Computerlab 3. for Electrodynamics with Vector analysis C and Electrodynamics using Comsol Multiphysics. Induction heating

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1 Department of Physics Olexii Iukhymenko Computerlab 3 for Electrodynamics with Vector analysis C and Electrodynamics using Comsol Multiphysics Induction heating Purposes of lab: To consider the phenomena of induction heating with the CMP (Comsol Multiphysics). In the low conductivity and low frequency case you solve the problem analytically and compare with the CMP result You consider heating numerically for higher conductivity or frequency cases. Preparation before this lab Read this lab specification. Work on the problems. If you also visit the lab and try to do some of the tasks in advance, then you will be able to use my support much more effectively. 1

2 Induction heating of a conducting cylinder in a solenoid Problem from Lorrain s textbook Electromagnetic phenomena is included on pages 5 and 6. Read this material. We will in this lab consider the same problem using CMP and the Heat Transfer module. Take graphite (Materials/ AC/DC /Graphite) cylinder of radius a=10 centimetres and its length as L=1 meter. Take the inner radius of the solenoid as 15 centimetres and its length as 2 meters. The winding of the solenoid is conveniently replaced by a spatially constant time-harmonic external current density in a layer. You may take this layer 10 millimetres thick. The other dimensions and numbers are those given in the text. You must (analytically) calculate the correct value for this external current to be used in the subdomain settings. In order to find the power heating the cylinder you may use Joule s law stating that Jr (, t) Er (, t) (the scalar product of the current density and the electric field) is the heating power per unit volume. About the report of this lab: 1. The report is a word document and a CMP-file (file with extension mph) that you send to me by as an attachment (oleksii.iukhymenko@physics.umu.se). Your last names must be included in the names of the documents. 2. Always fill in the Subject in the mail. For example write Eldyn_ab3. Otherwise your mail may easily be treated as Spam 3. A solution to problem in Lorrain (see below) must be included in the word document. 4. Find the same result as in problem (d) by calculating E J dv where Cylinder the bracket means time-average (this is an application of Joule s law). Thus you first have to find explicit analytical expressions for E and J in the cylinder and then calculate the integral. (Include this calculation in the Word document) 5. Solve the problem numerically by use of CMP. To do this you must Choose application mode in CMP. 2D axisymmetric/heat Transfer/Electromagnetic Heating/ Induction Heating/Frequency- Stationary Draw the geometry (dimensions are given above and in the problem text) Choose frequency 60 hertz (you may define frequency as global parameter in Global Definitions/Parameters so can use it in Parametric Sweep) Add such materials as graphite for the cylinder, cooper for the coil and air for the rest of the domain from the Materials. Use Multi-Turn Coil Domain from Induction Heating for the coil, applying appropriate parameters. We assume that coil and walls of the domain have constant temperature. Apply constant temperature to these boundaries. Compute the problem. Find the heating of the cylinder and compare numerical result with analytical result (as given in problem 22-12d). The numerical result may be 2

3 obtained by a Integration in Deriver Values available from the Results. But what shall we integrate? You have two options here: 1) you may perform Surface Integration of ih.qtot (Total heat sores in IH Heat transfer in solids) over the cylinder; 2) or you may calculate Line integration of ih.ntflux (Total normal heat flux) on the cylinder boundaries. Result of integration must appear in the left lower corner of CMP window in the Table 1. Compare with the number you get from the analytical result given in problem 22-12d. You should get a somewhat lower result (10% lower about). If this does not happen you must fix this before proceeding Remark: We obtain the power heating the cylinder by integrating over the cylinder volume/surface. CMP produces surface integrals...drdz so in order to get the corresponding rotational volume integral we must insert a factor 2π r (corresponding to the φ -integration). Pay attention to the fact that dimension of the frequency in COMSOL is hertz, and dimension of the frequency in analytical problem 22-12d is hertz/rad. 6. The next task is to produce the figure below. You must then use the Parametric Sweep in Study 1 in order to get solutions for several frequencies. You use Results/1D Plot Group to generate the plot. You may define the AnalyticHeating (i.e. the result given in Problem 22-12d) in Definitions/Variables. In order to get two plots in the same figure first create 1D Plot Group, then add the Global plot and Table Graf to it. In Global plot you draw an AnalyticHeating as a function of the frequency. In Table Graph you chose Table 1 in Data/Table (you must perform integral calculation before to have these option). It shows that the numerical value of the heating power is lower than the analytical value. Explain this figure. Why do the two curves agree better with lower frequency? Answer this question in the word document. Remark: How to use Parametric Sweep. Right click Study. Parametric sweep. In the Parameter names you choose parameter that you are going to vary (frequency or conductivity). Click Range. Set appropriate values for the sweep. 3

4 Plot 1 7. Make plot 1 but for a larger range of frequencies: 0 < f < 100 Hz (and include in the Word document) 4 8. Next keep the frequency fixed (take some fixed value in the interval 0 < f < 10 ). We now like to vary the conductivity of the cylinder. Find the value of the conductivity for which the heating has its maximum. Show this in a CMP plot (and include in the Word document) 9. Why would we expect there to exist such a maximum value? Explain in the Worddocument. 4

5 Problem from Lorrain Electromagnetic phenomena : 5

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