Vorname: Name: Matr.-Nr. 3 FDM (30 P) The temperature distribution of a electric cable with a insulation mantle is to be determined using the two-dimensional finite difference method. The heat dissipation of the electric cable is specified as a known heat flow ܳሶ_௧ as a boundary condition. Moreover, there is cooling air at the outside. In addition, it is assumed that the problem is symmetrical and the calculation of a 90° section is used. For a first step, this section was divided into the nodes shown below. a) Determine the side lengths of the nodes. You may combine identical elements. b) Determine the temperature equation for each node. The equation can be specified in implicit form (i.e. it does not have to be solved for the respective temperature). c) If the calculation is to be carried out automatically in a Python code, different temperature equations must be specified (inner nodes, boundary nodes). How many different regions need to be differentiated? Specify the corresponding equations in general form for ONE of those if the number of segments in the radial direction is to be m and the number of segments in the azimuthal direction (angle) is to be n. Also state for which values of m and n the equations should apply. Given data: Angle of the entire section ߮ௌ௧ = Angle of the nodes ο߮ = Electrical cable radius r = 10 mm గ ଶ గ Total length of the segment under consideration ܴ௧௧ = 3 ݉ Radial length nodes ο = ݎ1݉ 9
