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Effective Diffusivity in Porous Materials

Transport through porous structures is usually treated using simplified homogeneous models with effective transport properties. This is in most cases a necessity, since the typical dimensions of the pores and particles making up the porous structure are several orders of magnitude smaller than the size of the domain that is to be modeled. This model introduces the concept of effective ...

Axisymmetric Transient Heat Transfer

This is a benchmark model for an axisymmetric transient thermal analysis. The temperature on the boundaries changes from 0 degrees C to 1000 degrees C at the start of the simulation. The temperature at 190 s from the anlysis is compared with a NAFEMS benchmark solution.

Loaded Spring - Using Global Equations to Satisfy Constraints

Global equations are a way of adding an additional equation to a model. A global equation can be used to describe a load, constraint, material property, or anything else in the model that has a uniquely definable solution. In this example, a structural mechanics model of a spring is augmented by a global equation which solves for the load to achieve a desired spring displacement.

Joule Heating of a Microactuator

This tutorial model of a two-hot-arm thermal actuator couples three different physics phenomena: electric current conduction, heat conduction with heat generation, and structural stresses and strains due to thermal expansion. In this model version, the geometry is parameterized so that the effect of varying the actuator's dimensions can be analyzed.

Convective Cooling of a Busbar

This is a template MPH-file containing the physics interfaces and the parameterized geometry for the model Electrical Heating in a Busbar.


The development of mixers does often not only have to account for effectiveness, but also other factors must be involved, such as cost and complexity for manufacturing. The three models study a laminar static micro mixer with two parallel sets of split-reshape-recombine mixing elements. The mixer works through lamination of the streams without any moving parts and the mixing is obtained through ...

Eigenmodes of a Room

When designing a concert hall, it is extremely important to take the resonances into account. For a clear and neutral sound, the eigenfrequencies should be evenly spread through the registers. For the home stereo owner, who cannot actually change the shape of his living room, another question is more relevant: where should the speakers be put for the best sound? To illustrate the effects we are ...

Diffraction Patterns

This example resembles the well-known 2-slit interference experiment often demonstrated in schools with water waves or sound. This model mimics the plane-wave excitation with two thin waveguides leading to slits in a screen, and it computes the diffraction pattern on the screen’s other side. This diffraction pattern is clearly visible. The main effect of quantization is that the numerical ...

Process Control Using a PID Controller

This model shows how a flow model can be coupled to a process control mechanism. Controlling application parameters according to other application parameters is important within process engineering. Most control mechanisms use the data at a wall or an outlet to control inlet parameters. More accurate control can occur if you can control inlet parameters due to data found within a component ...

Conical Quantum Dot

Quantum dots are nano- or microscale devices created by confining free electrons in a 3D semiconducting matrix. Those tiny islands or droplets of confined “free electrons” (those with no potential energy) present many interesting electronic properties. They are of potential importance for applications in quantum computing, biological labeling, or lasers, to name only a few. Quantum dots can ...