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Steady-State Thermal Analysis

1,061 bytes removed, 02:27, 17 June 2018
<math> T(i,j,k) = \frac{1}{6} \big[ T(i+1,j,k) + T(i-1,j,k) + T(i,j+1,k) + T(i,j-1,k) + T(i,j,k+1) + T(i,j,k-1) \big] </math>
Two The standard types of domain boundary conditions take the following forms:
*Dirichlet boundary condition: T = k T<sub>0</sub> =const.*Neumann boundary condition: &part;T/&part;n = -q<sub>s0</sub>/k = const. In the above, &part;&psi;/&part;n denotes the normal derivative of the potential at the surface of the domain boundary. [[EM.Ferma]]'s default domain *Adiabatic boundary condition for both the electrostatic and magnetostatic solvers is Dirichlet. At the interface between different material media, additional boundary conditions must be applied. These boundary conditions involve electric or magnetic field components. The field components can be expressed as partial derivatives of the potential, i.e. in the form of : &part;&psi;T/&part;x, &part;&psi;/&part;y or &part;&psi;/&part;z. Using the respective finite difference approximations of these derivatives, one arrives at fairly complicated difference equations involving the constitutive parameters &epsilon;, &mu; and &sigma;, which must be solved simultaneously with the primary potential difference equations. Note that the electrostatic Poisson and Laplace equations are of the scalar type, while the magnetostatic Poisson and Laplace equations are vectorial. As a result, the size of the numerical problem in the latter case is three times as large as the former case for the same mesh sizen = 0.
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