[Heat conduction].

Heat conduction modelling ........................................................................................................................... 1 Case studies ........................................................................................................................................... 2 Analytical solutions....................................................................................................................................... 3 Conduction shape factor (steady state) ..................................................................................................... 3 Reduction to the main dimension (steady state) ....................................................................................... 5 Planar, cylindrical, and spherical energy sources, internal or interfacial ............................................. 6 Multilayer composite walls ................................................................................................................... 7 Critical radius ........................................................................................................................................ 8 Rods and fins ......................................................................................................................................... 8 Heat source moving at steady state along a rod .................................................................................. 11 Reduction by dimension similarity (unsteady state) ............................................................................... 12 Energy deposition in unbounded media .............................................................................................. 13 Thermal contact in semi-infinite media .............................................................................................. 17 Freezing and thawing .......................................................................................................................... 19 Reduction by separation of variables ...................................................................................................... 20 Unsteady problems in 1-D .................................................................................................................. 21 Periodic solutions in 1-D..................................................................................................................... 26 Steady problems in 2-D....................................................................................................................... 27 Other analytical methods to solve partial differential equations ............................................................. 31 Duhamel`s theorem ............................................................................................................................. 32 Numerical solutions .................................................................................................................................... 32 Global fitting ........................................................................................................................................... 34 Lumped network ..................................................................................................................................... 37 Spectral methods ..................................................................................................................................... 38 Residual fitting ........................................................................................................................................ 38 Collocation method ............................................................................................................................. 39 Least square method (LSM) ................................................................................................................ 39 Galerkin method .................................................................................................................................. 39 Finite differences..................................................................................................................................... 40 Finite elements ........................................................................................................................................ 44 Boundary elements .................................................................................................................................. 44