Thermal Conductivity of Low Density Polyethylene Foams Part I: Comprehensive Study of Theoretical Models
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摘要
Polymeric foams are one of the most applicable thermal-insulation materials due to their low thermal conductivity, high mechanical properties, and low cost. Optimization of thermal-insulation performance of polymeric foams needs a theoretical model in order to predict the overall thermal conductivity. So far, several theoretical approaches are presented in this regard but to the best knowledge of the authors, there is no comprehensive investigation on comparing the proposed models. Therefore, the study of validity of the theoretical models in comparison with the experimental results is one of the main goals of the present study. Low density polyethylene(LDPE) foams are selected as the case study due to the wide application range. Different models to predict the overall conductivity of the foam based on conduction through the combined gas and solid phases(λ_(gs)) as well as radiation thermal conductivity(λ_r) are presented. The results indicate that the best model is a model in which λ_(gs) is calculated using Gibson and Ashby model and λ_r is obtained using Williams and Aldao model based on the root mean square(RMS) parameter. The results show that the theoretical error of this model is smaller than 10%.
Polymeric foams are one of the most applicable thermal-insulation materials due to their low thermal conductivity, high mechanical properties, and low cost. Optimization of thermal-insulation performance of polymeric foams needs a theoretical model in order to predict the overall thermal conductivity. So far, several theoretical approaches are presented in this regard but to the best knowledge of the authors, there is no comprehensive investigation on comparing the proposed models. Therefore, the study of validity of the theoretical models in comparison with the experimental results is one of the main goals of the present study. Low density polyethylene(LDPE) foams are selected as the case study due to the wide application range. Different models to predict the overall conductivity of the foam based on conduction through the combined gas and solid phases(λ_(gs)) as well as radiation thermal conductivity(λ_r) are presented. The results indicate that the best model is a model in which λ_(gs) is calculated using Gibson and Ashby model and λ_r is obtained using Williams and Aldao model based on the root mean square(RMS) parameter. The results show that the theoretical error of this model is smaller than 10%.
Polymeric foams are one of the most applicable thermal-insulation materials due to their low thermal conductivity, high mechanical properties, and low cost. Optimization of thermal-insulation performance of polymeric foams needs a theoretical model in order to predict the overall thermal conductivity. So far, several theoretical approaches are presented in this regard but to the best knowledge of the authors, there is no comprehensive investigation on comparing the proposed models. Therefore, the study of validity of the theoretical models in comparison with the experimental results is one of the main goals of the present study. Low density polyethylene(LDPE) foams are selected as the case study due to the wide application range. Different models to predict the overall conductivity of the foam based on conduction through the combined gas and solid phases(λ_(gs)) as well as radiation thermal conductivity(λ_r) are presented. The results indicate that the best model is a model in which λ_(gs) is calculated using Gibson and Ashby model and λ_r is obtained using Williams and Aldao model based on the root mean square(RMS) parameter. The results show that the theoretical error of this model is smaller than 10%.
引文
[1]Canadian Energy Overview 2014,National Energy Board,2014.
[2]Cuce E.,Cuce P.M.,Wood C.J.,Riffat,S.B.,Toward aerogel based thermal superinsulation in buildings:a comprehensive review.Renewable and Sustainable Energy Reviews,2014,34:273-299.
[3]Hasanzadeh R.,Azdast T.,Eungkee Lee R.,Afsari Ghazi,A.,Experimental polymeric nanocomposite material selection for automotive bumper beam using multicriteria decision making methods.Iranian Journal of Materials Science and Engineering,2017,14(3):1-10.
[4]Gao K.,van Dommelen J.A.W.,Geers M.G.D.,Investigation of the effects of the microstructure on the sound absorption performance of polymer foams using a computational homogenization approach.European Journal of Mechanics-A/Solids,2017,61:330-344.
[5]Gwon J.G.,Kim S.K.,Kim J.H.,Sound absorption behavior of flexible polyurethane foams with distinct cellular structures.Materials&Design,2016,89:448-454.
