I would like to know how heat flux is calculated as per above conditions for both time dependent and time independent cases.
May be on this link you can find something to help you.
Best wishes
http://scholar.googleusercontent.com/scholar?q=cache:OYQPbrCYJvMJ:scholar.google.com/&hl=es&as_sdt=0,5
The equation for the total pulse energy is the integral of the product i (t) and u (t) over the period of the pulse duration. You need the energy densities on the cathode or anode surface, then you need to multiply this pulse energy by a factor corresponding to the respective proportion of energy to the total energy. Most of the energy goes into the structure of the plasma channel and its expansion, and its stability, for about 7 to 20% flow into the respective electrode surfaces. Very closely, you can determine this factor if you are able to determine the cathode drop or drop the anodes.
The prozenzualen proportions are different for the different process energy sources, the pulse duration and the overshoot of the current course.
Prof. Schulze,
Thank you for the reply.
Right now I'm finding the pulse energy transferred to cathode as (0.183*u*i*t). But as per Dibitonto et.al. paper "Theoretical models of the electrical discharge machining process. I. A simple cathode erosion model" (link provided below) they have taken heat flux in solving the heat conduction equation with a point heat source assumption. But to find heat flux, cross sectional area over which the pulse energy is applied is required. Due to point heat source assumption, the cross sectional area is zero. Thus heat flux cannot be computed. But they have computed heat flux in their work, but haven't clearly stated how or given the equation.
http://scitation.aip.org/content/aip/journal/jap/66/9/10.1063/1.343994
The correct approach is that it does not come from a "point source", but the breakdown beginning assigns an area which results from the size of the sweeping streamers. Also, for the calculation of the plasma channel expansion you need a starting radius, so that in general only a current can flow. Depending on their time discrediting They use only this part of energy. For a simplified invoice you can accept for the first 100 or 200 ns a radius of about 2.5 microns. Then you can not work with a constant radius and a Gaussian distribution but. For the radius expansion, I have developed a function in the Literatur "Simulation of the discharge expansion of a spark discharge at small distances between electrodes" (IEEE Vancouver 2007). According to the selection of the dielectric You can then use various approximations to calculate the expansion of the plasma channel and use these in your simulation program.
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