{"id":"W2006468123","doi":"10.1115/ht2009-88640","title":"Exact Solution of Two-Dimensional Hyperbolic Heat Conduction Equation With Combined Boundary Conditions and Arbitrary Initial Conditions","year":2009,"lang":"en","type":"article","venue":"Volume 1: Heat Transfer in Energy Systems; Thermophysical Properties; Heat Transfer Equipment; Heat Transfer in Electronic Equipment","topic":"Numerical methods in inverse problems","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University","funders":"","keywords":"Thermal conduction; Heat equation; Relativistic heat conduction; Heat kernel; Mathematical analysis; Boundary value problem; Hyperbolic partial differential equation; Mathematics; Boundary (topology); Fourier transform; Partial differential equation; FTCS scheme; Exact solutions in general relativity; Heat transfer; Mechanics; Physics; Differential equation; Thermodynamics; Heat flux","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004024975,0.0004136149,0.0006524266,0.0003223695,0.0002574496,0.0006551591,0.000610457,0.001027481,0.001552126],"category_scores_gemma":[0.001058972,0.0002492815,0.0005581947,0.0003024037,0.0008975912,0.001065245,0.001028718,0.0007813913,0.0003141246],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002595514,"about_ca_system_score_gemma":0.0006090649,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000705801,"about_ca_topic_score_gemma":0.0004985827,"domain_scores_codex":[0.9997333,0.00007303511,0.00001902239,0.00003663851,0.0001111827,0.00002680014],"domain_scores_gemma":[0.9997599,0.00009906785,0.00002702299,0.00003746468,0.00006442216,0.00001206722],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00009883084,0.0000951194,0.001300676,0.0006563239,0.00005231311,0.0008636793,0.0004488987,0.5828363,0.06028129,0.286311,0.002164253,0.06489135],"study_design_scores_gemma":[0.00002377613,0.00002949273,0.0001689636,0.00001837024,0.000006977919,0.0001797331,0.00003886615,0.9688812,0.006206983,0.02267688,0.001756299,0.00001238716],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04122575,0.0006126722,0.9451823,0.0002003565,0.0001041371,0.00005515186,0.00006616551,0.00008875895,0.01246478],"genre_scores_gemma":[0.7255199,0.00109864,0.2559124,0.00009391546,0.0001342218,0.0002033618,0.0001474553,0.00006456052,0.01682562],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.001552126,"threshold_uncertainty_score":0.005192399,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04572825122484327,"score_gpt":0.2875446757325028,"score_spread":0.2418164245076596,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}