{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/115610"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/115610","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Modified nodal integral method for non-linear coupled neutronics-heat conduction problems and exact solutions based on method of manufactured solutions","abstract":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01","abstract_html":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01","abstract_has_math":false,"creators":["Hegazy, Aya Hamdy"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Nuclear, Plasma, Radiolgc Engr","degree_department":null,"school":null,"contributors":["Uddin, Rizwan","Kozlowski, Tomasz"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-05","date_published":"2022-05","updated_at":"2026-07-22T22:24:54Z","subjects":["NIM","MMS"],"languages":["en","eng"],"rights":["© 2022 Aya Hamdy Hegazy"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/115610","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Uddin, Rizwan","Kozlowski, Tomasz"]},{"key":"dc:creator","label":"Author","values":["Hegazy, Aya Hamdy"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-05","2022-04-27"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Nuclear, Plasma, Radiolgc Engr"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["NIM","MMS"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["© 2022 Aya Hamdy Hegazy"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/115610"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01","The student, Aya Hegazy, accepted the attached license on 2022-04-25 at 12:54.","The student, Aya Hegazy, submitted this Thesis for approval on 2022-04-25 at 13:04.","This Thesis was approved for publication on 2022-04-27 at 11:36.","DSpace SAF Submission Ingestion Package generated from Vireo submission #17951 on 2022-11-11 at 12:12:05","To improve fidelity of nuclear reactor design and safety analyses, the multi-physics neutronics and thermalhydraulics should be solved as a coupled problem. However, coupled, non-linear problems are slow to converge and computationally expensive as they require fine mesh, if solved using conventional schemes. Another challenge is in the verification of any numerical scheme developed to solve highly non-linear problems. Both of these challenges have been addressed in this thesis. Nodal Integral Method (NIM) is a coarse-mesh method. Hence, NIM can achieve the same accuracy as many conventional numerical methods using coarser meshes and less CPU times. Method of Manufactured Solutions (MMS) is used to provide exact analytical solutions for code verification. A nodal integral method (NIM) is developed in this thesis to solve coupled neutron diffusion and heat conduction problems with temperature-dependent thermal conductivity, neutron diffusion coefficient, and cross-sections. A modified nodal integral approach is used for the one-dimensional geometries while ordinary nodal integral scheme is developed for higher dimensions. Method of manufactured solutions is used to provide exact solutions to verify the nodal integral method schemes. Numerical scheme is developed for 1D, 2D, and 3D problems. Numerical results are reported for two problems in 1D, two problems in 2D, and two problems in 3D. Results from the nodal integral method are compared to the exact manufactured solutions and the Root Mean Square (RMS) errors are reported, as well as, the CPU times, and the number of iterations needed to achieve the desired convergence criteria. The spatial order of accuracy of the nodal integral scheme for one-dimensional and multi-dimensional problems is calculated using the RMS errors. In all cases, the schemes are second or near-second order accurate."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Modified nodal integral method for non-linear coupled neutronics-heat conduction problems and exact solutions based on method of manufactured solutions"]}]}],"canonical_facts":{"dc:contributor":["Uddin, Rizwan","Kozlowski, Tomasz"],"dc:creator":["Hegazy, Aya Hamdy"],"dc:date":["2022-05","2022-04-27"],"dc:description":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01","The student, Aya Hegazy, accepted the attached license on 2022-04-25 at 12:54.","The student, Aya Hegazy, submitted this Thesis for approval on 2022-04-25 at 13:04.","This Thesis was approved for publication on 2022-04-27 at 11:36.","DSpace SAF Submission Ingestion Package generated from Vireo submission #17951 on 2022-11-11 at 12:12:05","To improve fidelity of nuclear reactor design and safety analyses, the multi-physics neutronics and thermalhydraulics should be solved as a coupled problem. However, coupled, non-linear problems are slow to converge and computationally expensive as they require fine mesh, if solved using conventional schemes. Another challenge is in the verification of any numerical scheme developed to solve highly non-linear problems. Both of these challenges have been addressed in this thesis. Nodal Integral Method (NIM) is a coarse-mesh method. Hence, NIM can achieve the same accuracy as many conventional numerical methods using coarser meshes and less CPU times. Method of Manufactured Solutions (MMS) is used to provide exact analytical solutions for code verification. A nodal integral method (NIM) is developed in this thesis to solve coupled neutron diffusion and heat conduction problems with temperature-dependent thermal conductivity, neutron diffusion coefficient, and cross-sections. A modified nodal integral approach is used for the one-dimensional geometries while ordinary nodal integral scheme is developed for higher dimensions. Method of manufactured solutions is used to provide exact solutions to verify the nodal integral method schemes. Numerical scheme is developed for 1D, 2D, and 3D problems. Numerical results are reported for two problems in 1D, two problems in 2D, and two problems in 3D. Results from the nodal integral method are compared to the exact manufactured solutions and the Root Mean Square (RMS) errors are reported, as well as, the CPU times, and the number of iterations needed to achieve the desired convergence criteria. The spatial order of accuracy of the nodal integral scheme for one-dimensional and multi-dimensional problems is calculated using the RMS errors. In all cases, the schemes are second or near-second order accurate."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/115610"],"dc:language":["en","eng"],"dc:rights":["© 2022 Aya Hamdy Hegazy"],"dc:subject":["NIM","MMS"],"dc:title":["Modified nodal integral method for non-linear coupled neutronics-heat conduction problems and exact solutions based on method of manufactured solutions"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Nuclear, Plasma, Radiolgc Engr"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:54Z"}