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Analysis of Flow and Heat Transfer in a Flat Solar Collector with Rectangular and Cylindrical Geometry Using CFD

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(1)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.. Ingeniería Investigación y Tecnología, volumen XIV (número 4), octubre-diciembre 2013: 553-561 ISSN 1405-7743 FI-UNAM (artículo arbitrado). Analysis of Flow and Heat Transfer in a Flat Solar Collector with Rectangular and Cylindrical Geometry Using CFD Análisis de flujo y de la transferencia de calor en un colector solar plano con geometría rectangular y cilíndrica utilizando CFD Marroquín-De Jesús Ángel Universidad Tecnológica de San Juan del Río, Querétaro E-mail: amarroquind@utsjr.edu.mx. Olivares-Ramírez Juan Manuel Universidad Tecnológica de San Juan del Río, Querétaro E-mail: jmolivar01@yahoo.com. Jiménez-Sandoval Omar. Zamora-Antuñano Marco Antonio Universidad Tecnológica de San Juan del Río, Querétaro E-mail: mazamoraa@utsjr.edu.mx. Encinas-Oropesa Armando Universidad Autónoma de San Luis Potosí E-mail:armando.encinas@gmail.com. Centro de Investigación y de Estudios Avanzados (CINVESTAV) Instituto Politécnico Nacional, Unidad Querétaro E-mail: ojimenez@qro.cinvestav.mx. Information on the article: received: June 2012, accepted: November 2012. Abstract The present investigation describes the construction and experimentation of  ˜ȱœ˜•Š›ȱŽ—Ž›¢ȱŠ‹œ˜›‹Ž›œžœ’—ȱ ŠŽ›ȱŠœȱ ˜›”’—ȱ̞’ȱŠ—ȱ’œȱœ’–ž•Š’˜—ȱ in Computational Fluid Dynamics (CFD). For Absorber A with rectangular cross section and Absorber B with circular cross section, water temperature was calculated using solar radiation and ambient temperature measurements showing increases of up to 62.5°C for both absorbers. The maximum ‘Ž›–˜œ’™‘˜—’Œȱ ̘ ȱ –ŽŠœž›Ž–Ž—ȱ ’—ȱ ‹œ˜›‹Ž›ȱ ȱ  Šœȱ ŝŖ•Ȧ‘ȱ Š—ȱ ŝş•Ȧ‘ȱ ’—ȱ ‹œ˜›‹Ž›ȱǯȱ—ȱ‘’œȱ‹Šœ’œǰȱꗒŽȱŽ•Ž–Ž—ȱ–Ž‘˜ȱŠ—ȱȱ Ž›ŽȱžœŽȱ˜ȱŠ—Š•¢£Žȱ‘Žȱ’쎛Ž—ŒŽȱ‹Ž ŽŽ—ȱ‹˜‘ȱ̘ œǰȱ ’‘ȱŚśǰȱśŖǰȱśśǰȱŜŖǰȱŜśȱŠ—ȱŝŖȱ•Ȧ‘ȱŠœȱ simulation values. With the simulation results the Reynolds numbers were ŽŽ›–’—Žǰȱꗍ’—ȱ‘Šȱ‘Žȱ–Š¡’–ž–ȱ̘ ȱǻŝŖȱ•Ȧ‘Ǽȱ’ŸŽœȱ‘Žȱ•Š›ŽœȱŽ¢—˜•œȱ—ž–‹Ž›ȱŸŠ›’Š’˜—DZȱŘśȱǂȱŽȱǂȱŗŗśȱ˜›ȱ‹œ˜›‹Ž›ȱȱŠ—ȱŗşşȱǂȱŽȱǂȱŘřśȱ˜›ȱ ‹œ˜›‹Ž›ȱ ǯȱ ’‘ȱ Šȱ œ–Š••Ž›ȱ ŸŠ›’Š’˜—ȱ ’—ȱ‹œ˜›‹Ž›ȱ ǰȱ ‘Žȱ ̘ ȱ Šȱ Š••ȱ žŒœȱ turns out to be more uniform, which results in more ducts transferring heat ˜ȱ‘Žȱ ˜›”’—ȱ̞’ǯ. Keywords: ‡ ‡ ‡ ‡ ‡. IORZVWUXFWXUH IODWVRODUFROOHFWRUV VLPXODWLRQFIG KHDWWUDQVIHU VRODUUDGLDWLRQ.

