ. surface área, m2 hydraulic diameter, m ȱ ǰȱȦ2 ȱǰȱ ȱȱĜȱȦ2°C ȱȱĜȱȱ ǰȱȦ2°C ¢ǰȱȦ2. 560. kȱ Re v W ̇x. ȱ¢ȱȦ2.°C Reynolds number (–) velocity, m channel width, m wall thickness, m. *UHHNV\PEROV Εȱ Ή2 ΐȱ. ¢ǰȱȦř emissivity Ěȱ¢ȱ¢ǰȱȦǻȱǼ. References ȱǯǯǯǰȱ ȱǯǯǰȱȬ¢ȱǯǰȱȱǯ ǯȱ ȱȱȱȱȱȱȱǯȱEnergy, volȱřśȱǻȱŗǼǰȱŘŖŗŖDZȱŗŖŗȬŗŗŖǯ ȱ
(28) ǯǰȱ
(29) Ȭȱǯǰȱȱǯȱ ȱȱȱȱȱȱȱ ȱ £¢ȱ ȱȱǯȱlar EnergyǰȱȱŞŗȱǻȱŗŘǼǰȱŘŖŖŝDZȱŗśŖŗȬŗśŗŗǯ ȱ ǯȱ ȱ ǯȱ ǯȱ ȱ ȱ ¢ȱ ȱ ȱ Ȭ ȱȱ¢ȱǯȱȱ¢ǰȱȱŗşȱǻȱ śǼǰȱŗşŝŝDZȱŚşřȬśŖŘǯ. ȱ
(30) ǯǯȱ ȱ ǰȱ ŝȱ ǯǰȱ ȱ ǰȱ ȱ ȱ ǰȱ ŘŖŖŗǯ ȱǯǯȱȱȱǯǯȱ¢ȱȱȱ ȱȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱ Using CFD. ȱ¢ǰȱȱŞŚȱǻȱřǼǰȱŘŖŗŖDZȱŚŖşȬŚŗŝǯ ȱǯȱȱȱǯǯȱȱȱȱ¢ȱȱȱȱ ȱȱȱ ȱęȱǯȱRenewable Energy,ȱȱřŚȱǻȱśǼǰȱŘŖŖŞDZȱŗŘŞśȬŗŘşŗǯ ȱǯǰȱȱ ǯǰȱ ȱǯǰȱȱǯǰȱ
(31) ȱ ǯǰȱ ȱ ȱ
(32) ǯȱ ȱ ȱ ȱ ȱ ȱȱ¢ȱȱȱȱȱ ǻȦǼȱ ¢ȱ ęǯȱ ȱ ¢ȱ ȱ ǭȱ ȱǰȱȱşśȱǻȱŗǼǰȱŘŖŗŗDZȱřşŖȬřşřǯ Rudnick A., Kaplan Y., Kudish A.I., Wolf D. A Study of Solar ȱǰȱ ȱ ȱ ȱ ǯȱ ȱ Energy,ȱȱřŜȱǻȱřǼǰȱŗşŞŜDZȱŘŘŝȬŘŚŖǯ ȱ ǯǰȱ ȱ
(33) ǯǰȱ ȱǯǰȱȱ ǯȱ ȱȱȱȱȱȱȱȱ¢ǯȱRenewable EnergyǰȱȱřřȱǻȱřǼǰȱŘŖŖŞDZȱřŞřȬřŞŝǯ ĵȱǯǰȱ £ȱǯǰȱȱǯǰȱ ȱ ǯȱ¡ȱ ȱȱȱȱȱȱ ȱ¢ȱȱ¢phonic Flow. ȱ¢ǰȱȱŘŘȱǻȱŗǼǰȱŘŖŖřDZȱŘŝȬřśǯ ȱǯǰȱȱǯǰȱȱǯǰȱȱǯǰȱ ȱǯȱȱěȱ ȱ ȱ ȱ ȱ ¢ȱ ȱ ȱ ȱ ȱ. ȱǯȱȱ¢ȱȱǭȱȱ, volȱşŚȱǻȱŘǼǰȱŘŖŗŖDZȱŗřřȬŗŚŖǯ. Ingeniería Investigación y Tecnología, volumen XIV (número 4), octubre-diciembre 2013: 553-561 ISSN 1405-7743 FI-UNAM.
