{"id":"https://openalex.org/W4404635784","doi":"https://doi.org/10.1016/j.jfoodeng.2024.112409","title":"Development of an analytical solution to diffusion equation for multidimensional solids of arbitrary shape","display_name":"Development of an analytical solution to diffusion equation for multidimensional solids of arbitrary shape","publication_year":2024,"publication_date":"2024-11-22","ids":{"openalex":"https://openalex.org/W4404635784","doi":"https://doi.org/10.1016/j.jfoodeng.2024.112409"},"language":"en","primary_location":{"id":"doi:10.1016/j.jfoodeng.2024.112409","doi":"https://doi.org/10.1016/j.jfoodeng.2024.112409","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jfoodeng.2024.112409","pdf_url":null,"source":{"id":"https://openalex.org/S137362610","display_name":"Journal of Food Engineering","issn_l":"0260-8774","issn":["0260-8774","1873-5770"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","ki-jl-1","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Food Engineering","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.jfoodeng.2024.112409","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091361119","display_name":"K.H. Est\u00e9vez-S\u00e1nchez","orcid":"https://orcid.org/0000-0001-5539-5466","observed_orcids":["https://orcid.org/0000-0001-5539-5466"]},"institutions":[{"id":"https://openalex.org/I721619","display_name":"Benem\u00e9rita Universidad Aut\u00f3noma de Puebla","ror":"https://ror.org/03p2z7827","country_code":"MX","type":"education","lineage":["https://openalex.org/I721619"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"K.H. Est\u00e9vez-S\u00e1nchez","raw_affiliation_strings":["Facultad de Ciencias de la Electr\u00f3nica, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla, Av. San Claudio y 18 Sur, Ciudad Universitaria, C.P. 72570, Puebla, Puebla, Mexico"],"raw_orcid":"https://orcid.org/0000-0001-5539-5466","affiliations":[{"raw_affiliation_string":"Facultad de Ciencias de la Electr\u00f3nica, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla, Av. San Claudio y 18 Sur, Ciudad Universitaria, C.P. 72570, Puebla, Puebla, Mexico","institution_ids":["https://openalex.org/I721619"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086931538","display_name":"Francisco M. Pacheco-Aguirre","orcid":"https://orcid.org/0000-0001-9266-8216","observed_orcids":["https://orcid.org/0000-0001-9266-8216"]},"institutions":[{"id":"https://openalex.org/I721619","display_name":"Benem\u00e9rita Universidad Aut\u00f3noma de Puebla","ror":"https://ror.org/03p2z7827","country_code":"MX","type":"education","lineage":["https://openalex.org/I721619"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"F.M. Pacheco-Aguirre","raw_affiliation_strings":["Facultad de Ingenier\u00eda Qu\u00edmica, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla, Av. San Claudio y 18 Sur, Ciudad Universitaria, C.P. 72570, Puebla, Puebla, Mexico"],"raw_orcid":"https://orcid.org/0000-0001-9266-8216","affiliations":[{"raw_affiliation_string":"Facultad de Ingenier\u00eda Qu\u00edmica, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla, Av. San Claudio y 18 Sur, Ciudad Universitaria, C.P. 72570, Puebla, Puebla, Mexico","institution_ids":["https://openalex.org/I721619"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050677640","display_name":"Hector Ruiz-Espinosa","orcid":"https://orcid.org/0000-0001-5592-4436","observed_orcids":["https://orcid.org/0000-0001-5592-4436"]},"institutions":[{"id":"https://openalex.org/I721619","display_name":"Benem\u00e9rita Universidad Aut\u00f3noma de Puebla","ror":"https://ror.org/03p2z7827","country_code":"MX","type":"education","lineage":["https://openalex.org/I721619"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"H. Ruiz-Espinosa","raw_affiliation_strings":["Facultad de Ingenier\u00eda Qu\u00edmica, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla, Av. San Claudio y 18 Sur, Ciudad Universitaria, C.P. 72570, Puebla, Puebla, Mexico"],"raw_orcid":"https://orcid.org/0000-0001-5592-4436","affiliations":[{"raw_affiliation_string":"Facultad de Ingenier\u00eda Qu\u00edmica, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla, Av. San Claudio y 18 Sur, Ciudad Universitaria, C.P. 72570, Puebla, Puebla, Mexico","institution_ids":["https://openalex.org/I721619"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030822343","display_name":"Miguel \u00c1ngel Garc\u00eda-Alvarado","orcid":"https://orcid.org/0000-0002-4921-411X","observed_orcids":["https://orcid.org/0000-0002-4921-411X"]},"institutions":[{"id":"https://openalex.org/I4210146858","display_name":"Instituto Tecnol\u00f3gico de Veracruz","ror":"https://ror.org/05gwc3q21","country_code":"MX","type":"education","lineage":["https://openalex.org/I1302736544","https://openalex.org/I4210090124","https://openalex.org/I4210146858","https://openalex.org/I4405258672"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"M.A. Garc\u00eda-Alvarado","raw_affiliation_strings":["Departamento de Ingenier\u00eda Qu\u00edmica y Bioqu\u00edmica, Tecnol\u00f3gico Nacional de M\u00e9xico Campus Veracruz, Av. M.A. de Quevedo S/N, C.P. 91860, Veracruz, Veracruz, Mexico"],"raw_orcid":"https://orcid.org/0000-0002-4921-411X","affiliations":[{"raw_affiliation_string":"Departamento de Ingenier\u00eda Qu\u00edmica y Bioqu\u00edmica, Tecnol\u00f3gico Nacional de M\u00e9xico Campus Veracruz, Av. M.A. de Quevedo S/N, C.P. 91860, Veracruz, Veracruz, Mexico","institution_ids":["https://openalex.org/I4210146858"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050052328","display_name":"Orlenda Cort\u00e9s-Zavaleta","orcid":"https://orcid.org/0000-0002-0236-0486","observed_orcids":["https://orcid.org/0000-0002-0236-0486"]},"institutions":[{"id":"https://openalex.org/I721619","display_name":"Benem\u00e9rita Universidad Aut\u00f3noma de Puebla","ror":"https://ror.org/03p2z7827","country_code":"MX","type":"education","lineage":["https://openalex.org/I721619"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"O. Cort\u00e9s-Zavaleta","raw_affiliation_strings":["Facultad de Ciencias Biol\u00f3gicas, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla, Av. San Claudio y 18 Sur, Ciudad Universitaria, C.P. 72570, Puebla, Puebla, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Facultad de Ciencias Biol\u00f3gicas, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla, Av. San Claudio y 18 Sur, Ciudad Universitaria, C.P. 72570, Puebla, Puebla, Mexico","institution_ids":["https://openalex.org/I721619"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027596591","display_name":"Carlos Enrique Ochoa\u2010Velasco","orcid":"https://orcid.org/0000-0002-9624-6616","observed_orcids":["https://orcid.org/0000-0002-9624-6616"]},"institutions":[{"id":"https://openalex.org/I721619","display_name":"Benem\u00e9rita Universidad Aut\u00f3noma de Puebla","ror":"https://ror.org/03p2z7827","country_code":"MX","type":"education","lineage":["https://openalex.org/I721619"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"C.E. Ochoa-Velasco","raw_affiliation_strings":["Facultad de Ciencias Qu\u00edmicas, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla, Av. San Claudio y 18 Sur, Ciudad Universitaria, C.P. 72570, Puebla, Puebla, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Facultad de Ciencias Qu\u00edmicas, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla, Av. San Claudio y 18 Sur, Ciudad Universitaria, C.P. 72570, Puebla, Puebla, Mexico","institution_ids":["https://openalex.org/I721619"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079564210","display_name":"I.I. Ruiz-L\u00f3pez","orcid":"https://orcid.org/0000-0002-6592-6838","observed_orcids":["https://orcid.org/0000-0002-6592-6838"]},"institutions":[{"id":"https://openalex.org/I721619","display_name":"Benem\u00e9rita Universidad Aut\u00f3noma de Puebla","ror":"https://ror.org/03p2z7827","country_code":"MX","type":"education","lineage":["https://openalex.org/I721619"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"I.I. Ruiz-L\u00f3pez","raw_affiliation_strings":["Facultad de Ingenier\u00eda Qu\u00edmica, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla, Av. San Claudio y 18 Sur, Ciudad Universitaria, C.P. 72570, Puebla, Puebla, Mexico"],"raw_orcid":"https://orcid.org/0000-0002-6592-6838","affiliations":[{"raw_affiliation_string":"Facultad de Ingenier\u00eda Qu\u00edmica, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla, Av. San Claudio y 18 Sur, Ciudad Universitaria, C.P. 