(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 abœ˜›‹Ž˜›ŽœȱŽȱŽ—Ž›ÇŠȱœ˜•Š›ȱšžŽȱž’•’£Š—ȱŠžŠȱŒ˜–˜ȱ̞’˜ȱŽȱ›Š‹Š“˜ȱ¢ȱœžȱœ’–ž•ŠŒ’à—ȱ Ž—ȱ ’—¤–’ŒŠȱ Žȱ ̞’˜œȱ Œ˜–™žŠŒ’˜—Š•ȱ ǻǼǯȱ Š›Šȱ Ž•ȱ Š‹œ˜›‹Ž˜›ȱ ȱ Œ˜—ȱ œŽŒŒ’à—ȱ transversal rectangular y el absorbedor B con sección transversal circular, la temperatura del agua se calculó utilizando la radiación solar y las mediciones de temperaž›ŠȱŠ–‹’Ž—Žȱ–žŽœ›Š—ȱ’—Œ›Ž–Ž—˜œȱŽȱ‘ŠœŠȱŜŘǯśǚȱ™Š›ŠȱŠ–‹˜œȱŠ‹œ˜›‹Ž˜›ŽœǯȱŠȱ –Ž’Œ’à—ȱŽ•ȱ̞“˜ȱŽ›–˜œ’à—’Œ˜ȱ–¤¡’–˜ȱŽ—ȱŽ•ȱŠ‹œ˜›‹Ž˜›ȱȱžŽȱŽȱŝŖ•Ȧ‘ȱ¢ȱŽ—ȱŽ•ȱŠ‹œ˜›‹Ž˜›ȱȱŽȱŝş•Ȧ‘ǯȱ˜‹›ŽȱŽœŠȱ‹ŠœŽǰȱŽ•ȱ–·˜˜ȱŽȱŽ•Ž–Ž—˜ȱꗒ˜ȱ¢ȱȱœŽȱž’•’£Šȱ ™Š›ŠȱŠ—Š•’£Š›ȱ•Šȱ’Ž›Ž—Œ’ŠȱŽ—›ŽȱŠ–‹˜œȱ̞“˜œǰȱŒ˜—ȱŚśǰȱśŖǰȱśśǰȱŜŖǰȱŜśȱ¢ȱŝŖ•Ȧ‘ȱŒ˜–˜ȱ ŸŠ•˜›ŽœȱŽȱœ’–ž•ŠŒ’à—ǯȱ˜—ȱ•˜œȱ›Žœž•Š˜œȱŽȱ•Šȱœ’–ž•ŠŒ’à—ȱœŽȱŽŽ›–’—Š›˜—ȱ•˜œȱ—ø–Ž›˜œȱ Žȱ Ž¢—˜•œǰȱ Ž—Œ˜—›¤—˜œŽȱ šžŽȱ Ž•ȱ ŒŠžŠ•ȱ –¤¡’–˜ȱ ǻŝŖ•Ȧ‘Ǽȱ ˜›ŽŒŽȱ •Šȱ –Š¢˜›ȱ ŸŠ›’ŠŒ’à—ȱŽ•ȱ—ø–Ž›˜ȱŽȱŽ¢—˜•œDZȱŘśȱǂȱŽȱǂȱŗŗśȱ™Š›ŠȱŽ•ȱŠ‹œ˜›‹Ž˜›ȱȱ¢ȱŗşşȱǂȱŽȱǂȱ Řřśȱ™Š›ŠȱŽ•ȱŠ‹œ˜›‹Ž˜›ȱǯȱ˜—ȱž—ŠȱŸŠ›’ŠŒ’à—ȱ–Ž—˜›ȱŽ—ȱŽ•ȱŠ‹œ˜›‹Ž˜›ȱǰȱŽ•ȱ̞“˜ȱŽ—ȱ ˜˜œȱ•˜œȱŒ˜—žŒ˜œȱ›Žœž•ŠȱœŽ›ȱ–¤œȱž—’˜›–Žǰȱ•˜ȱšžŽȱ’–™•’ŒŠȱ–¤œȱŒ˜—žŒ˜œȱ›Š—œę›’Ž—˜ȱŒŠ•˜›ȱŠ•ȱ̞’˜ȱŽȱ›Š‹Š“˜ǯ. 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 ˜–Žœ’Œȱ ŠŽ›ȱ‘ŽŠ’—ȱž™ȱ˜ȱŝŖƖǯȱ˜›ŽȱŠĴŽ—’˜—ȱ Šœȱ ™Š’ȱ˜ȱ‘’œȱ˜™’Œȱ’—ȱ‘ŽȱŽŠ›•¢ȱŝŖœȱžŽȱ˜ȱ‘Žȱ•˜‹Š•ȱ˜’•ȱ Œ›’œ’œȱ˜ȱŗşŝřȱǻŽ•–’ȱet alǯǰȱŘŖŖŞǼǰȱ’—Œ›ŽŠœ’—ȱ‘Žȱ—ŽŽȱ˜›ȱ ‹ŽĴŽ›ȱ ‘ŽŠȱ Š‹œ˜›™’˜—Ȭ™Ž›˜›–Š—ŒŽȱ ’—ȱ ‘Žȱ Žšž’™–Ž—ǯȱ —ȱ ‘Žȱ Žœ’—ȱ Š—ȱ Œ˜—ꐞ›Š’˜—ȱ ˜ȱ œ˜•Š›ȱ ‘ŽŠ’—ȱ œ¢œtems, Naewngerndee et alǯȱ ǻŘŖŗŗǼȱ ‘Šœȱ ŽŸŽ•˜™Žȱ Šȱ ›ŽœŽŠ›Œ‘ȱ˜—ȱ̘ œȱ ’‘ȱŒ¢•’—›’ŒŠ•ȱŽ˜–Ž›¢ǰȱŽŸŠ•žŠ’—ȱ ‘Žȱ™Ž›˜›–Š—ŒŽȱ ‘Ž—ȱ‘ŽœŽȱ̘ œȱŠ›Žȱ™•ŠŒŽȱ’—ȱ•˜—ǰȱ œšžŠ›ŽȱŠ—ȱ ’ŽȱŠ››Š¢ȱ–˜ž•Žœǰȱ›Žœž•’—ȱ’—ȱŠ—ȱ˜™’–’£Š’˜—ȱ˜ȱ‘Žȱ̘ ȱ›˜–ȱŗȱ•Ȧ–’—ȱ˜ȱřȱ•Ȧ–’—ȱ ‘Ž—ȱœšžŠ›ŽȬ array modules are used. Design and validation were ˜—Žȱžœ’—ȱ‘ŽȱꗒŽȱŽ•Ž–Ž—ȱ–Ž‘˜ȱ ‘’Œ‘ȱ Šœȱœ˜•ŸŽȱ  ’‘ȱ ǯȱ ˜›Ž˜ŸŽ›ȱ ‘žȱ et alǯȱ ǻŘŖŗŗǼȱ ŽŸŠ•žŠŽȱ ‘Žȱ Š–˜ž—ȱ ˜ȱ ‘ŽŠȱ ‘Šȱ ŠŒœȱ ˜—ȱ Šȱ œž›ŠŒŽȱ  ‘Ž—ȱ ‘Žȱ ̞’ȱ velocity varies, validating the simulation results by ǯȱ ž–Š›ȱ Š—ȱ Š’—’ȱ ǻŘŖŖŞǼȱ ‹ž’•ȱ Šȱ œ˜•Š›ȱ Š’›ȱ ‘ŽŠŽ›ȱ Š—ȱžœŽȱȱ˜ȱŽŸŠ•žŠŽȱ‘Žȱ‘ŽŠȱ›Š—œŽ›ȱŽěŽŒȱ˜—ȱŠȱ bow-shaped geometry working with the Reynolds —ž–‹Ž›ȱŠ—ȱ‘Žȱ”ȬΉȱ–˜Ž•ȱžœŽȱ˜—ȱ‘’œȱ’—ŸŽœ’Š’˜—ǯ ›˜œœ–Š—ȱŠ—ȱŸ’›’—ȱǻŗşŝŝǼȱŒ˜—žŒŽȱŽ¡™Ž›’–Ž—œȱ 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 deter–’—Žȱ‘Ž’›ȱŽĜŒ’Ž—Œ¢ǰȱ ›˜œœ–Š—ȱŒ˜—Œ•žŽȱ‘Šȱ›ŽžŒ’—ȱ ‘Žȱ œŽ™Š›Š’˜—ȱ ’—Œ›ŽŠœŽœȱ ‘Žȱ ŽĜŒ’Ž—Œ¢ǯȱ ˜ ŽŸŽ›ǰȱ reducing the separation between the plates also deŒ›ŽŠœŽœȱ‘Žȱ̘ ȱ›ŠŽœǯȱ‘’œȱ¢™Žȱ˜ȱŽ˜–Ž›¢ȱ™›˜Ÿ’Žœȱ. 554. Descriptores: ‡ ‡ ‡ ‡ ‡. IOXMRHVWUXFWXUDO FROHFWRUVRODUSODQR VLPXODFLyQHQ&)' WUDQVIHUHQFLDGHFDORU UDGLDFLyQVRODU. ‘’‘ȱ Œ˜—ŠŒȱ Š›ŽŠȱ ‹Ž ŽŽ—ȱ ‘Žȱ ̞’ȱ Š—ȱ ‘Žȱ Š‹œ˜›‹Ž›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 ’œȱœ’–ž•Š’˜—ȱ˜ȱ̘ ȱŠ—ȱ‘ŽŠȱ›Š—œŽ›ǯ. Experimental &RQVWUXFWLRQRISURWRW\SH ‘Žȱ œ˜•Š›ȱ ‘ŽŠŽ›ȱ ‘˜žœ’—ȱ ǻ’ž›Žȱ ŗǼȱ  ’‘ȱ ’–Ž—œ’˜—œȱ ŖǯŖşśȱ –ȱ ‘’‘ǰȱ ŗǯŖŖȱ –ȱ  ’Žȱ Š—ȱ ŗǯŜŖȱ –ȱ •˜—ȱ  Šœȱ ‹ž’•ȱ  ’‘ȱ ȬŗśŖȱ œŽŽ•ȱ ™›˜ę•Žȱ ǻ›Š–ŽǼȱ Š—ȱ ŘŘȱ ŠžŽȱ Š•ŸŠnized steel sheet. The joints were sealed with silicone to prevent air leakage and the inner part was covered with ŠȱŖǯŖŘȱ–Ȭ‘’Œ”ȱ™˜•¢œ¢›Ž—Žȱ™•ŠŽǯȱ‹œ˜›‹Ž›ȱȱ Šœȱ‹ž’•ȱ ˜ȱ˜—Žȱȃ’—›˜ȄȱŒ‘Š——Ž•Ȭœ‘Š™ŽȱœŽŽ•ȱ™•ŠŽȱǻŖǯŖŗȱ–ȱ‘’‘ǰȱ ŖǯŞşȱ–ȱ ’ŽȱŠ—ȱŗǯŚŝȱ–ȱ•˜—Ǽȱ Ž•Žȱ˜ȱŠȱ̊ȱŘŘȱŠžŽȱ Š•ŸŠ—’£Žȱ œŽŽ•ȱ œ‘ŽŽǰȱ ˜›–’—ȱ ŗŖȱ ›ŽŒŠ—ž•Š›ȱ Œ›˜œœȱ œŽŒ’˜—ȱŒ‘Š——Ž•œȱǻŖǯŖŗȱ–ȱ‘’‘ǰȱŖǯŖŞȱ–ȱ ’ŽȱŠ—ȱŗǯŚŝȱ–ȱ •˜—Ǽȱ œŽ™Š›ŠŽȱ ŖǯŖŗȱ –ȱ ›˜–ȱ ŽŠŒ‘ȱ ˜‘Ž›ǯȱ ‘Žȱ ˜›–Žȱ channels were welded to two heads of galvanized pipe ǻŖǯŖřŞŗȱ–ȱ’Š–ŽŽ›ȱŠ—ȱŗǯŗŖȱ–ȱ•˜—ǼȱŠ—ȱ‘ŽȱŽ—’›ŽȱŠ‹sorber painted with fast dry black paint. Absorber B  Šœȱ ‹ž’•ȱ  ’‘ȱ —’—Žȱ Œ˜™™Ž›ȱ ™’™Žœȱ ǻŖǯŖŗŘŝȱ –ȱ ’Š–ŽŽ›ȱ Š—ȱŗǯŚŝȱ–ȱ•˜—ǼȱœŽ™Š›ŠŽȱŖǯŖşȱ–ȱ›˜–ȱŽŠŒ‘ȱ˜‘Ž›ȱŠ—ȱ  Ž•Žȱ˜ȱ ˜ȱ‘ŽŠœȱ˜ȱŒ˜™™Ž›ȱ™’™ŽȱǻŖǯŖřŞŗȱ–ȱ’Š–ŽŽ›ȱ Š—ȱŗǯŗŖȱ–ȱ•˜—Ǽǯȱ’”Žȱ‹œ˜›‹Ž›ȱǰȱ‘Žȱ ‘˜•ŽȱŠ‹œ˜›‹Ž›ȱ  Šœȱ™Š’—Žȱ ’‘ȱŠœȱ›¢ȱ‹•ŠŒ”ȱ™Š’—ǯȱ‘ŽȱŒ˜ŸŽ›ȱ’œȱŠȱ̊ȱ ›ŽŒŠ—ž•Š›ȱ  ’—˜ Ȭ•Šœœȱ ŖǯŖŖŚȱ –ȱ ‘’Œ”ǰȱ ŗǯŖŖȱ –ȱ  ’Žȱ. 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). Š—ȱŗǯŜŖȱ–ȱ•˜—ǯȱ‘Žȱ ŠŽ›ȱŠ—”ȱ’œȱ˜›–Žȱ‹¢ȱ ˜ȱŒ˜—ŒŽ—›’ŒȱŒ¢•’—Ž›œǯȱ‘Žȱ’Š–ŽŽ›œȱŠ›ŽȱŖǯśŘȱ–ȱ˜›ȱ‘Žȱ’——Ž›ȱ Œ¢•’—Ž›ȱŠ—ȱŖǯŝŘȱ–ȱ˜›ȱ‘Žȱ˜žŽ›ȱ˜—ŽȱŠ—ȱ‘Žȱ•Ž—‘œȱ ŖǯŝŘȱ–ȱŠ—ȱŖǯşŘȱ–ǰȱ›Žœ™ŽŒ’ŸŽ•¢ǯȱ‘Žȱœ™ŠŒŽȱ‹Ž ŽŽ—ȱ‘Žȱ  ˜ȱŒ¢•’—Ž›œȱ ŠœȱꕕŽȱ ’‘ȱ™˜•¢ž›Ž‘Š—Žȱ˜Š–ǯ. 0RGHOLQJ´$QV\V:RUNEHQFKµ²WKHSUHSURFHVV ‘Žȱ˜–Š’—ȱŽ˜–Ž›¢ȱ˜ȱ‘Žȱ̞’ȱ Šœȱ™›Ž™Š›Žȱžœ’—ȱ ȃŽœ’—ȱ ˜Ž•Ž›Ȅǯȱ ‘¢œ’Œœȱ ›ŽŽ›Ž—ŒŽǰȱ ǰȱ Žœ‘ȱ Ž‘˜ȱŠ—ȱȬŽœ‘ȱ Ž›ŽȱŒ˜—œ’Ž›Žȱ˜›ȱ‘Žȱ–Žœ‘’—ǯȱ ‘Žȱ ŠŒŽȱ œ™ŠŒ’—ȱ œŽĴ’—œȱ ˜›ȱ‹œ˜›‹Ž›ȱȱ  Ž›Žȱ ‘Žȱ ˜••˜ ’—DZȱŽŽȱ•Ž—‘ȱ‹Ž ŽŽ—ȱŖǯŖŖŚȱ–ȱŠ—ȱŖǯŖŞȱ–Dzȱ‘Žȱ Š—ž•Š›ȱ›Žœ˜•ž’˜—ȱ˜›ȱ‘Žȱ˜™ȱŠ—ȱ‹˜Ĵ˜–ȱœž›ŠŒŽœȱ Šœȱ œŽȱ˜ȱřŖǚDzȱ‘ŽȱŠ—ž•Š›ȱ›Žœ˜•ž’˜—ȱ˜›ȱ‘Žȱ•ŠŽ›Š•ȱœž›ŠŒŽœȱ ˜ȱ‘ŽȱŒ‘Š——Ž•ȱ ŠœȱœŽȱ˜ȱŗŞǚDzȱ‘ŽȱŽŽȱ•Ž—‘ȱ˜›ȱ‘Žȱ‘ŽŠȱ ™’™Žœȱ ŠœȱœŽȱ˜ȱŖǯŖŖśȱ–ȱ ’‘ȱŠȱ–Š¡’–ž–ȱ‘’Œ”—Žœœȱ’—ĚŠ’˜—ȱ˜ȱŖǯŖŞȱ–ǯȱ‘ŽȱŠŒŽȱœ™ŠŒ’—ȱœŽĴ’—œȱ˜›ȱ‹œ˜›‹Ž›ȱ ȱ Ž›Žȱ‘Žȱ˜••˜ ’—DZȱ˜›ȱ‘ŽȱŖǯŖŗŘŝȱ–ȱ’Š–ŽŽ›ȱ™’™Žǰȱ‘Žȱ ŽŽȱ•Ž—‘ȱ ŠœȱœŽȱ‹Ž ŽŽ—ȱŖǯŖŖśȱ–ȱŠ—ȱŖǯŖŘśȱ–ǰȱ ’‘ȱ řŖǚȱ’—ȱ‘ŽȱŠ—ž•Š›ȱ›Žœ˜•ž’˜—Dzȱ˜›ȱ‘Žȱ‘ŽŠȱ™’™Žœȱ‘ŽȱŽŽȱ •Ž—‘ȱ  Šœȱ œŽȱ ‹Ž ŽŽ—ȱ ŖǯŖŖśȱ –ȱ Š—ȱ ŖǯŖŖŞȱ –ȱ Š—ȱ ‘Žȱ –Š¡’–ž–ȱ‘’Œ”—Žœœȱ’—ĚŠ’˜—ȱ ŠœȱœŽȱ˜ȱŖǯŖŘśȱ–ǰȱŽ—Ž›ating the mesh shown in Figure 2.. $. . . . %. System equations +HDWWUDQVIHU œȱœ‘˜ —ȱ’—ȱ’ž›ŽȱřȱŒ˜—œ’Ž›’—ȱ‘Šȱ‘Ž›Žȱ’œȱ—˜ȱŠ‹sorption of solar energy in the glass, the radiosity for the absorber is: Jŗ = E‹ŗ and the energy supplied to surŠŒŽȱŗȱ’œ 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

