Heat conduction models with triangles continued

	11. Non-zero temperature on the boundary (nonzero essential boundary conditions). Mechanical system of four particles. Partitioned stiffness matrix. Solving for unknowns, reactions. Prescribed temperatures. Loading due to prescribed temperatures. Postprocessing of the results. Level curves of the temperature. Gradient of the temperature.
	12. Layered wall example. Elementary geometry to construct gradients (rise over run). Assemble elementwise matrices. Complete conductivity matrix. Prescribed temperatures on the boundaries (two faces of the wall). Free-free matrix. Estimating the gradient of the temperature and the heat flux. Normal component of the heat flux. "Equivalent" sets of boundary conditions. Heat-flux loading. integral over the boundary. Boundary of the mesh, mesh of the boundary. Line-segment finite elements. Heat-flux heat load vector. Physical units of the heat load vector. Abaqus solution for prescribed temperatures, and for prescribed heat fluxes. Sign of the heat flux load. Properties of the global conductivity matrix. Singular matrix.
	13. Examples of boundary conditions when the coefficient matrix is singular. Bar on rollers. Eigenvalue and eigenvector. Singular stiffness matrix. Example of two water tanks. Heat conduction through a wall, prescribed heat fluxes.
	14. Natural boundary conditions in Abaqus. Temperature solution not unique. Heat flux magnitude. Job monitor. Singular matrix. Gaussian elimination. Pivot position numbers. Balance possible. Loading for which balance is not possible. Error in the monitor.
	15. Film Boundary Condition type. Boundary layer. Method of weighted residuals additional terms. Elementwise calculations. Example of film condition: wall with film conditions on either end. Singular global conductivity matrix. Film boundary condition contributions. Calculation of the heat flux. Changing values of the film condition coefficients.