72570, Puebla, Puebla, Mexico","institution_ids":["https://openalex.org/I721619"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079564210"],"corresponding_institution_ids":["https://openalex.org/I721619"],"apc_list":{"value":4220,"currency":"USD","value_usd":4220},"apc_paid":{"value":4220,"currency":"USD","value_usd":4220},"fwci":0.389,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.63793479,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"390","issue":null,"first_page":"112409","last_page":"112409"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10650","display_name":"Food Drying and Modeling","score":0.9711999893188477,"subfield":{"id":"https://openalex.org/subfields/1106","display_name":"Food Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10650","display_name":"Food Drying and Modeling","score":0.9711999893188477,"subfield":{"id":"https://openalex.org/subfields/1106","display_name":"Food Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T13116","display_name":"Heat Transfer and Numerical Methods","score":0.021400000900030136,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12063","display_name":"Heat and Mass Transfer in Porous Media","score":0.005200000014156103,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mass-diffusion","display_name":"mass diffusion","score":0.5830000042915344},{"id":"https://openalex.org/keywords/caffeine-extraction","display_name":"caffeine extraction","score":0.6690000295639038},{"id":"https://openalex.org/keywords/green-coffee","display_name":"green coffee beans","score":0.9440000057220459},{"id":"https://openalex.org/keywords/inverse-problems","display_name":"inverse problems","score":0.6620000004768372}],"concepts":[{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5851238369941711},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.5471925735473633},{"id":"https://openalex.org/C71104824","wikidata":"https://www.wikidata.org/wiki/Q1476639","display_name":"Structural equation modeling","level":2,"score":0.48654523491859436},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.354367196559906},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3534659147262573},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33061471581459045},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32302212715148926},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.3085140585899353},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.25688862800598145},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24690696597099304},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20519527792930603},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.1208600103855133},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.jfoodeng.2024.112409","doi":"https://doi.org/10.1016/j.jfoodeng.2024.112409","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jfoodeng.2024.112409","pdf_url":null,"source":{"id":"https://openalex.org/S137362610","display_name":"Journal of Food Engineering","issn_l":"0260-8774","issn":["0260-8774","1873-5770"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","ki-jl-1","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Food Engineering","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/j.jfoodeng.2024.112409","doi":"https://doi.org/10.1016/j.jfoodeng.2024.112409","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jfoodeng.2024.112409","pdf_url":null,"source":{"id":"https://openalex.org/S137362610","display_name":"Journal of Food Engineering","issn_l":"0260-8774","issn":["0260-8774","1873-5770"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","ki-jl-1","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Food Engineering","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.40450000762939453,"id":"https://metadata.un.org/sdg/2","display_name":"Zero