[6]Hasanzadeh R.,Azdast T.,Doniavi A.,Lee R.E.,Multi-objective optimization of heat transfer mechanisms of microcellular polymeric foams from thermal-insulation point of view.Thermal Science and Engineering Progress,2019,9:21-29.
[7]Wang G.,Zhao G.,Dong G.,Mu Y.,Park C.B.,Wang G.,Lightweight,super-elastic,and thermal-sound insulation bio-based PEBA foams fabricated by high-pressure foam injection molding with mold-opening.European Polymer Journal,2018,103:68-79.
[8]Wang G.,Zhao J.,Mark L.H.,Wang G.,Yu K.,Wang C.,Park C.B.,Zhao G.,Ultra-tough and super thermalinsulation nanocellular PMMA/TPU.Chemical Engineering Journal,2017,325:632-646.
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[10]Glicksman L.,Schuetz M.,Sinofsky M.,Radiation heat transfer in foam insulation.International Journal of Heat and Mass Transfer,1987,30(1):187-197.
[11]Campo-Arnáiz R.A.,Rodríguez‐Pérez M.A.,Calvo B.,De Saja J.A.,Extinction coefficient of polyolefin foams.Journal of Polymer Science Part B:Polymer Physics,2005,43(13):1608-1617.
[12]Alvarez-Lainez M.,Rodriguez‐Perez M.A.,De Saja J.A.,Thermal conductivity of open‐cell polyolefin foams.Journal of Polymer Science Part B:Polymer Physics,2008,46(2):212-221.
[13]Placido E.,Arduini-Schuster M.C.,Kuhn J.,Thermal properties predictive model for insulating foams.Infrared Physics&Technology,2005,46(3):219-231.
[14]Kaemmerlen A.,Vo C.,Asllanaj F.,Jeandel G.,Baillis D.,Radiative properties of extruded polystyrene foams:predictive model and experimental results.Journal of Quantitative Spectroscopy and Radiative Transfer,2010,111(6):865-877.
[15]Williams R.J.J.,Aldao C.M.,Thermal conductivity of plastic foams.Polymer Engineering&Science,1983,23(6):293-298.
[16]Almanza O.A.,Rodríguez‐Pérez M.A.,De Saja J.A.,Prediction of the radiation term in the thermal conductivity of crosslinked closed cell polyolefin foams.Journal of Polymer Science Part B:Polymer Physics,2000,38(7):993-1004.
[17]Wang G.,Wang C.,Zhao J.,Wang G.,Park C.B.,Zhao G.,Modelling of thermal transport through a nanocellular polymer foam:toward the generation of a new superinsulating material.Nanoscale,2017,9(18):5996-6009.
[18]Gong P.,Zhai S.,Lee R.,Zhao C.,Buahom P.,Li G.,Park C.B.,Environmentally friendly polylactic acid-based thermal insulation foams blown with supercritical CO2.Industrial&Engineering Chemistry Research,2018,57(15):5464-5471.
[19]Gong P.,Wang G.,Tran M.P.,Buahom P.,Zhai S.,Li G.,Park C.B.,Advanced bimodal polystyrene/multi-walled carbon nanotube nanocomposite foams for thermal insulation.Carbon,2017,120:1-10.
[20]Wang G.,Zhao J.,Wang G.,Mark L.H.,Park C.B.,Zhao G.,Low-density and structure-tunable microcellular PMMA foams with improved thermal-insulation and compressive mechanical properties.European Polymer Journal,2017,95:382-393.
[21]Ameli A.,Jahani D.,Nofar M.,Jung P.U.,Park C.B.,Development of high void fraction polylactide composite foams using injection molding:Mechanical and thermal insulation properties.Composites Science and Technology,2014,90:88-95.
[22]Lees C.H.,On the conductivities of certain heterogeneous media for a steady flux having a potential.The London,Edinburgh,and Dublin Philosophical Magazine and Journal of Science,1900,49(297):221-226.
