O'Reilly logo

Electrothermics by Javad Fouladgar

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

1.5. Solving the electromagnetic and thermal equations

The electromagnetic and thermal equations are partial differential equations, where the unknown is either a scalar or a vector quantity dependent on spatial coordinates and time. Numerical methods are often used to solve these equations. Nevertheless, in certain simple cases and for the comprehension of the involved physical phenomena, analytic methods are interesting.

1.5.1. Analytic methods

1.5.1.1. Transient state

In the one-dimensional case, the general form of the electromagnetic and thermal equations is as follows:

[1.58] images

where, z is the propagation direction of the wave U and, p, represents internal sources.

For example, the one-dimensional formulation of magnetic potential A is:

[1.59] images

and for the formulation in H, we obtain:

[1.60] images

As for the thermal equation, it can be written as:

[1.61] images

1.5.1.2. Harmonic state

For a sinusoidal variation, the general form is given by:

[1.62] images

where with as the penetration depth of wave ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required