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An Integro-Partial Differential Equation

The heat distribution in a hollow pipe, whose ends are held at two different temperatures, is studied. The outside surface is assumed to be thermally isolated and the inner surfaces have radiation boundary conditions. The role of convection in the heat transfer is taken to be negligible. The temperature is assumed to be constant along the thickness of the pipe and rotational symmetry is also ...

Stiffness Analysis of a Communication Mast's Diagonal Mounting

Communication masts usually have a framework with a bolted triangular lattice design. The diagonals of the framework are assembled from several parts and welded together. When operating under a given wind load at a specific location, the antenna’s total rotation angle should stay below a certain limit to ensure uninterrupted communications. For the type of mast in this model, the engineers ...

Rock Fracture Flow

A potential flow model of fluid flow in a rock fracture uses the so-called Reynolds equation. It shows how to use experimental data interpolated to a function used in the equation.

Implementing a Point Source

This model solves the Poisson equation on a unit disk with a point source in the origin. The easiest way to describe a point source in COMSOL Multiphysics is by using an extra weak term. To obtain the weak formulation of the general Poisson equation, we multiply it with a test function u_test and integrate over the domain. The mesh density is dense, close to the origin, so as to resolve the ...

Electric Sensor

This is a model from electric impedance tomography, a method of imaging the interior permittivity distribution of a body by measuring current and voltage at the surface. This model demonstrates how the shape and placement of figures with different material properties inside a closed box can be determined with this non-invasive technique. Applying a potential difference on the boundaries of ...

Marangoni Convection

Marangoni convection occurs when the surface tension of an interface (generally liquid-air) depends on the concentration of a species or on the temperature distribution. In the case of temperature dependence, the Marangoni effect is also called thermo-capillary convection. The Marangoni effect is of primary importance in the fields of welding, crystal growth and electron beam melting of ...

The KdV Equation and Solitons

The Korteweg-de Vries (KdV) equation models water waves. It contrasts sharply to the Burgers equation, because it introduces no dissipation and the waves travel seemingly forever. Solitons have their primary practical application in optical fibers. Specifically, a fiber’s linear dispersion properties level out a wave while the nonlinear properties give a focusing effect. The result is a very ...

Lorenz Attractor

A Lorenz attractor can be described by a system of ordinary differential equations: the Lorenz system. In the early 1960s, Lorenz discovered the chaotic behavior of this system for certain parameter values and initial conditions. The solution, when plotted as a phase space, resembles the figure eight. This example uses the Dormand-Prince explicit method for solving the ODEs and a Point ...

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 ...

Eigenvalue Analysis of a Crankshaft

This model describes a modal analysis of a crankshaft. The pistons’ reciprocating movement is transferred to the crankshaft through connecting rods by means of crankshaft throws. The forces, torques, and bending moments, which are highly variable both in time and space, subject the crankshaft to very high and complex loading. The crankshaft design must therefore incorporate careful and ...