[23]Russell H.W.,Principles of heat flow in porous insulators.Journal of the American Ceramic Society,1935,18(1-12):1-5.
[24]Doherty J.A.,Verma R.S.,Shrivastava S.,Saxena S.C.,Heat transfer from immersed horizontal tubes of different diameter in a gas-fluidized bed.Energy,1986,11(8):773-783.
[25]Collishaw P.G.,Evans J.R.G.,An assessment of expressions for the apparent thermal conductivity of cellular materials.Journal of Materials Science,1994,29(9):2261-2273.
[26]Ashby M.F.,Gibson L.J.,Cellular solids:structure and properties.Cambridge,UK:Press Syndicate of the University of Cambridge,1997.
[27]Reglero Ruiz J.A.,Saiz-Arroyo C.,Dumon M.,Rodríguez-Perez M.A.,Gonzalez L.,Production,cellular structure and thermal conductivity of microcellular(methyl methacrylate)-(butyl acrylate)-(methyl methacrylate)triblock copolymers.Polymer international,2011,60(1):146-152.
[28]Mojaver P.,Khalilarya S.,Chitsaz A.,Performance assessment of a combined heat and power system:Anovel integrated biomass gasification,solid oxide fuel cell and high-temperature sodium heat pipe system part I:Thermodynamic analysis.Energy Conversion and Management,2018,171:287-297.
[2]Cuce E.,Cuce P.M.,Wood C.J.,Riffat,S.B.,Toward aerogel based thermal superinsulation in buildings:a comprehensive review.Renewable and Sustainable Energy Reviews,2014,34:273-299.
[3]Hasanzadeh R.,Azdast T.,Eungkee Lee R.,Afsari Ghazi,A.,Experimental polymeric nanocomposite material selection for automotive bumper beam using multicriteria decision making methods.Iranian Journal of Materials Science and Engineering,2017,14(3):1-10.
[4]Gao K.,van Dommelen J.A.W.,Geers M.G.D.,Investigation of the effects of the microstructure on the sound absorption performance of polymer foams using a computational homogenization approach.European Journal of Mechanics-A/Solids,2017,61:330-344.
[5]Gwon J.G.,Kim S.K.,Kim J.H.,Sound absorption behavior of flexible polyurethane foams with distinct cellular structures.Materials&Design,2016,89:448-454.
[6]Hasanzadeh R.,Azdast T.,Doniavi A.,Lee R.E.,Multi-objective optimization of heat transfer mechanisms of microcellular polymeric foams from thermal-insulation point of view.Thermal Science and Engineering Progress,2019,9:21-29.
[7]Wang G.,Zhao G.,Dong G.,Mu Y.,Park C.B.,Wang G.,Lightweight,super-elastic,and thermal-sound insulation bio-based PEBA foams fabricated by high-pressure foam injection molding with mold-opening.European Polymer Journal,2018,103:68-79.
[8]Wang G.,Zhao J.,Mark L.H.,Wang G.,Yu K.,Wang C.,Park C.B.,Zhao G.,Ultra-tough and super thermalinsulation nanocellular PMMA/TPU.Chemical Engineering Journal,2017,325:632-646.
[9]Schuetz M.A.,Glicksman L.R.,A basic study of heat transfer through foam insulation.Journal of Cellular Plastics,1984,20(2):114-121.
[10]Glicksman L.,Schuetz M.,Sinofsky M.,Radiation heat transfer in foam insulation.International Journal of Heat and Mass Transfer,1987,30(1):187-197.
[11]Campo-Arnáiz R.A.,Rodríguez‐Pérez M.A.,Calvo B.,De Saja J.A.,Extinction coefficient of polyolefin foams.Journal of Polymer Science Part B:Polymer Physics,2005,43(13):1608-1617.