hunger"}],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G778855985","display_name":null,"funder_award_id":"CF19-194782","funder_id":"https://openalex.org/F4320321739","funder_display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda"}],"funders":[{"id":"https://openalex.org/F4320321739","display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","ror":"https://ror.org/059ex5q34"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1968349037","https://openalex.org/W1979116428","https://openalex.org/W2008654730","https://openalex.org/W2013821309","https://openalex.org/W2066032897","https://openalex.org/W2082689208","https://openalex.org/W2090385590","https://openalex.org/W2095158887","https://openalex.org/W2098337247","https://openalex.org/W2233916553","https://openalex.org/W2490308617","https://openalex.org/W2605150486","https://openalex.org/W2889180167","https://openalex.org/W2901343497","https://openalex.org/W2937045139","https://openalex.org/W2980797044","https://openalex.org/W3008597976","https://openalex.org/W3049621789","https://openalex.org/W3118642978","https://openalex.org/W3135815248","https://openalex.org/W4283015304","https://openalex.org/W4283326028","https://openalex.org/W4321766143","https://openalex.org/W4387540095","https://openalex.org/W4389238157","https://openalex.org/W4391102787","https://openalex.org/W4391611443","https://openalex.org/W4391617179","https://openalex.org/W4396696547","https://openalex.org/W4397043467","https://openalex.org/W6676589310","https://openalex.org/W6761170823"],"related_works":["https://openalex.org/W2024934382","https://openalex.org/W2303173273","https://openalex.org/W2513767888","https://openalex.org/W3147308590","https://openalex.org/W1528049813","https://openalex.org/W1968285868","https://openalex.org/W2364043478","https://openalex.org/W1734603769","https://openalex.org/W2922935260","https://openalex.org/W1592131421"],"abstract_inverted_index":{"Mass":[0,186,244],"transfer":[1,179,222,239,245],"processes":[2],"between":[3,99],"solids":[4,67,249],"and":[5,14,102,152,193,233,278],"fluids":[6],"are":[7,32],"ubiquitous":[8],"in":[9,65,190,196,240,248],"the":[10,61,76,82,85,100,106,112,123,129,140,171,176,182,200,219,225,272,284,291],"food":[11,50,273],"engineering":[12],"field":[13],"using":[15,158,181],"simple":[16,40,57,232],"analytical":[17,86],"models":[18],"for":[19,35,139,188,194],"their":[20],"simulation":[21],"or":[22,78],"estimation":[23,141,293],"of":[24,39,68,81,88,115,128,142,148,175,250,261,294],"mass":[25,178,221,238,295],"diffusivities":[26,187],"remains":[27],"widespread.":[28],"Unfortunately,":[29],"these":[30],"solutions":[31],"available":[33,160],"only":[34],"a":[36,56,89,95,231,262],"limited":[37],"number":[38],"solid":[41],"geometries":[42],"which":[43],"might":[44],"not":[45,205],"be":[46],"applicable":[47],"to":[48,59,110,213,236],"all":[49],"shapes;":[51],"thus,":[52],"this":[53],"study":[54],"introduces":[55],"method":[58,74,107,229],"obtain":[60],"volume":[62],"average":[63],"concentration":[64],"multidimensional":[66],"arbitrary":[69,251],"shape":[70,252],"(SAS).":[71,253],"The":[72,126,163],"proposed":[73],"approximates":[75],"(analytical":[77],"numerical)":[79],"solution":[80,87,174,256,269],"SAS":[83,255],"from":[84,161],"properly":[90,263],"sized":[91,264],"box":[92,103,131,202,268,285],"by":[93,135,170,216,259],"minimizing":[94],"weighted":[96],"similitude":[97],"index":[98],"original":[101],"shapes.":[104],"Besides,":[105],"was":[108,133,246,257],"generalized":[109],"consider":[111,271],"isotropic":[113],"shrinkage":[114],"foods":[116],"(that":[117],"is,":[118],"size":[119],"reduction":[120],"while":[121],"maintaining":[122],"aspect":[124],"ratio).":[125],"applicability":[127],"equivalent":[130,201],"approach":[132,203,289],"exemplified":[134],"solving":[136,218],"inverse":[137],"problems":[138],"caffeine":[143,189],"diffusivity":[144,154],"during":[145,155],"aqueous":[146],"extraction":[147,277],"green":[149,191],"coffee":[150,192],"beans":[151],"water":[153,195],"lentil":[156,279],"drying":[157,280],"data":[159],"literature.":[162],"results":[164],"were":[165,204,281],"compared":[166],"with":[167,199,283],"those":[168,214],"obtained":[169],"finite":[172],"element":[173],"3D":[177,220],"model":[180,223,237],"real":[183],"product":[184],"shape.":[185],"lentils":[197],"estimated":[198,215,282],"statistically":[206],"different":[207],"(":[208],"p":[209],">":[210],"0.05":[211],")":[212],"numerically":[217],"under":[224],"same":[226],"assumptions.":[227],"This":[228],"represents":[230],"reliable":[234],"way":[235],"complex-shaped":[241],"foods.":[242],"\u2022":[243,254,266,275,287],"investigated":[247],"approximated":[258],"that":[260],"box.":[265],"Analytical":[267],"can":[270],"shrinkage.":[274],"Caffeine":[276],"model.":[286],"Box":[288],"allowed":[290],"accurate":[292],"diffusivities.":[296]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}
