## Space-Time Transformation of Heat Conduction

## Space-Time Transformation of Heat Conduction

This example considers transient heat diffusion in a solid 1 m rod where one end is kept at T = 25 degrees and the other subject to constant heat flux q_n = 1. This one-dimensional time dependent problem is transformed to a static two dimensional one. The computed results can both be compared with the analytical …

## Microstrip Transmission Line

## Microstrip Transmission Line

A shielded electrical microstrip transmission line is fixed to a substrate and placed in a shielded container of air. The simulation applies a known voltage to the strip to calculate the resulting capacitance and compares this with the theoretical result. The problem assumes symmetry in the lengthwise direction so that …

## Stress Distribution in a Solenoid

## Stress Distribution in a Solenoid

This multiphysics model examines how magnetic forces give rise to stresses in a long thick cylindrical solenoid. A current density of 106 A/m2 is running through a wound coil with 1 cm inner to 2 cm outer radii. The material of the coil is assumed to have a modulus of elasticity of 1.075⋅1011 N/m2 and Poisson’s …

## Inductance in Parallel Wires

## Inductance in Parallel Wires

This example calculates the inductance between parallel wires. Two 1 m wires with 4 mm radius 1 A current are placed 0.5 m apart in a large domain of non-conducting air or vacuum. The inductance is computed with both using the magnetic field energy and flux linkage, and compared against the analytical solution L = …

## Conducting Sphere

## Conducting Sphere

This verification example considers a perfectly conducting sphere placed between two charged capacitor plates. An axisymmetric solution for the electrostatic potential is compared with a full 3D one, and verified against the analytical solution U(xi) = E0*(r3/xi2 - xi), where the electrical field is the potential …

## Thermal Bridge

## Thermal Bridge

This is a benchmark test case for modeling the steady-state temperature distribution in a thermal bridge in building construction. The model consists of a 6 mm concrete slab subjected to an outside temperature of 0 °C and heat loss due to convection. The inside features a 4 cm layer of air enclosed within a 1.5 mm …

## Orthotropic Heat Conduction

## Orthotropic Heat Conduction

This is an example of modeling anisotropic heat conduction in an orthotropic material where a heated solid bar suddenly is cooled by submerging it in a cool fluid. The material features different thermal conductivities in the x and y-directions which is accounted for by modifying the diffusion term in the heat transfer …