[12]Alvarez-Lainez M.,Rodriguez‐Perez M.A.,De Saja J.A.,Thermal conductivity of open‐cell polyolefin foams.Journal of Polymer Science Part B:Polymer Physics,2008,46(2):212-221.
[13]Placido E.,Arduini-Schuster M.C.,Kuhn J.,Thermal properties predictive model for insulating foams.Infrared Physics&Technology,2005,46(3):219-231.
[14]Kaemmerlen A.,Vo C.,Asllanaj F.,Jeandel G.,Baillis D.,Radiative properties of extruded polystyrene foams:predictive model and experimental results.Journal of Quantitative Spectroscopy and Radiative Transfer,2010,111(6):865-877.
[15]Williams R.J.J.,Aldao C.M.,Thermal conductivity of plastic foams.Polymer Engineering&Science,1983,23(6):293-298.
[16]Almanza O.A.,Rodríguez‐Pérez M.A.,De Saja J.A.,Prediction of the radiation term in the thermal conductivity of crosslinked closed cell polyolefin foams.Journal of Polymer Science Part B:Polymer Physics,2000,38(7):993-1004.
[17]Wang G.,Wang C.,Zhao J.,Wang G.,Park C.B.,Zhao G.,Modelling of thermal transport through a nanocellular polymer foam:toward the generation of a new superinsulating material.Nanoscale,2017,9(18):5996-6009.
[18]Gong P.,Zhai S.,Lee R.,Zhao C.,Buahom P.,Li G.,Park C.B.,Environmentally friendly polylactic acid-based thermal insulation foams blown with supercritical CO2.Industrial&Engineering Chemistry Research,2018,57(15):5464-5471.
[19]Gong P.,Wang G.,Tran M.P.,Buahom P.,Zhai S.,Li G.,Park C.B.,Advanced bimodal polystyrene/multi-walled carbon nanotube nanocomposite foams for thermal insulation.Carbon,2017,120:1-10.
[20]Wang G.,Zhao J.,Wang G.,Mark L.H.,Park C.B.,Zhao G.,Low-density and structure-tunable microcellular PMMA foams with improved thermal-insulation and compressive mechanical properties.European Polymer Journal,2017,95:382-393.
[21]Ameli A.,Jahani D.,Nofar M.,Jung P.U.,Park C.B.,Development of high void fraction polylactide composite foams using injection molding:Mechanical and thermal insulation properties.Composites Science and Technology,2014,90:88-95.
[22]Lees C.H.,On the conductivities of certain heterogeneous media for a steady flux having a potential.The London,Edinburgh,and Dublin Philosophical Magazine and Journal of Science,1900,49(297):221-226.
[23]Russell H.W.,Principles of heat flow in porous insulators.Journal of the American Ceramic Society,1935,18(1-12):1-5.
[24]Doherty J.A.,Verma R.S.,Shrivastava S.,Saxena S.C.,Heat transfer from immersed horizontal tubes of different diameter in a gas-fluidized bed.Energy,1986,11(8):773-783.
[25]Collishaw P.G.,Evans J.R.G.,An assessment of expressions for the apparent thermal conductivity of cellular materials.Journal of Materials Science,1994,29(9):2261-2273.
[26]Ashby M.F.,Gibson L.J.,Cellular solids:structure and properties.Cambridge,UK:Press Syndicate of the University of Cambridge,1997.
[27]Reglero Ruiz J.A.,Saiz-Arroyo C.,Dumon M.,Rodríguez-Perez M.A.,Gonzalez L.,Production,cellular structure and thermal conductivity of microcellular(methyl methacrylate)-(butyl acrylate)-(methyl methacrylate)triblock copolymers.Polymer international,2011,60(1):146-152.
[28]Mojaver P.,Khalilarya S.,Chitsaz A.,Performance assessment of a combined heat and power system:Anovel integrated biomass gasification,solid oxide fuel cell and high-temperature sodium heat pipe system part I:Thermodynamic analysis.Energy Conversion and Management,2018,171:287-297.