(8)  h Tř  TŘ

(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 ̞’ 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  ˜›”’—ȱ̞’ȱǻ ˜•–Š—ǰȱŘŖŖŗǼ. ‘Žȱ ̞’ȱ ’—Ž›ŠŒ’˜—ȱ  ’‘ȱ ’œȱ œž››˜ž—’—œȱ ŒŠ—ȱ ‹Žȱ ŒŠ•Œž•ŠŽȱžœ’—ȱŒ˜–™žŠ’˜—Š•ȱ˜˜•œȱ ‘Ž—ȱ’ȱ›Žšž’›Žœȱ thousands of calculations. In these complex situations it is almost impossible to manually do the calculations. ‘ŽȱŒ˜–™žŠ’˜—Š•ȱ˜˜•œȱŒŠ•Œž•ŠŽȱ̞’ȱ™›˜™Ž›’Žœȱ™˜’—ȱ ‹¢ȱ ™˜’—ȱ ˜›ȱ ŽŠŒ‘ȱ ™›˜ŒŽœœȱ Š—ȱ ‘Žȱ –Š‘Ž–Š’ŒŠ•ȱ ̞’ȱ relations are often solved numerically with a computer. ‘Žȱ™‘¢œ’ŒŠ•ȱŠœ™ŽŒœȱ˜ȱŠ—¢ȱ̞’ȱ̘ ȱŠ›Žȱ˜ŸŽ›—Žȱ‹¢ȱ ‘›ŽŽȱž—Š–Ž—Š•ȱ™›’—Œ’™•ŽœDZȱ‘ŽȱŒ˜—’—ž’¢ȱŽšžŠ’˜—DZ w wt. ³³ ³ Udv

(16)  ³³ UVds v. Ŗȱ. ǻşǼ. Ž ˜—ȂœȱŽŒ˜—ȱŠ ȱ˜ȱ˜’˜—DZ § 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,  ‘’Œ‘ȱ Šȱ ‘Žȱ œŠ–Žȱ ’–Žȱ Š›Žȱ œ˜•ŸŽȱ ˜ȱ ˜‹Š’—ȱ ‘Žȱ ꎕȱ ™Š›Š–ŽŽ›œȱ ˜ȱ ‘Žȱ ̘ ȱ ’—ȱ ’œŒ›ŽŽȱ ™˜’—œǰȱ ’–Žȱ Š—ȱ œ™ŠŒŽȱǻ Š›–Š›ŽȱŠ—ȱ’”Ž”Š›ǰȱŘŖŗŖǼǯ. )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 ‘ŽȱŖǯŖŗŘŝȱ–ȱ’Š–ŽŽ›ȱ™’™Žȱǻ•œ‘ŠŽ’ȱet alǯǰȱŘŖŗŖǼǯ. Test conditions 3URWRW\SHGDWD ‘ŽȱŽ¡™Ž›’–Ž—Š’˜—ȱ ŠœȱŽŸŽ•˜™Žȱž›’—ȱŠ¢ȱŘŖŗŖǰȱ ’—ȱ‘ŽȱŒ’¢ȱ˜ȱŠ—ȱ

