# chap81 - CHAPTER 8 Thermal Analysis Thermal Analysis...

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1 CHAPTER 8: Thermal Analysis ± Thermal Analysis: calculation of temperatures in a solid body. ± Magnitude and direction of heat flow can also be calculated from temperature gradients in the body. ± Modes of heat transfer: ² by conduction within a body ² by convection and radiation to/from a body ± There may be internal heat generation due to electric current, chemical reaction, dielectric heating, etc. ± Temperatures may be prescribed on a boundary or in the interior.

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2 Modes of Heat Transfer and Boundary Conditions
3 Finite Element Form for Steady State Problem ± A domain can be discretized for thermal analysis, i.e., a FE mesh can be created. ± The steady-state heat-transfer discretized equation is written: K T T = Q where T : vector of nodal temperatures Q : vector of thermal loads due to internal heat generation, convection and radiation to/from the body K T : matrix depending on conductivity of the material and convection and radiation

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4 Nonlinearity ± Material properties such as conductivity depend on temperature. K T = K T ( T ) in general Nonlinear problem!! ± Radiative heat transfer is inherently nonlinear. ± Note the similarity of K T T = Q to the equilibrium equation KD = R in stress analysis. Same element types, same FE mesh can be used for both stress and thermal analysis. Genesis uses same names. ± Internal heat source: analogous to body force in stress analysis. ± Prescribed temperatures: analogous to prescribed displacements
5 Heat Flow Equations: Isotropic Material ± Fourier law of heat conduction for an isotropic material:

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6 Heat Flow Equations: Anisotropic Material ± Heat conduction for an anisotropic material: where κ is a matrix of thermal conductivities.
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chap81 - CHAPTER 8 Thermal Analysis Thermal Analysis...

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