Journal of Heat Transfer · 1971 · 33 citations · 0 references
Numerical AnalysisEngineeringMechanical EngineeringComputational MechanicsConvective Heat TransferRefrigerationHeat Transfer ProcessTransient Heat ConductionNumerical SimulationSystematic ProceduresThermodynamicsThermal ModelingThermal ConductionBoundary Element MethodElectrical EngineeringEfficient Solution ProcessesThermal TransportHeat TransferFinite Element AnalysisFinite Element MethodThermal EngineeringMatrix Differential EquationMultiscale Modeling
Systematic procedures are presented for reducing the order of a matrix differential equation governing transient heat conduction in solids. Two principal aspects of this development are a condensation of the set of gridpoint temperature degrees of freedom using steady-state relations and the introduction of generalized (modal) temperature degrees of freedom to achieve a further reduction. These processes are illustrated in an elementary one-dimensional transient heat conduction problem.