(18) žŠ—ȱŽ•ȱǘǰȱœŠŽȱ˜ȱžŽ›·Š›˜ǰȱ·¡’Œ˜Dzȱ’ȱ’œȱ•˜ŒŠŽȱŘŖǚȱŘřȂǰȱşşǚȱśşȂȱǰȱ ’‘ȱ‘’‘ȱœ˜•Š›ȱ›Šdiation levels during the year. The collectors were side ‹¢ȱœ’Žȱ ’‘ȱŠ—ȱ’—Œ•’—Š’˜—ȱŠ—•ŽȱŽšžŠ•ȱ˜ȱ‘Žȱ™•ŠŒŽȱ•Š’tude for both collectors. Between the thermo tank and ‘Žȱœ˜•Š›ȱŒ˜••ŽŒ˜›œȱ‘Ž›Žȱ ŠœȱŠȱŸŽ›’ŒŠ•ȱ’œŠ—ŒŽȱ˜ȱŖǯŘśȱ m to prevent the return of water overnight according to Rudnick et alǯȱǻŗşŞŜǼǯ Solar radiation was measured with an Eppleypyrheli˜–ŽŽ›ȱ–˜Ž•ȱ ǰȱŒŠ™Š‹•Žȱ˜ȱ–ŽŠœž›’—ȱŠȱ›Š—Žȱ˜ȱ›˜–ȱ. )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%. Ŗȱ˜ȱŗŚŖŖȱ––2ǰȱ–˜ž—Žȱ˜—ȱŠȱœ˜•Š›ȱ›ŠŒ”Ž›ȱȬŗǯȱ‘ŽȱŠ–‹’Ž—ȱŽ–™Ž›Šž›Žȱ Šœȱ•˜Žȱ ’‘ȱŠȱȬśřśȱŠŠȱŒ˜••ŽŒtor. With the radiation and ambient temperature data, the heat transfer model was solved to determine the working ̞’ȱŽ–™Ž›Šž›Žǯȱ‘Žȱ›Žœž•œȱŠ›Žȱœ‘˜ —ȱ’—ȱ’ž›ŽȱŚǯ Water temperature was measured at the zenith time,  ’‘ȱŠȱŠŠȱŒ˜••ŽŒ˜›ȱȬśřśȱŽšž’™™Žȱ ’‘ȱŠ—ȱȬŘřŘȱ communication port, programmable sampling rate and ŠŠȱ ȬŠ‹ȱ ™›˜ŒŽœœ’—ȱ œ¢œŽ–ǯȱ ŽŠœž›Ž–Ž—œȱ  Ž›Žȱ ˜‹Š’—ŽȱŠ•˜—ȱ‘ŽȱŒ‘Š——Ž•œǰȱ ‘Ž›Žȱ™˜’—ȱŗȱ Šœȱ•˜ŒŠŽȱ —ŽŠ›ȱ‘Žȱ‘ŽŠȱ’—•ŽȱŠ—ȱ™˜’—ȱŝȱ—ŽŠ›ȱ‘Žȱ‘ŽŠȱ˜ž•Žǰȱ‘Žȱ rest of the points were distributed evenly throughout each channel or pipe (depending on the absorber). Figure 5 shows the typical temperatures reached on chan—Ž•œȱŗǰȱŜǰȱŠ—ȱŗŖȱ˜ȱ‹œ˜›‹Ž›ȱȱŠ—ȱ™’™ŽœȱŗǰȱŜǰȱŠ—ȱşȱ˜ȱ Absorber B.. A Blue-White®ȱ̘ ȱ–ŽŽ›ǰȱ ’‘ȱ–ŽŠœž›Ž–Ž—ȱ›Š—Žȱ ›˜–ȱŖǯŚȱ˜ȱŚǯŖȱ•Ȧ–’—ǰȱ ŠœȱŒ˜——ŽŒŽȱ’—ȱœŽ›’Žœȱ‹Ž ŽŽ—ȱ the collector and the thermo tank. The temperature of the water contained in the thermo tank was measured  ’‘ȱŠȱŠŠȱŒ˜••ŽŒ˜›ȱȬśřśǯȱ‘Žȱ›Žœž•œȱŠ›Žȱœ‘˜ —ȱ’—ȱ Figure 6.. $QDO\VLVLQ&)' Flow analysis was developed in CFD considering: The general domain as water, a Thermal Energy process, ‘Žȱ”ȬΉȱ–˜Ž•ǰȱŠȱŞŖŖȱȦ–2ȱ‘ŽŠȱ̘ ȱ˜—ȱ‘Žȱ Š••ǰȱŠȱŗŘǯŗŝȱ ¡ȱŗŖȬřȱ–ȦœȱŽ—›¢ȱ̘ ȱŸŽ•˜Œ’¢ǰȱŠȱŘşřȱ ȱŽ–™Ž›Šž›ŽȱŠ—ȱ ŠȱŖǯŖŖȱŠȱ˜ž•Žȱ›Ž•Š’ŸŽȱ™›Žœœž›Žǯȱ‘Žȱ›Žœž•œȱŠ›Žȱœ‘˜ —ȱ ’—ȱ’ž›Žȱŝǯ. )LJXUH0HDVXUHGWHPSHUDWXUHYHUVXVORFDWLRQD

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(21) XSLSHഊSLSHżSLSH. Ingeniería Investigación y Tecnología, volumen XIV (número 4), octubre-diciembre 2013: 553-561 ISSN 1405-7743 FI-UNAM. 557.