(34) Documento descargado de http://www.elsevier.es el 25/06/2016. Copia para uso personal, se prohíbe la transmisión de este documento por cualquier medio o formato.. Marroquín-De Jesús Ángel, Olivares-Ramírez Juan Manuel, Jiménez-Sandoval Omar, Zamora-Antuñano Marco Antonio, Encinas-Oropesa Armando. Citation for this article: Chicago citation style 0DUURTXtQ'H-HV~VÉQJHO-XDQ0DQXHO2OLYDUHV5DPtUH]2PDU -LPpQH]6DQGRYDO 0DUFR $QWRQLR =DPRUD$QWXxDQR $UPDQGR (QFLQDV2URSHVD$QDO\VLVRI)ORZDQG+HDW7UDQVIHULQD)ODW6RODU &ROOHFWRUZLWK5HFWDQJXODUDQG&\OLQGULFDO*HRPHWU\8VLQJ&)' ,QJHQLHUtD,QYHVWLJDFLyQ\7HFQRORJtD;,9
(35) ISO 690 citation style 0DUURTXtQ'H -HV~V $ 2OLYDUHV5DPtUH] -0 -LPpQH]6DQGRYDO 2- =DPRUD$QWXxDQR 0$ (QFLQDV2URSHVD $( $QDO\VLV RI )ORZ DQG +HDW 7UDQVIHU LQ D )ODW 6RODU &ROOHFWRU ZLWK 5HFWDQJXODU DQG&\OLQGULFDO*HRPHWU\8VLQJ&)',QJHQLHUtD,QYHVWLJDFLyQ\7HFQRORJtDYROXPH;,9 LVVXH
(36) 2FWREHU'HFHPEHU. About the authors ȱÇȬȱȱ
(37) øǯȱ ȱȱȱȼȱȱȱȱȱȱȱ¡ȱȱ ȱ ǻȱ¡Ǽǰȱȱȱȱȱȱȱȱȱȱȱ ǯȱ ȱȱȱȱȱȱȱ¢ȱ ǰȱȱ¢ȱȱ ȱȱȱȱǰȱ Ȭ ǰȱ·ȱǯȱȱȱȱȱȱȱȱȱȱ¢ȱȱȱ
(38) ȱȱÇǯȱ ȱȱ¢ȱǰȱ ǰȱȱȱȱ ȱ ȱȱȱȱ¢ǯȱ ȱȱȱȱȱȱ¢ȱȱȱȱȱŜŖȱȱȱȱǯ
(39) ȱȱȬÇ£ǯȱ ȱȱȱȼȱȱȱȱȱȱȱȱȱ ȱǻȱ¡Ǽǰȱȱȱȼȱȱȱȱȱȱȱȱǯȱ ȱȱȱȱȱȱ ȱ¢ȱ ǰȱȱ¢ȱȱ ȱȱȱȱǰȱ Ȭ ǰȱ·ȱ Section. At present he is an associate professor at the Technological University in San Juan del Río, in the state of Querétaro.. ȱȱȱȱȱȱ¢ȱȱǯȱ ȱȱ ȱȱȱȱȱȱ¢ȱǰȱȱ¢ǰȱȱȱęǰȱȱĚ ȱȱȱǯ ȱ
(40) ·£Ȭǯȱȱȱ¢ǰȱ¢ȱȱ¢ǰȱȱȱ¢ȱȱ¡ǰȱȱŗşşŘǯȱ. ȱǯȱȱȱ¢ȱǻȱ¢Ǽǰȱ¢ȱȱ¢ǰȱȱȱ¢ȱȱ ¡ǰȱȱŗşşŝǯȱȱ¢ǰȱȱȱ¢ȱȱ¢ǰȱ¢ȱȱ¡ȱȱǰȱǰȱ ȬȱŗşşśǯȱȱDZȱǰȱ¢ȱȱȱ£ȱȱ ȱ¢ȱȱ ȱ¢ȱ¢ȱǯȱȱȱȱ¡ȱ¢ȱȱȬȱȱȱȱȱ£ǰȱ ȱȱȱȱȱȱǯȱȱȱ£ȱȱȱęȱȱȱ ȱ¢ȱȱĴȱȱȱȱȱȱǯ ȱȱ ȬÛǯȱ ȱ ȱ ȱ ȱ ȱ ȱ ǯȱ ȱ ȱ ȱ ȱ Ȭȱ ȱ ȱ ȱ ȱ¢ȱȱȱ
(41) ȱȱȱȱ¡ǯȱ ȱȱȱȱȱȱȱȱȱȱȱȱ ȱȱ¡ǯȱ ȱ ȱȱȱȱ¢ȱȱ ȱȱȱȱȱȱȱȱ¡ǯȱ ȱȱȱ ŗŖȱ¢ȱ¡ȱȱǯȱ ȱȱȱȱ¢ȱȱȱ¢ȱ¢ǯȱ ȱȱȱȱȱ ȱ¢ȱȱȱȱǰȱȱȱȱ¢ȱ¢ǯ ȱȬǯȱ ȱȱȱȼȱȱȱ¢ȱȱȱ¢ȱȱȱǻŞŞȬşŘǼǯȱȱȱȱ ǻ¢Ǽȱȱȱ ȱȱ¢ǰȱ¢ȱȱȱȱȱǻşřȬşśǼǯȱȱȱȱȱȱ ȱȱȱȱ¢ȱȱȱǰȱ¢ǰȱȱǻşśȬşşǼǯȱ¢ȱřȬ¢ȱȱ ȱȱȱȱȱ¢ȱ¢ȱȱ¢ȱȱȱȱȱȱ¢ȱȱȱȱȱǻşşȬŖŘǼǯȱȱ ȱȱȱ ȱȱ¢ǰȱ¢ȱȱȱȱȱȱŘŖŖŘǯȱȱȱȱȱȱȱing and metal magnetic nanomaterial and the study of magnetic properties of magneto-resistance.. Ingeniería Investigación y Tecnología, volumen XIV (número 4), octubre-diciembre 2013: 553-561 ISSN 1405-7743 FI-UNAM. 561.
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