Note that this direction coincides with that of the direction of the current flow.
The arrows show the direction of the normal vector of this boundary. Spatial variation in the magnitude of current density on one of the internal geometric boundaries. Now, let’s turn our attention to one of the internal boundaries that connects the straight and curved regions. It is largest near the inner radius and smallest near the outer radius. Spatial variation in the magnitude of current density and direction of current flow.Īs moving charges try to take the shortest path (least resistance), we see that, in the curved section of the conductor, the current density varies through the volume significantly. Variation in Current Densityīefore we proceed to compute the total current in the conductor, let’s take a look at the current density variation inside the conductor. Representation of the problem in the COMSOL software. Here, we use the Electric Currents interface and a stationary study to solve a DC current conduction problem. All geometric units are in millimeters (mm). Overview of the electric current conduction model set-up. Let’s solve a DC electric current conduction problem on a bent copper wire whose two ends are at a potential difference of 1 mV. When the planar surface is not a part of the modeling geometry, but is created during postprocessing, using the Cut Plane data set feature.When the planar surface is a 2D boundary (internal or external) of a 3D modeling geometry.Now let’s find out how you can compute the total normal flux on a planar surface in the COMSOL software. Here, we will follow the principles of integral calculus to find that out.Īn arbitrary boundary (∂Ω) in 3D space whose normal vector is \hat( n_xJ_x+n_yJ_y+n_zJ_z ) Computing Total Normal Flux in COMSOL Multiphysics What would you do for the three-dimensional case with the flux vector? For a straight cylinder with a constant cross-section area, we can easily find the total current passing through any section, by multiplying the cross-section area with the current density (flux). Going back to our simple example, let’s say we are interested in finding out the total current passing through any arbitrary cross section of the conductor. J=-\sigma\nabla V Computing Total Normal Flux Using Ohm’s Law, the current density (J) through this cross section can be computed from the following expression: For electric current conduction, the flux physically signifies the total number of electrons flowing through the cross section per unit time (referred to as current density). The electrical conductivity is denoted by σ. The electric potential on the left and right ends of the disk are V 1 and V 2, respectively. The left and right ends of the disk are at position x 1 and x 2, respectively, and have a constant cross-section area of A. Now, let’s focus on a small section of the conductor along its length (shown above as the red-dashed disk). Imagine a cylindrical conductor (shown above) through which electric current flows as a result of a potential difference across its two ends.
Now, let’s look at an example to find out the simple math behind computing flux.Ī simple example of computing current through a conductor. Heat flux or Power per unit area (Unit: W/m 2) Mass flux or Mass flow rate per unit area (Unit: kg/m 2s) The following table provides a summary of flux-type physical quantities from different physics areas.Įlectric displacement or Surface charge density (Unit: C/m 2) This is because most physics are mathematically formulated based on some form of conservation equation. Although this idea has its origin in the field of transport processes, the concept of flux and total flux can be related to many physics. The total flux through the cross section is then the sum total of flux coming out of that boundary. Correspondingly, the boundary through which we compute the flux would be surface (in 3D), edge (in 2D), and point (in 1D), respectively. The domain could be a volume (in 3D), surface (in 2D), or edge (in 1D). The approach discussed here works for any type of physics problem as long as we can identify the appropriate flux term corresponding to that physics.įlux refers to the area density of any quantity that flows through a well-defined boundary of a domain. This can help us bridge the gap between simulations and experiments where, in the latter, it is often easier to physically measure the total flux.
#Calculate flux integral 3d how to
Today, we will find out how to compute the total normal flux through a cross-section plane, passing through your simulation geometry.
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