(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

(23) ƑIORZRXWOHWLQ$EVRUEHU$ǻWHPSHUDWXUHPHDQLQWKHUPRWDQNZLWK$EVRUEHU$DQGE

(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 Śǯȱ‘ŽœŽȱŒŠ•Œž•ŠŽȱ›Žœž•œȱŠ›ŽȱŒ˜—œ’œŽ—ȱ ’‘ȱ‘ŽȱŽ¡™Ž›’mental data shown in Figure 5. The water temperature is similar in both absorbers according to the theoretical ǻ’ž›Žȱ ŚǼȱ Š—ȱ Ž¡™Ž›’–Ž—Š•ȱ ǻ’ž›Žȱ śǼȱ ›Žœž•œǯȱ—ȱ 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 ŽŽ—ȱžŒœȱ’œȱřǯŚȱ ȱ˜›ȱ‹˜‘ȱŠ‹œ˜›‹Ž›œǯȱ˜—œ’Ž›’—ȱ‘’œȱ low temperature increases according to the thermal test’—ȱ‘Ž›Žȱœ‘˜ž•ȱ‹ŽȱŠȱœ’–’•Š›ȱ‘Ž›–˜œ’™‘˜—’ŒȱŽěŽŒȱ˜›ȱŠ••ȱ žŒœǯȱ ˜ ŽŸŽ›ǰȱ‘Žȱ̘ ȱ–ŽŠœž›Ž–Ž—ȱŸŠ•žŽœȱǻ’ž›ŽȱŜǼȱ œ‘˜ ȱ’쎛Ž—ȱ›Žœž•œDZȱ‘Ž›Žȱ’œȱŠȱ‹’Ž›ȱŠ›ŽŠȱž—Ž›ȱ‘Žȱ ̘ ȱŒž›ŸŽȱ˜›ȱ‹œ˜›‹Ž›ȱǰȱŽĴ’—ȱ‘’‘Ž›ȱŽ–™Ž›Šž›Žȱ˜ȱ the water contained in the thermo tank, which repreœŽ—œȱŠȱ‘’‘Ž›ȱ̘ ȱŒ˜–™Š›Žȱ˜ȱ‹œ˜›‹Ž›ȱǯȱ‘Ž›Ž˜›Žǰȱ if the temperature variation between ducts for both absorbers is similar, this could mean that the amount of ̘ ȱŒŠ—ȱ‹ŽȱŠěŽŒŽȱ‹¢ȱ‘Žȱ̞’ȱ–ŽŒ‘Š—’ŒœȱŠ—ȱ—˜ȱ—ŽŒŽœœŠ›’•¢ȱ˜—•¢ȱ‹¢ȱ‘Ž›–Š•ȱŽěŽŒœǯ. 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 simu•Š’˜—ȱ Šœȱ–ŠŽȱŸŠ›¢’—ȱ‘Žȱ̘ ȱ›˜–ȱŚśȱ•Ȧ‘ȱ˜ȱŝŖȱ•Ȧ‘ǰȱ 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 ’ž›ŽȱŞǯ. •˜ ȱŸŽ•˜Œ’’Žœȱ˜›ȱ‘ŽȱꛜȱŝȱŒ‘Š——Ž•œȱŒ˜–™Š›Žȱ˜ȱŒ‘Š——Ž•œȱŞǰȱşȱŠ—ȱŗŖǯȱ‘Ž›Ž˜›ŽǰȱŽŸŽ—ȱ’ȱ‘ŽȱŽ–™Ž›Šž›ŽȱŠȱ ‘Žȱ’쎛Ž—ȱŒ‘Š——Ž•œȱ’œȱœ’–’•Š›ǰȱ‘Žȱ–Š’—ȱ‘ŽŠȱŒ˜—›’‹ž’˜—ȱ˜ȱ‘Žȱ‘Ž›–˜ȱŠ—”ȱ’œȱ–ŠŽȱ–˜œ•¢ȱ‹¢ȱ‘Žȱ•Šœȱřȱ channels from left to right in Absorber A. For Absorber B, the Reynolds numbers are higher ǻ’ž›Žȱ şǼȱ ‹ŽŒŠžœŽǰȱ ŠŒŒ˜›’—ȱ ˜ȱ ‘Žȱ ȱ œ’–ž•Š’˜—ǰȱ the velocity is higher compared to Absorber A. The ŸŠ›’Š’˜—ȱ˜ȱ‘ŽȱŽ¢—˜•œȱ—ž–‹Ž›œȱ‹Ž ŽŽ—ȱŒ‘Š——Ž•ȱŗȱ Š—ȱŒ‘Š——Ž•ȱşȱ˜›ȱŠȱ̘ ȱ˜ȱŚśȱ•Ȧ‘ȱ’œȱŘŘȱž—’œǰȱŠ—ȱ˜›ȱ‘Žȱ –Š¡’–ž–ȱ œ’–ž•ŠŽȱ ̘ ȱ ǻŝŖȱ •Ȧ‘Ǽȱ ‘Žȱ ’쎛Ž—ŒŽȱ ’œȱ 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 ‘Šœȱ ‹ŽĴŽ›ȱ ̘ ȱ ŸŠ•žŽœȱ Š—ȱ Œ˜—œŽšžŽ—•¢ǰȱ ‘’‘Ž›ȱ Ž–perature values at the thermo tank, due to the possibil’¢ȱ˜ȱ‹ŽĴŽ›ȱ̞’ȱ–ŽŒ‘Š—’Œœȱ™Ž›˜›–Š—ŒŽǯ. &RPSDULVRQVZLWKSUHYLRXVZRUN. )LJXUH5H\QROGVQXPEHUYHUVXVFKDQQHOIRUDEVRUEHU$ ¸OKOKƑOKżOK×OKǻOK. œȱ ’ȱ ŒŠ—ȱ ‹Žȱ —˜’ŒŽǰȱ ‘Ž›Žȱ Š›Žȱ ‹’ȱ ’쎛Ž—ŒŽœȱ ’—ȱ ‘Žȱ Ž¢—˜•œȱ—ž–‹Ž›œǯȱ‘Žȱ›Žœž•œȱœ‘˜ ȱŠȱ’쎛Ž—ŒŽȱ˜ȱŚŘȱ ž—’œȱ ‹Ž ŽŽ—ȱ Œ‘Š——Ž•ȱ ŗȱ Š—ȱ Œ‘Š——Ž•ȱ ŗŖȱ ˜›ȱ Šȱ Śśȱ •Ȧ‘ȱ ̘ ǰȱŠ—ȱ˜›ȱ‘Žȱ–Š¡’–ž–ȱœ’–ž•ŠŽȱ̘ ȱǻŝŖȱ•Ȧ‘Ǽȱ‘Žȱ ’쎛Ž—ŒŽȱ’œȱşŖȱž—’œǯȱ ȱŒŠ—ȱ‹ŽȱŒ˜—œ’Ž›Žȱ‘Šȱ‘Ž›ŽȱŠ›Žȱ. )LJXUH5H\QROGVQXPEHUYHUVXVSLSHIRUDEVRUEHU%¸OK +OKƑOKżOK×OKǻOK. Selmi et alǯȱǻŘŖŖŞǼȱŒ˜—žŒŽȱŠȱ›ŽœŽŠ›Œ‘ȱ˜—ȱœ˜•Š›ȱŒ˜••ŽŒ˜›œǯȱȱŖǯŖŗŘŝȱ–ȱŒ˜™™Ž›ȱ™’™Ž Šœȱ™•ŠŒŽȱ’—œ’ŽȱŠȱ ˜˜Ž—ȱ housing with a glass cover. The heat absorber was composed of the copper pipe and a sheet of aluminum with Šȱ™˜•¢ž›Ž‘Š—Žȱ‹ŠœŽȱŠȱ‘Žȱ‹˜Ĵ˜–ǯȱ‘’œȱœ’—•ŽȬ™’™Žȱœ˜•Š›ȱ collector was exposed to sunlight radiation to heat up  ŠŽ›ȱ ’‘ȱŠȱ‘ŽŠȱ̘ ȱ˜ȱśŚŖȱȦ–2Dzȱ‘Žȱ ŠŽ›ȱŽ–™Ž›Šž›Žȱ–ŽŠœž›ŽȱŽ¡™Ž›’–Ž—Š••¢ȱ ŠœȱřŘŜȱ ȱŠ—ȱ‘Žȱœ’–ž•ŠŽȱ˜—ŽȱřŘŝȱ ǯȱ˜›ȱ‘ŽȱœŠ–ŽȱŒŠ•Œž•ŠŽȱ‘ŽŠȱ̘ ȱžœ’—ȱ ‘ŽȱŽšžŠ’˜—œȱ’—ȱ‘’œȱ’—ŸŽœ’Š’˜—ǰȱ‘Žȱ›Žœž•ȱ Šœȱřřŗȱ ǯȱ ‘ŽȱŸŠ›’Š’˜—ȱ˜ȱŚȱ ȱ˜ȱŽ–™Ž›Šž›Žȱ–Š¢ȱ‹ŽȱžŽȱ˜ȱ’쎛ences between the materials used in the construction of the prototype and design considerations. For his analyœ’œǰȱŽ•–’ȱžœŽȱ‘ŽȱꗒŽȱŽ•Ž–Ž—ȱ–Ž‘˜ȱ˜ȱŸŠ•’ŠŽȱ‘Žȱ CFD results. On this basis, CFD is considered a consistent solving method for this research work. Fan et alǯȱ ǻŘŖŖŝǼȱ ’—ŸŽœ’ŠŽȱ ‘Žȱ ™Ž›˜›–Š—ŒŽȱ ǻŽ¡perimentation and CFD simulation) of a U-type solar Œ˜••ŽŒ˜›ǰȱ  ‘Ž›Žȱ ‘Žȱ ̘ ȱ ™ŠœœŽœȱ ‘›˜ž‘ȱ Šȱ ›‘˜–‹žœȬ œ‘Š™Žȱ Œ›˜œœȱ œŽŒ’˜—ȱ ’—ȱ Šȱ ŗŜȬœŽŒ’˜—ȱ Š››Š¢ȱ  ’‘ȱ ‘’œȱ Ž˜–Ž›¢ǯȱŠ›¢’—ȱ‘Žȱ̘ ȱ›˜–ȱŗśŖȱ•Ȧ‘ȱ˜ȱŗśŖŖȱ•Ȧ‘ǰȱ‘Žȱ velocity characteristic curves show similar performancŽœȱ˜ȱ‘˜œŽȱœ‘˜ —ȱ’—ȱ’ž›ŽȱŞǰȱ’—ȱ ‘’Œ‘ȱ‘ŽȱŠ›‘Ž›ȱ‘Žȱ žŒȱ’œȱ›˜–ȱ‘Žȱ̞’ȱ’—•Žǰȱ‘Žȱ‘’‘Ž›ȱ‘Žȱ̘ ȱŸŽ•˜Œ’¢ȱ ’œȱ’—ȱ‘Šȱ›Žœ™ŽŒ’ŸŽȱžŒȱǻ˜›ȱ‘Žȱꛜȱ‘Š•ȱ˜ȱ‘Žȱ˜Š•ȱ amount of ducts). For the other half, a mirror view of such curves can be considered because Fan used a U¢™ŽȱŒ˜••ŽŒ˜›ǰȱ ‘’•Žȱ‘’œȱœž¢ȱŽŸŠ•žŠŽœȱŠȱȬ¢™Žȱ˜—Žǯ In the experimental work for Absorber A, the water ’—•Žȱ Š—ȱ ˜ž•Žȱ Ž–™Ž›Šž›Žȱ  Šœȱ –ŽŠœž›Žȱ ŽĴ’—ȱ Šȱ ŸŠ›’Š’˜—ȱ˜ȱŗřȱ ȱŠȱ‘Žȱ£Ž—’‘ȱ’–Žǰȱ ‘’•Žȱ‘’ĵŽ›ȱet al. ǻŘŖŖřǼȱ›Ž™˜›ȱŠȱŽ–™Ž›Šž›ŽȱŸŠ›’Š’˜—ȱ˜ȱŗŚȱ 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 ‘’œȱœž¢ȱœ‘˜ œȱ‘Žȱ‘ŽŠȱ›Š—œŽ›ȱŠ—ȱ̞’ȱ–ŽŒ‘Š—’Œœȱ performance of two absorbers from experimental data. The calculated and simulated values show consistency  ’‘ȱ ŽŠŒ‘ȱ ˜‘Ž›ȱ Š—ȱ  ’‘ȱ œ’–’•Š›ȱ œž’Žœȱ ‹¢ȱ ’쎛Ž—ȱ 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 ŸŠ›’Š’˜—ȱ’œȱ—˜Žȱ’—ȱ‘Žȱ–’•Žȱ˜ȱ‘Žȱ̞’ȱ™Š‘ȱ ’‘ȱ ŸŠ•žŽœȱ˜ȱřŚŝȱ ǰȱřŚŜȱ ȱŠ—ȱřŚśȱ ȱ˜›ȱŒ‘Š——Ž•œȱŗǰȱŜȱŠ—ȱ ŗŖǰȱ›Žœ™ŽŒ’ŸŽ•¢ǯȱ˜›ȱŽšž’ŸŠ•Ž—ȱ•˜ŒŠ’˜—œȱ’—ȱ‹œ˜›‹Ž›ȱȱ ‘Žȱ›Žœž•œȱ Ž›ŽȱřŚśǯśȱ ǰȱřŚŚǯśȱ ȱŠ—ȱřŚŚǯśȱ ȱ˜›ȱ™’™Žœȱŗǰȱ ŜȱŠ—ȱşǰȱ›Žœ™ŽŒ’ŸŽ•¢ǯȱ‘ŽȱŽ–™Ž›Šž›ŽȱŠŸŽ›ŠŽȱŸŠ•žŽœȱ for each absorber were calculated from the experimenŠ•ȱŠŠȱŠ—ȱŒ˜–™Š›ŽDzȱ˜‹Š’—’—ȱ‘Šȱ‘ŽȱŽ–™Ž›Šž›Žȱ average variation from one absorber to the other is only ŗȱ ǯȱ —ȱœ™’Žȱ˜ȱœžŒ‘ȱŠȱœ–Š••ȱŽ–™Ž›Šž›Žȱ’쎛Ž—ŒŽǰȱ‘Žȱ ȱœ’–ž•Š’˜—ȱ˜›ȱŠȱśŖȱ•Ȧ‘ȱ̘ ȱœ‘˜ Žȱ‘Šȱ‘Žȱ–Š¡’–ž–ȱŸŽ•˜Œ’¢ȱ˜›ȱ‹œ˜›‹Ž›ȱȱ ŠœȱŗǯřŞȱƼȱŗŖ–2ȱ–Ȧœȱ–Š’—•¢ȱ ˜—ȱŒ‘Š——Ž•œȱŞǰȱşȱŠ—ȱŗŖǰȱ ‘’•Žȱ˜›ȱ‹œ˜›‹Ž›ȱȱ‘ŽȱŸŽ•˜Œ’¢ȱ›ŽŠŒ‘ŽȱŸŠ•žŽœȱ˜ȱž™ȱ˜ȱŗǯŝȱƼȱŗŖ–2ȱ–Ȧœȱ’—ȱ‘Žȱşȱ™’™Žœǰȱ  ‘’Œ‘ȱ–ŽŠ—œȱ‘Šȱ‘Ž›Žȱ’œȱŠȱ–˜›Žȱž—’˜›–ȱ̘ ȱ’—ȱ‹sorber B similarly the Reynolds is a function of velocity Š—ȱ ‘Žȱ ›Žœž•œȱ  ‘Ž—ȱ ¢˜žȱ ‘ŠŸŽȱ ̘ ȱ ˜ȱ ŝŖȱ •Ȧ‘ȱ ‘Žȱ‹œ˜›‹Ž›ȱǰȱŽ¢—˜•œȱ™›ŽœŽ—œȱŸŠ•žŽœȱ›˜–ȱŘśȱ˜ȱŗŗśȱ˜›ȱ Œ‘Š——Ž•ȱ ŗȱ Š—ȱ Œ‘Š——Ž•ȱ ŗŖȱ ›Žœ™ŽŒ’ŸŽ•¢ǰȱ ‘ŠŸ’—ȱ •Š›Žȱ variations in velocity, however for Absorber B under ‘Žȱ œŠ–Žȱ ̘ ȱ ŸŠ›’Š’˜—œȱ Š›Žȱ ŘŖŖȱ ˜ȱ ŘŘśȱ œžŒ‘ȱ ‘Šȱ ‘Žȱ ŸŽ•˜Œ’¢ȱ ’‘’—ȱşȱž‹Žœȱ’œȱ–˜›Žȱœ’–’•Š›ȱ ‘Ž—ȱŒ˜–™Š›Žȱ ˜ȱ‹œ˜›‹Ž›ȱǰȱ‘Ž›Ž˜›Žȱ–Š”’—ȱ’ȱŠȱ–˜›ŽȱŽĜŒ’Ž—ȱ‘ŽŠing system.. Acknowledgements ‘ŽȱŠž‘˜›œȱŠ›ŽȱŽŽ™•¢ȱ‘Š—”ž•ȱ˜ȱ›˜ǯȱ

