Introduction:
Historical Perspective of FEM and applicability to Thermal Engineering problems.
Conduction Heat Transfer and Formulation:
Modelling heat conduction; formulation of governing equation, differential and Variational formulation. Initial, boundary and interface conditions. Approximate methods, Ritz and Galerkin’s methods, Finite element approximation and basic concepts.
Linear Steady state problems:
Problems with one dimensional linear element, Formulation of element characteristic matrices and vectors. Assembly considerations and boundary conditions. Quadratic elements and their advantages and disadvantages. Two dimensional elements; triangular and quadrilateral elements, natural coordinates, parametric representation, Subparametric, superparametric and Isoparametric elements. Formulation of conductive, convective matrices and nodal heat rate vectors. Analysis procedure for 2 D conduction with convection
Nonlinear Heat conduction Analysis:
Galerkin’s method to nonlinear transient heat conduction; Governing equation with initial and boundary conditions, one dimensional nonlinear steady-state problems and transient state problems.
Viscous Incompressible Flows:
Governing equations, weak form, finite element model, penalty finite element models, problems in two dimensional flow fields, finite element models of porous flow
Convective Heat Transfer:
Basic equations, steady convection diffusion problems and transient convection-diffusion problems, Velocity-pressure-temperature formulation, Examples of heat transfer in a fluid flowing between parallel planes.
Structural problems:
Finite element formulation for structural problems, 1 dimensional stress analysis problems with bar, beam, truss and frame elements, FE formulation in plane stress, plane strain and axi-symmetric problems. Introduction to plate bending and shell elements.