 ## General

#### What is the result item TENE? How is it defined, what is its physical significance, and how is it related to Joule heating in a SOLID69 thermoelectric model?

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The best way to determine how TENE is calculated and therefore what it represents physically is to create a test model using SOLID69. In the attached input file, APDL was used in POST1 to determine alternate ways of calculating both JHEAT and TENE. JHEAT is relatively straightforward. It is the ohmic heating per unit volume (W/m^3): JHEAT = J^2 * rho where J = calculated current density (A/m^2) Rho = electric resistivity (ohm-m) It appears that TENE follows the calculation of mechanical strain energy (element table item SENE). SENE is calculated as one half of the product of stress, strain, and element volume to give the stored elastic energy in each element (in Joules, not in Joules/m^3): SENE = 0.5*stress*strain*volume Following this logic, TENE should be equal to one-half the product of thermal flux, thermal gradient, and element volume. This can be thought of in terms of “across” (or “direct”) results data (displacement for structural, temperature for thermal), and “through” (or derived or reaction) results data (force for structural, heat for thermal). The analogous quantities for evaluating these energies are then: ACROSS RESULTS DATA Structural: displacement U => strain Thermal: temperature TEMP => thermal gradient TG THROUGH RESULTS DATA Structural: force F => stress Thermal: heat => thermal flux TF In the attached input file, TENE is read in and called TENE_1. APDL is then used to perform an alternate calculation of TENE that was called TENE_2: TENE_2 = 0.5*TF*TG*volume It can be seen that contours of TENE_1 and TENE_2 are almost identical, as are their distributions along the path running down the length of the conducting bar. Now, what is the physical significance of TENE? The MKS units of TENE appear to be W-K (watts times degrees Kelvin or Centigrade). This does not seem to have direct relevance to Joule heat or even to thermal conduction, though it may be more-closely related to the latter. Additionally, it does not have units of energy, so its name is perhaps misleading. It may be a convenient way to assess/quantify discretization error, but has little practical engineering value. 