(27) ž•’˜ȱ ž’·››Ž£ȱ Villarreal for his guidance, useful suggestions, and for ›Š—’—ȱŠŒŒŽœœȱ˜ȱȱ™›˜“ŽŒȱ˜ǯȱŗŚŗŞŞşȱ’—ȱ‘’œȱ study.. Nomenclature A Dh Ebȱ. ȱ hȱ hwȱ Jȱ. surface área, m2 hydraulic diameter, m Ž–’œœ’ŸŽȱ™˜ Ž›ǰȱȦ–2 Œ‘Š——Ž•ȱ‘Ž’‘ǰȱ– ‘ŽŠȱ›Š—œŽ›ȱŒ˜ŽĜŒ’Ž—ȱȦ–2°C ‘ŽŠȱ›Š—œŽ›ȱŒ˜ŽĜŒ’Ž—ȱ˜ȱ ŠŽ›ǰȱȦ–2°C ›Š’˜œ’¢ǰȱȦ–2. 560. kȱ Re v W ̇x. ‘Ž›–Š•ȱŒ˜—žŒ’Ÿ’¢ȱȦ–2.°C Reynolds number (–) velocity, m channel width, m wall thickness, m. *UHHNV\PEROV Εȱ Ή2 ΐȱ. Ž—œ’¢ǰȱ”Ȧ–ř emissivity ̞’ȱ¢—Š–’ŒȱŸ’œŒ˜œ’¢ǰȱ”Ȧǻ–ȱœǼ. References •œ‘ŠŽ’ȱǯǯǯǰȱ Šȱǯǯǰȱ•ȬŽ’›¢ȱǯǰȱ•’ȱǯ ǯȱ ŽŠȱ›Š—œŽ›ȱŠ—ȱ›Žœœž›Žȱ›˜™ȱ’—ȱ˜››žŠŽȱ‘Š——Ž•œǯȱEnergy, volž–Žȱřśȱǻ’œœžŽȱŗǼǰȱŘŖŗŖDZȱŗŖŗȬŗŗŖǯ Š—ȱ

(28) ǯǰȱ

(29) ’ŸŠ—Ȭ‘Š‘ȱǯǰȱž›‹˜ȱǯȱ•˜ ȱ’œ›’‹ž’˜—ȱ’—ȱŠȱ˜•Š›ȱ˜••ŽŒ˜›ȱŠ—Ž•ȱ ’‘ȱ ˜›’£˜—Š••¢ȱ —Œ•’—Žȱ‹œ˜›‹Ž›ȱ›’™œǯȱ˜lar EnergyǰȱŸ˜•ž–ŽȱŞŗȱǻ’œœžŽȱŗŘǼǰȱŘŖŖŝDZȱŗśŖŗȬŗśŗŗǯ ›˜œœ–Š—ȱ ǯȱ Š—ȱ ǯȱ Ÿ’›’—ǯȱ ŽŠȱ ›Š—œŽ›ȱ —Š•¢œ’œȱ ˜ȱ Šȱ •ŠȬ •ŠŽȱ˜•Š›ȱ—Ž›¢ȱ˜••ŽŒ˜›ǯȱ˜•Š›ȱ—Ž›¢ǰȱŸ˜•ž–Žȱŗşȱǻ’œœžŽȱ śǼǰȱŗşŝŝDZȱŚşřȬśŖŘǯ. ˜•–Š—ȱ

