The Dirichlet Boundary Condition sets the incident light intensity within the material. At the face opposite to the incident face, the default Zero Flux boundary condition can be physically interpreted as meaning that any light reaching that boundary will leave the domain. This condition is implemented with a Dirichlet Boundary Condition. Some of the laser light will be reflected at the dielectric interface, so the intensity of light at the surface of the material is reduced to 0.95 of the incident intensity. At the origin, and immediately above the material, the incident intensity is 3 W/mm 2. We will assume that the incident laser light intensity follows a Gaussian distribution with respect to distance from the origin. It is appropriate on most faces, with the exception of the illuminated face. The Zero Flux boundary condition is the natural boundary condition and does not impose a constraint or loading term. Since this equation is linear and stationary, the Initial Values do not affect the solution for the intensity variable. Implementation of the Beer-Lambert law with the General Form PDE interface. This one line implements the Beer-Lambert law for a material with a temperature-dependent absorption coefficient, assuming that we will also solve for the temperature field, T, in our model. The source term is set to Iz-(50*(1+(T-300)/40))*I, where the partial derivative of light intensity with respect to the z-direction is Iz, and the absorption coefficient is (50*(1+(T-300)/40)), which introduces a temperature dependency for illustrative purposes. Aside from the source term, f, all terms within the equation are set to zero thus, the equation being solved is f=0. Next, the equation itself is implemented via the General Form PDE interface, as illustrated in the following screenshot. Settings for the implementing the Beer-Lambert law. To implement the Beer-Lambert law, we will begin by adding the General Form PDE interface with the Dependent Variables and Units settings, as shown in the figure below. These volumes will represent the same material, but we will only solve the Beer-Lambert law on the inside domain - the only region that the beam is heating up. We will also partition the domain up into two volumes. To reduce the model size, we will exploit symmetry and consider only one quarter of the entire cylinder. We will consider the problem shown above, which depicts a solid cylinder of material (20 mm in diameter and 25 mm in length) with a laser incident on the top. These two equations present a bidirectionally coupled multiphysics problem that is well suited for modeling within the core architecture of COMSOL Multiphysics. Where the heat source term, Q, equals the absorbed light. \rho C_p \frac-\nabla \cdot (k \nabla T)= Q = \alpha(T) I
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