(30) ǯǯȱ ŽŠȱ ›Š—œŽ›ǰȱ ŝ‘ȱ Žǯǰȱ Ž ȱ ˜›”ǰȱ Œȱ ›Š ȱ ’••ǰȱ ŘŖŖŗǯ Š›–Š›ŽȱǯǯȱŠ—ȱ’”Ž”Š›ȱǯǯȱ—Š•¢œ’œȱ˜ȱ•ž’ȱ•˜ ȱŠ—ȱ ŽŠȱ ›Š—Ž›ȱ ’—ȱ Šȱ ’‹ȱ ›’ȱ ˜ž‘Ž—Žȱ ž›ŠŒŽȱ ˜•Š›ȱ ’›ȱ ŽŠŽ›ȱ Using CFD. ˜•Š›ȱ—Ž›¢ǰȱŸ˜•ž–ŽȱŞŚȱǻ’œœžŽȱřǼǰȱŘŖŗŖDZȱŚŖşȬŚŗŝǯ ž–Š›ȱǯȱŠ—ȱŠ’—’ȱǯǯȱȱŠœŽȱŽ›˜›–Š—ŒŽȱ—Š•¢œ’œȱ˜ȱ˜•Š›ȱ’›ȱ ŽŠŽ›ȱžŒȱ›˜Ÿ’Žȱ ’‘ȱ›’ęŒ’Š•ȱ˜ž‘—ŽŽœǯȱRenewable Energy,ȱŸ˜•ž–ŽȱřŚȱǻ’œœžŽȱśǼǰȱŘŖŖŞDZȱŗŘŞśȬŗŘşŗǯ ŠŽ —Ž›—ŽŽȱǯǰȱ””ŠŒ‘Š›ȱ ǯǰȱ Š–˜—™Š—ȱǯǰȱ˜—™˜˜•ȱǯǰȱ

(31) ’›Š™‘˜—ȱ ǯǰȱ ȱ ’›’–˜—”‘˜•ȱ

(32) ǯȱ ’—’Žȱ •Ž–Ž—ȱ Ž‘˜ȱ ˜›ȱ ˜–™žŠ’˜—ȱ•ž’ȱ¢—Š–’Œœȱ˜ȱŽœ’—ȱ‘˜˜Ÿ˜•Š’Œȱ‘Ž›–Š•ȱ ǻȦǼȱ ¢œŽ–ȱ ˜—ꐞ›Š’˜—ǯȱ ˜•Š›ȱ —Ž›¢ȱ ŠŽ›’Š•œȱ ǭȱ ˜•Š›ȱŽ••œǰȱŸ˜•ž–Žȱşśȱǻ’œœžŽȱŗǼǰȱŘŖŗŗDZȱřşŖȬřşřǯ Rudnick A., Kaplan Y., Kudish A.I., Wolf D. A Study of Solar ˜••ŽŒ˜›ȱ’—ǰȱ —œŠ••Š’˜—ȱ Š—ȱ ŠŽ›’Š•œȱ ›˜‹•Ž–œǯȱ ˜•Š›ȱ Energy,ȱŸ˜•ž–ŽȱřŜȱǻ’œœžŽœȱřǼǰȱŗşŞŜDZȱŘŘŝȬŘŚŖǯ Ž•–’ȱ ǯǰȱ ˜‘Š––Žȱ

(33) ǯǰȱ ‘Š Š“Šȱǯǰȱ‹ž•‘Š–’ȱ ǯȱ Š•’Š’˜—ȱ˜ȱȱ’–ž•Š’˜—ȱ˜›ȱ•Šȱ•ŠŽȱ˜•Š›ȱ—Ž›¢ǯȱRenewable EnergyǰȱŸ˜•ž–Žȱřřȱǻ’œœžŽȱřǼǰȱŘŖŖŞDZȱřŞřȬřŞŝǯ ‘’ĵŽȱǯǰȱ Š•–Š—˜Ÿ’£ȱǯǰȱŸ’›’—ȱǯǰȱ ›˜œœ–Š—ȱ ǯȱ¡™Ž›’–Ž—œȱ  ’‘ȱŠȱ•Šȱ•ŠŽȱ˜•Š›ȱŠŽ›ȱ ŽŠ’—ȱ¢œŽ–ȱ’—ȱ‘Ž›–˜œ¢phonic Flow. ˜•Š›ȱ—Ž›¢ǰȱŸ˜•ž–ŽȱŘŘȱǻ’œœžŽȱŗǼǰȱŘŖŖřDZȱŘŝȬřśǯ ‘žȱǯǰȱŠ—ȱǯǰȱŠ—ȱǯǰȱž—ȱǯǰȱ žŠ—ȱǯȱ—ȱ쎌’ŸŽȱ ŽŠȱ ’œœ’™Š’˜—ȱ Ž‘˜ȱ ˜›ȱ Ž—œŽ•¢ȱ ŠŒ”Žȱ ˜•Š›ȱ Ž••œȱ —Ž›ȱ. ’‘ȱ˜—ŒŽ—›Š’˜—ǯȱ˜•Š›ȱ—Ž›¢ȱŠŽ›’Š•œȱǭȱ˜•Š›ȱŽ••œ, volž–ŽȱşŚȱǻ’œœžŽȱŘǼǰȱŘŖŗŖDZȱŗřřȬŗŚŖǯ. 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 —Ž•ȱŠ››˜šžÇ—ȬȱŽȱ

(37) Žœøœǯȱ Žȱ˜‹Š’—Žȱ‘’œȱ‹ŠŒ‘Ž•˜›ȼœȱŽ›ŽŽȱ’—ȱ•ŽŒ›’ŒŠ•ȱ—’—ŽŽ›’—ȱ›˜–ȱ‘ŽȱŠ¡ŠŒŠȱŽŒ‘—˜•˜’ŒŠ•ȱ —œ’žŽȱ ǻ’—ȱŽ¡’Œ˜ǼǰȱŠ—ȱ‘’œȱ–ŠœŽ›ȱ˜ȱœŒ’Ž—ŒŽȱŽ›ŽŽȱ›˜–ȱ‘Žȱ˜›Ž•’ŠȱŽŒ‘—˜•˜’ŒŠ•ȱ —œ’žŽǯȱ ’œȱ˜Œ˜›Š•ȱŽ›ŽŽȱ’œȱ›˜–ȱ‘ŽȱŠ’˜—Š•ȱ˜•¢ŽŒ‘—’Œȱ —œ’žŽǰȱŒ˜—Ž››Žȱ‹¢ȱ‘Žȱ ›ŠžŠŽȱ›˜›Š–ȱ’—ȱŸŠ—ŒŽȱŽŒ‘—˜•˜’Žœǰȱ Ȭ ǰȱžŽ›·Š›˜ȱŽŒ’˜—ǯȱȱ™›ŽœŽ—ȱ‘Žȱ’œȱŠȱ™›˜Žœœ˜›ȱŠȱ‘ŽȱŽŒ‘—˜•˜’ŒŠ•ȱ—’ŸŽ›œ’¢ȱ˜ȱŠ—ȱ

(38) žŠ—ȱŽ•ȱǘǯȱ Žȱ‘Šœȱ–Š‘Ž–Š’ŒŠ••¢ȱ–˜Ž••Žǰȱ Žœ’—ŽǰȱŠ—ȱ‹ž’•ȱŠ™™•’Š—ŒŽœȱ ‘’Œ‘ȱ ˜›”ȱ‹ŠœŽȱ˜—ȱœ˜•Š›ȱŽ—Ž›¢ǯȱ Žȱ‘Šœȱ™ž‹•’œ‘Žȱ˜ž›ȱŠ›’Œ•Žœȱ’—ȱœ›’Œ•¢ȱ›ŽŽ›ŽŽȱ“˜ž›—Š•œȱŠ—ȱ˜ŸŽ›ȱŜŖȱŠ›’Œ•Žœȱ’—ȱ—Š’˜—Š•ȱ–ŽŽ’—œǯ

(39) žŠ—ȱŠ—žŽ•ȱ•’ŸŠ›ŽœȬŠ–Ç›Ž£ǯȱ Žȱ˜‹Š’—Žȱ‘’œȱ‹ŠŒ‘Ž•˜›ȼœȱŽ›ŽŽȱ’—ȱ–ŽŒ‘Š—’ŒŠ•ȱŽ—’—ŽŽ›’—ȱ›˜–ȱ‘Žȱ˜›Ž•’ŠȱŽŒ‘—˜•˜’ŒŠ•ȱ —œ’žŽȱǻ’—ȱŽ¡’Œ˜ǼǰȱŠ—ȱ‘’œȱ–ŠœŽ›ȼœȱŽ›ŽŽȱ’—ȱ–ŠŽ›’Š•œȱœŒ’Ž—ŒŽȱ›˜–ȱ‘ŽȱœŠ–Žȱ’—œ’ž’˜—ǯȱ ’œȱ˜Œ˜›Š•ȱŽ›ŽŽȱ’œȱ›˜–ȱ‘Žȱ Š’˜—Š•ȱ˜•¢ŽŒ‘—’Œȱ —œ’žŽǰȱŒ˜—Ž››Žȱ‹¢ȱ‘Žȱ ›ŠžŠŽȱ›˜›Š–ȱ’—ȱŸŠ—ŒŽȱŽŒ‘—˜•˜’Žœǰȱ Ȭ ǰȱžŽ›·Š›˜ȱ Section. At present he is an associate professor at the Technological University in San Juan del Río, in the state of Querétaro.. Žȱ‘Šœȱ™ž‹•’œ‘Žȱ˜ž›ȱŠ›’Œ•Žœȱ’—ȱœ›’Œ•¢ȱ›ŽŽ›ŽŽȱ“˜ž›—Š•œǯȱ ’œȱ›ŽœŽŠ›Œ‘ȱ ˜›”ȱ‘ŠœȱŒŽ—Ž›Žȱ˜—ȱ–Ž‘˜œȱ˜ȱ‘¢›˜Ž—ȱ™›˜žŒ’˜—ǰȱ›Ž›’Ž›Š’˜—ȱœ¢œŽ–œǰȱȱŽ•Ž–Ž—ȱꗒŽǰȱ–ŽŒ‘Š—’Œȱ̘ ȱŠ—ȱ‘ŽŠȱ›Š—œŽ›ǯ –Š›ȱ

(40) ’–·—Ž£ȬŠ—˜ŸŠ•ǯȱŽ›ŽŽȱ’—ȱŒ‘Ž–’œ›¢ǰȱŠŒž•¢ȱ˜ȱ‘Ž–’œ›¢ǰȱŠ’˜—Š•ȱž˜—˜–˜žœȱ—’ŸŽ›œ’¢ȱ˜ȱŽ¡’Œ˜ǰȱžžœȱŗşşŘǯȱ. ˜—˜›Š‹•Žȱ–Ž—’˜—ǯȱ‘ȱ’—ȱŒ‘Ž–’œ›¢ȱǻ’—˜›Š—’ŒȱŒ‘Ž–’œ›¢ǼǰȱŠŒž•¢ȱ˜ȱ‘Ž–’œ›¢ǰȱŠ’˜—Š•ȱž˜—˜–˜žœȱ—’ŸŽ›œ’¢ȱ˜ȱ Ž¡’Œ˜ǰȱŽ™Ž–‹Ž›ȱŗşşŝǯȱŽœŽŠ›Œ‘ȱœŠ¢ǰȱŽ™Š›–Ž—ȱ˜ȱ‘Ž–’œ›¢ȱŠ—ȱ’˜Œ‘Ž–’œ›¢ǰȱ—’ŸŽ›œ’¢ȱ˜ȱŽ¡ŠœȱŠȱžœ’—ǰȱǰȱ Ž™Ž–‹Ž›ȬŽŒŽ–‹Ž›ȱŗşşśǯȱŽœŽŠ›Œ‘ȱŠ›ŽŠœDZȱŽœ’—ǰȱœ¢—‘Žœ’œȱŠ—ȱœ›žŒž›Š•ȱŒ‘Š›ŠŒŽ›’£Š’˜—ȱ˜ȱ—Ž ȱŽ•ŽŒ›˜ŒŠŠ•¢œœ˜›ȱžŽ•ȱ ŒŽ••ȱ™˜•¢–Ž›ȱŽ•ŽŒ›˜•¢Žȱ–Ž–‹›Š—Žǯȱ‹Š’—’—ȱ˜ȱ–ŽŠ•ȱ˜¡’Žœȱ‹¢ȱ‘Žȱœ˜•ȬŽ•ȱŽŒ‘—’šžŽȱŠ—ȱ‘Ž’›ȱœ›žŒž›Š•ȱŒ‘Š›ŠŒŽ›’£Š’˜—ǰȱ ˜™’ŒŠ•ȱŠ—ȱ–˜›™‘˜•˜’ŒŠ•ȱŒ‘Š›ŠŒŽ›’œ’Œœȱ˜›ȱŸŠ›’˜žœȱŠ™™•’ŒŠ’˜—œǯȱ›Ž™Š›Š’˜—ȱŠ—ȱŒ‘Š›ŠŒŽ›’£Š’˜—ȱ˜ȱ‘’—ȱꕖœȱ˜ȱŸŠ›’˜žœȱ –ŠŽ›’Š•œȱ‹¢ȱȱœ™žĴŽ›’—ȱŽŒ‘—’šžŽȱ˜›ȱŠ™™•’ŒŠ’˜—ȱ’—ȱ˜™˜Ž•ŽŒ›˜—’ŒȱŽŸ’ŒŽœǯ Š›Œ˜ȱ—˜—’˜ȱ Š–˜›ŠȬ—žÛŠ—˜ǯȱ Žȱ ‘˜•œȱ Šȱ –ŠœŽ›ȱ ’—ȱ ŽžŒŠ’˜—Š•ȱ œŒ’Ž—ŒŽœǯȱ Žȱ ’œȱ ™›˜Žœœ˜›ȱ Š—ȱ ž••Ȭ’–Žȱ ›ŽœŽŠ›Œ‘Ž›ȱ Šȱ ‘Žȱ ŽŒ‘—˜•˜’ŒŠ•ȱ—’ŸŽ›œ’¢ȱ˜ȱŠ—ȱ

(41) žŠ—ȱŽ•ȱ’˜ȱ’—ȱŽ¡’Œ˜ǯȱ ȱ’œȱŠ•œ˜ȱŠȱ™›˜Žœœ˜›ȱ˜ȱ›ŠžŠŽȱœž’ŽœȱŠȱ‘Žȱ—’ŸŽ›œ’ŠȱŽ•ȱ Š••ŽȱŽȱŽ¡’Œ˜ǯȱ Žȱ Šœȱ™›Žœ’Ž—ȱ˜ȱ‘ŽȱŒŠŽ–¢ȱ˜ȱ ›ŠžŠŽȱž’ŽœȱŠȱ‘Žȱ—’ŸŽ›œ’ŠȱŽ•ȱŠ••ŽȱŽȱŽ¡’Œ˜ǯȱ Žȱ‘Šœȱ˜ŸŽ›ȱ ŗŖȱ¢ŽŠ›œȱŽ¡™Ž›’Ž—ŒŽȱ’—ȱŽŠŒ‘’—ǯȱ Žȱ’œȱŒ‘Š’›–Š—ȱ˜ȱŠŒž•¢ȱ˜ȱŠ—ŠŽ–Ž—ȱ¢œŽ–œȱžŠ•’¢ǯȱ ’œȱ–Š’—ȱ›ŽœŽŠ›Œ‘ȱ’—Ž›ŽœœȱŠ›Žȱ ‘ŽȱšžŠ•’¢ȱ˜ȱŽžŒŠ’˜—ȱŠ—ȱŽŸŠ•žŠ’˜—ǰȱŠ—ȱŽŸŽ•˜™–Ž—ȱ˜ȱšžŠ•’¢ȱœ¢œŽ–œǯ ›–Š—˜ȱ—Œ’—ŠœȬ›˜™ŽœŠǯȱ Žȱ˜‹Š’—Žȱ‘’œȱ‹ŠŒ‘Ž•˜›ȼœȱŽ›ŽŽȱ’—ȱ™‘¢œ’ŒœȱŠȱ‘Žȱ—’ŸŽ›œ’¢ȱ˜ȱ˜—˜›ŠȱǻŞŞȬşŘǼǯȱŠœŽ›ȱ˜ȱœŒ’Ž—ŒŽȱ ǻ™‘¢œ’ŒœǼȱŠȱ‘Žȱ —œ’žŽȱ˜ȱ‘¢œ’Œœǰȱ—’ŸŽ›œ’¢ȱ˜ȱŠ—ȱž’œȱ˜˜œ’ȱǻşřȬşśǼǯȱ˜Œ˜›Š•ȱœž’Žœȱ’—ȱ–ŠŽ›’Š•œȱœŒ’Ž—ŒŽȱ Ž›Žȱ™Ž›˜›–ŽȱŠȱ‘Žȱ—’ŸŽ›œ’¢ȱ˜ȱŠ›’œȱžǰȱ›œŠ¢ǰȱ›Š—ŒŽȱǻşśȬşşǼǯȱž‹œŽšžŽ—•¢ȱřȬ¢ŽŠ›ȱ™˜œ˜Œ˜›Š•ȱŽ••˜ œ‘’™ȱŠȱ‘ŽȱŽ™Š›–Ž—ȱ˜ȱ‘¢œ’ŒŠ•ȱ‘Ž–’œ›¢ȱŠ—ȱ‘¢œ’Œœȱ˜ȱŠŽ›’Š•œȱŠȱ‘ŽȱŠ‘˜•’Œȱ—’ŸŽ›œ’¢ȱ˜ȱŽžŸŽ—ȱ’—ȱŽ•’ž–ȱǻşşȬŖŘǼǯȱŽœŽŠ›Œ‘ȱ ™›˜Žœœ˜›ȱŠȱ‘Žȱ —œ’žŽȱ˜ȱ‘¢œ’Œœǰȱ—’ŸŽ›œ’¢ȱ˜ȱŠ—ȱž’œȱ˜˜œ’ȱ’—ȱŘŖŖŘǯȱ‘Žȱ›ŽœŽŠ›Œ‘ȱŒ˜—žŒŽȱ’œȱŠ’–ŽȱŠȱ–Š—žŠŒž›ing 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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